1
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Hetzel M, Pezzè L, Pür C, Quensen M, Hüper A, Geng J, Kruse J, Santos L, Ertmer W, Smerzi A, Klempt C. Tomography of a Number-Resolving Detector by Reconstruction of an Atomic Many-Body Quantum State. PHYSICAL REVIEW LETTERS 2023; 131:260601. [PMID: 38215377 DOI: 10.1103/physrevlett.131.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 10/10/2023] [Indexed: 01/14/2024]
Abstract
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.
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Affiliation(s)
- Mareike Hetzel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Cebrail Pür
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Martin Quensen
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Andreas Hüper
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Jiao Geng
- Key Laboratory of 3D Micro/Nano Fabrication and Characterization of Zhejiang Province, School of Engineering, Westlake University, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
- Institute of Advanced Technology, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
| | - Jens Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - Wolfgang Ertmer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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2
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Meyer-Hoppe B, Anders F, Feldmann P, Santos L, Klempt C. Excited-State Phase Diagram of a Ferromagnetic Quantum Gas. PHYSICAL REVIEW LETTERS 2023; 131:243402. [PMID: 38181136 DOI: 10.1103/physrevlett.131.243402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Revised: 06/26/2023] [Accepted: 10/12/2023] [Indexed: 01/07/2024]
Abstract
The ground-state phases of a quantum many-body system are characterized by an order parameter, which changes abruptly at quantum phase transitions when an external control parameter is varied. Interestingly, these concepts may be extended to excited states, for which it is possible to define equivalent excited-state quantum phase transitions. However, the experimental mapping of a phase diagram of excited quantum states has not yet been realized. Here we present the experimental determination of the excited-state phase diagram of an atomic ferromagnetic quantum gas, where, crucially, the excitation energy is one of the control parameters. The obtained phase diagram exemplifies how the extensive Hilbert state of quantum many-body systems can be structured by the measurement of well-defined order parameters.
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Affiliation(s)
- B Meyer-Hoppe
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - F Anders
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - P Feldmann
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, D-30167 Hannover, Germany
- Stewart Blusson Quantum Matter Institute, The University of British Columbia, 2355 East Mall, Vancouver, British Columbia V6T 1Z4, Canada
- Department of Physics and Astronomy, The University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada
| | - L Santos
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, D-30167 Hannover, Germany
| | - C Klempt
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
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3
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Krešić I, Robb GRM, Oppo GL, Ackemann T. Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms. PHYSICAL REVIEW LETTERS 2023; 131:163602. [PMID: 37925717 DOI: 10.1103/physrevlett.131.163602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 09/07/2023] [Indexed: 11/07/2023]
Abstract
We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.
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Affiliation(s)
- Ivor Krešić
- Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Vienna, A-1040, Austria
- Centre for Advanced Laser Techniques, Institute of Physics, Bijenička cesta 46, 10000, Zagreb, Croatia
| | - Gordon R M Robb
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Thorsten Ackemann
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
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4
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Xin L, Barrios M, Cohen JT, Chapman MS. Long-Lived Squeezed Ground States in a Quantum Spin Ensemble. PHYSICAL REVIEW LETTERS 2023; 131:133402. [PMID: 37832022 DOI: 10.1103/physrevlett.131.133402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 09/07/2023] [Indexed: 10/15/2023]
Abstract
We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum-critical point separating the different spin phases of the interacting ensemble using a novel nonadiabatic technique. In contrast to typical nonequilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time stationary with a constant quadrature squeezing angle. A squeezed ground state with 6-8 dB of squeezing and a constant squeezing angle is demonstrated. The long-term evolution of the squeezed ground state is measured and shows gradual decrease in the degree of squeezing over 2 s that is well modeled by a slow tuning of the Hamiltonian due to the loss of atomic density. Interestingly, modeling the gradual decrease does not require additional spin decoherence models despite a loss of 75% of the atoms.
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Affiliation(s)
- Lin Xin
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Maryrose Barrios
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Julia T Cohen
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Michael S Chapman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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5
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Cao JH, Chen F, Liu Q, Mao TW, Xu WX, Wu LN, You L. Detection of Entangled States Supported by Reinforcement Learning. PHYSICAL REVIEW LETTERS 2023; 131:073201. [PMID: 37656843 DOI: 10.1103/physrevlett.131.073201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Revised: 06/05/2023] [Accepted: 07/14/2023] [Indexed: 09/03/2023]
Abstract
Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30} dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.
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Affiliation(s)
- Jia-Hao Cao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Feng Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Tian-Wei Mao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Wen-Xin Xu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ling-Na Wu
- Center for Theoretical Physics and School of Science, Hainan University, Haikou 570228, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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6
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Chu Y, Li X, Cai J. Strong Quantum Metrological Limit from Many-Body Physics. PHYSICAL REVIEW LETTERS 2023; 130:170801. [PMID: 37172232 DOI: 10.1103/physrevlett.130.170801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Revised: 03/05/2023] [Accepted: 04/03/2023] [Indexed: 05/14/2023]
Abstract
Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that does not come without a price. The exceptional time overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here, we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to characterize the metrological potential of quantum resource states during their preparation. Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit in a generic many-body lattice system with bounded one-site energy. It enables us to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology, and brings an interesting connection between many-body quantum dynamics and quantum metrology.
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Affiliation(s)
- Yaoming Chu
- School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiangbei Li
- School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jianming Cai
- School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
- Shanghai Key Laboratory of Magnetic Resonance, East China Normal University, Shanghai 200062, China
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7
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Entanglement-enhanced matter-wave interferometry in a high-finesse cavity. Nature 2022; 610:472-477. [PMID: 36261551 PMCID: PMC9581775 DOI: 10.1038/s41586-022-05197-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 08/05/2022] [Indexed: 11/30/2022]
Abstract
An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit1–3 set by projections of individual atoms. Large amounts of entanglement4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity \documentclass[12pt]{minimal}
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\begin{document}$$3\,.\,{4}_{-0.9}^{+1.1}$$\end{document}3.4−0.9+1.1 dB and \documentclass[12pt]{minimal}
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\begin{document}$$2\,.\,{5}_{-0.6}^{+0.6}$$\end{document}2.5−0.6+0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity \documentclass[12pt]{minimal}
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\begin{document}$$1\,.\,{7}_{-0.5}^{+0.5}$$\end{document}1.7−0.5+0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors17,18, searches for new physics, particles and fields19–23, future advanced gravitational wave detectors24,25 and accessing beyond mean-field quantum many-body physics26–30. A matter-wave interferometer is demonstrated with an interferometric phase noise below the standard quantum limit, combining two core concepts of quantum mechanics, that a particle can simultaneously be in two places at once and entanglement between distinct particles.
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8
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Xu K, Zhang YR, Sun ZH, Li H, Song P, Xiang Z, Huang K, Li H, Shi YH, Chen CT, Song X, Zheng D, Nori F, Wang H, Fan H. Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits. PHYSICAL REVIEW LETTERS 2022; 128:150501. [PMID: 35499907 DOI: 10.1103/physrevlett.128.150501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 03/15/2022] [Indexed: 06/14/2023]
Abstract
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
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Affiliation(s)
- Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yu-Ran Zhang
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
| | - Zheng-Hang Sun
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Pengtao Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhongcheng Xiang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kaixuan Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yun-Hao Shi
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chi-Tong Chen
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaohui Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - H Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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9
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Anders F, Idel A, Feldmann P, Bondarenko D, Loriani S, Lange K, Peise J, Gersemann M, Meyer-Hoppe B, Abend S, Gaaloul N, Schubert C, Schlippert D, Santos L, Rasel E, Klempt C. Momentum Entanglement for Atom Interferometry. PHYSICAL REVIEW LETTERS 2021; 127:140402. [PMID: 34652182 DOI: 10.1103/physrevlett.127.140402] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 09/03/2021] [Indexed: 06/13/2023]
Abstract
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise is large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers promise unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
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Affiliation(s)
- F Anders
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - A Idel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - P Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - D Bondarenko
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - S Loriani
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - K Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - J Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - M Gersemann
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - B Meyer-Hoppe
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - S Abend
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - N Gaaloul
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Schubert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - D Schlippert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - E Rasel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
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10
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An FA, Sundar B, Hou J, Luo XW, Meier EJ, Zhang C, Hazzard KRA, Gadway B. Nonlinear Dynamics in a Synthetic Momentum-State Lattice. PHYSICAL REVIEW LETTERS 2021; 127:130401. [PMID: 34623847 DOI: 10.1103/physrevlett.127.130401] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 08/27/2021] [Indexed: 06/13/2023]
Abstract
The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, the idea of synthetic dimensions-in which transport occurs in a space spanned by internal or motional states coupled by field-driven transitions-has played a key role in this expansion. While approaches based on synthetic dimensions have led to rapid advances in single-particle Hamiltonian engineering, strong interaction effects have been conspicuously absent from most synthetic dimensions platforms. Here, in a lattice of coupled atomic momentum states, we show that atomic interactions result in large and qualitative changes to dynamics in the synthetic dimension. We explore how the interplay of nonlinear interactions and coherent tunneling enriches the dynamics of a one-band tight-binding model giving rise to macroscopic self-trapping and phase-driven Josephson dynamics with a nonsinusoidal current-phase relationship, which can be viewed as stemming from a nonlinear band structure arising from interactions.
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Affiliation(s)
- Fangzhao Alex An
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Bhuvanesh Sundar
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
- JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Eric J Meier
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Kaden R A Hazzard
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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11
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Evrard B, Qu A, Dalibard J, Gerbier F. Observation of fragmentation of a spinor Bose-Einstein condensate. Science 2021; 373:1340-1343. [PMID: 34529460 DOI: 10.1126/science.abd8206] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 75005 Paris, France
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12
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Bai SY, An JH. Generating Stable Spin Squeezing by Squeezed-Reservoir Engineering. PHYSICAL REVIEW LETTERS 2021; 127:083602. [PMID: 34477431 DOI: 10.1103/physrevlett.127.083602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Revised: 07/13/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that N two-level systems (TLSs) located near a one-dimensional waveguide can generate SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent driving on the TLSs. Incorporating the mediation role of the common waveguide and the technique of squeezed-reservoir engineering, our scheme exhibits the advantages over previous ones in the scaling relation of the SS parameter with the number of the TLSs. The long-range correlation feature of the generated SS along the waveguide in our scheme may endow it with certain superiority in quantum sensing, e.g., improving the sensing efficiency of spatially unidentified weak magnetic fields.
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Affiliation(s)
- Si-Yuan Bai
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Jun-Hong An
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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13
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Xie T, Zhao Z, Kong X, Ma W, Wang M, Ye X, Yu P, Yang Z, Xu S, Wang P, Wang Y, Shi F, Du J. Beating the standard quantum limit under ambient conditions with solid-state spins. SCIENCE ADVANCES 2021; 7:7/32/eabg9204. [PMID: 34362736 PMCID: PMC8346219 DOI: 10.1126/sciadv.abg9204] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 06/21/2021] [Indexed: 05/16/2023]
Abstract
The use of entangled sensors improves the precision limit from the standard quantum limit (SQL) to the Heisenberg limit. Most previous experiments beating the SQL are performed on the sensors that are well isolated under extreme conditions. Here, we demonstrate a sub-SQL interferometer at ambient conditions by using a multispin system, namely, the nitrogen-vacancy (NV) defect in diamond. We achieve two-spin interference with a phase sensitivity of 1.79 ± 0.06 dB beyond the SQL and three-spin interference with a phase sensitivity of 2.77 ± 0.10 dB. Besides, a magnetic sensitivity of 0.87 ± 0.09 dB beyond the SQL is achieved by two-spin interference for detecting a real magnetic field. Particularly, the deterministic and joint initialization of NV negative state, NV electron spin, and two nuclear spins is realized at room temperature. The techniques used here are of fundamental importance for quantum sensing and computing, and naturally applicable to other solid-state spin systems.
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Affiliation(s)
- Tianyu Xie
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhiyuan Zhao
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xi Kong
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Wenchao Ma
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Mengqi Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiangyu Ye
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Pei Yu
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhiping Yang
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shaoyi Xu
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Pengfei Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ya Wang
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Fazhan Shi
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China.
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jiangfeng Du
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China.
- CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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Feldmann P, Klempt C, Smerzi A, Santos L, Gessner M. Interferometric Order Parameter for Excited-State Quantum Phase Transitions in Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2021; 126:230602. [PMID: 34170156 DOI: 10.1103/physrevlett.126.230602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 03/05/2021] [Accepted: 04/19/2021] [Indexed: 06/13/2023]
Abstract
Excited-state quantum phase transitions extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for excited-state quantum phase transitions poses, however, a major challenge. We introduce a topological order parameter that distinguishes excited-state phases in a large class of mean-field models and can be accessed by interferometry in current experiments with spinor Bose-Einstein condensates. Our work opens a way for the experimental characterization of excited-state quantum phases in atomic many-body systems.
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Affiliation(s)
- Polina Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - Augusto Smerzi
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
| | - Manuel Gessner
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005 Paris, France
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15
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Evrard B, Qu A, Dalibard J, Gerbier F. From Many-Body Oscillations to Thermalization in an Isolated Spinor Gas. PHYSICAL REVIEW LETTERS 2021; 126:063401. [PMID: 33635710 DOI: 10.1103/physrevlett.126.063401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin-1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the nonlinearity of the spectrum leads to irreversibility, characterized by a universal behavior. When the integrability of the Hamiltonian is broken, a chaotic dynamics emerges and leads to thermalization, in agreement with the eigenstate thermalization hypothesis paradigm.
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Affiliation(s)
- Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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16
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Guo SF, Chen F, Liu Q, Xue M, Chen JJ, Cao JH, Mao TW, Tey MK, You L. Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning. PHYSICAL REVIEW LETTERS 2021; 126:060401. [PMID: 33635691 DOI: 10.1103/physrevlett.126.060401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20 dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.
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Affiliation(s)
- Shuai-Feng Guo
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Feng Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ming Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jun-Jie Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jia-Hao Cao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Tian-Wei Mao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Meng Khoon Tey
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
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17
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Lyu C, Lv C, Zhou Q. Geometrizing Quantum Dynamics of a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2020; 125:253401. [PMID: 33416381 DOI: 10.1103/physrevlett.125.253401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 11/12/2020] [Indexed: 06/12/2023]
Abstract
We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincaré disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the metric of this hyperbolic space. This approach leads to a unique geometric interpretation of stable and unstable modes as closed and open trajectories on the Poincaré disk, respectively. The resonant modes that follow geodesics naturally equate fundamental quantities including the time, the length, and the temperature. Our work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes. In the presence of perturbations breaking the SU(1,1) symmetry, SU(1,1) echoes deliver a new means to measure these perturbations such as the interactions between excited particles.
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Affiliation(s)
- Changyuan Lyu
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Chenwei Lv
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
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18
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Davis EJ, Periwal A, Cooper ES, Bentsen G, Evered SJ, Van Kirk K, Schleier-Smith MH. Protecting Spin Coherence in a Tunable Heisenberg Model. PHYSICAL REVIEW LETTERS 2020; 125:060402. [PMID: 32845652 DOI: 10.1103/physrevlett.125.060402] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Revised: 05/15/2020] [Accepted: 06/09/2020] [Indexed: 05/09/2023]
Abstract
Using an ensemble of atoms in an optical cavity, we engineer a family of nonlocal Heisenberg Hamiltonians with continuously tunable anisotropy of the spin-spin couplings. We thus gain access to a rich phase diagram, including a paramagnetic-to-ferromagnetic Ising phase transition that manifests as a diverging magnetic susceptibility at the critical point. The susceptibility displays a symmetry between Ising interactions and XY (spin-exchange) interactions of the opposite sign, which is indicative of the spatially extended atomic system behaving as a single collective spin. Images of the magnetization dynamics show that spin-exchange interactions protect the coherence of the collective spin, even against inhomogeneous fields that completely dephase the noninteracting and Ising systems. Our results underscore prospects for harnessing spin-exchange interactions to enhance the robustness of spin squeezing protocols.
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Affiliation(s)
- Emily J Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Avikar Periwal
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Eric S Cooper
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Gregory Bentsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
| | - Simon J Evered
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Katherine Van Kirk
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Monika H Schleier-Smith
- Department of Physics, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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19
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Qu A, Evrard B, Dalibard J, Gerbier F. Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level. PHYSICAL REVIEW LETTERS 2020; 125:033401. [PMID: 32745434 DOI: 10.1103/physrevlett.125.033401] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.
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Affiliation(s)
- An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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20
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21
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Quantum entanglement between an atom and a molecule. Nature 2020; 581:273-277. [DOI: 10.1038/s41586-020-2257-1] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 03/02/2020] [Indexed: 02/03/2023]
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22
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Xie D, Deng TS, Xiao T, Gou W, Chen T, Yi W, Yan B. Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2020; 124:050502. [PMID: 32083915 DOI: 10.1103/physrevlett.124.050502] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Accepted: 01/15/2020] [Indexed: 05/22/2023]
Abstract
We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.
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Affiliation(s)
- Dizhou Xie
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tian-Shu Deng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Teng Xiao
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Wei Gou
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Tao Chen
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Wei Yi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
| | - Bo Yan
- Interdisciplinary Center of Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device of Physics Department, Zhejiang University, Hangzhou 310027, China
- Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Key Laboratory of Quantum Optics, Chinese Academy of Sciences, Shanghai 200800, China
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23
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Pezzè L, Gessner M, Feldmann P, Klempt C, Santos L, Smerzi A. Heralded Generation of Macroscopic Superposition States in a Spinor Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2019; 123:260403. [PMID: 31951461 DOI: 10.1103/physrevlett.123.260403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 06/17/2019] [Indexed: 06/10/2023]
Abstract
Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.
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Affiliation(s)
- L Pezzè
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, IT-50125 Firenze, Italy
| | - M Gessner
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, IT-50125 Firenze, Italy
- Département de Physique, École Normale Supérieure, PSL Université, CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - P Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, DE-30167 Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
| | - A Smerzi
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, IT-50125 Firenze, Italy
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24
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Makhalov V, Satoor T, Evrard A, Chalopin T, Lopes R, Nascimbene S. Probing Quantum Criticality and Symmetry Breaking at the Microscopic Level. PHYSICAL REVIEW LETTERS 2019; 123:120601. [PMID: 31633983 DOI: 10.1103/physrevlett.123.120601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Indexed: 06/10/2023]
Abstract
We report on an experimental study of the Lipkin-Meshkov-Glick model of quantum spins interacting at infinite range in a transverse magnetic field, which exhibits a ferromagnetic phase transition in the thermodynamic limit. We use dysprosium atoms of electronic spin J=8, subjected to a quadratic Zeeman light shift, to simulate 2J=16 interacting spins 1/2. We probe the system microscopically using single magnetic sublevel resolution, giving access to the spin projection parity, which is the collective observable characterizing the underlying Z_{2} symmetry. We measure the thermodynamic properties and dynamical response of the system, and we study the quantum critical behavior around the transition point. In the ferromagnetic phase, we achieve coherent tunneling between symmetry-broken states, and we test the link between symmetry breaking and the appearance of a finite order parameter.
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Affiliation(s)
- Vasiliy Makhalov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Tanish Satoor
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Alexandre Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Thomas Chalopin
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Raphael Lopes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Sylvain Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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25
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Xu P, Yi S, Zhang W. Efficient Generation of Many-Body Entangled States by Multilevel Oscillations. PHYSICAL REVIEW LETTERS 2019; 123:073001. [PMID: 31491105 DOI: 10.1103/physrevlett.123.073001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/10/2023]
Abstract
We generate high-fidelity massively entangled states in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC) by utilizing multilevel oscillations. Combining the multilevel oscillations with additional adiabatic drives, we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting, from microgauss to milligauss, for a ^{23}Na spinor BEC. The achieved high fidelities over 96% show that two kinds of massively entangled states, the many-body singlet state and the twin-Fock state, are almost perfectly generated. The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of atom number fluctuations and stray magnetic fields, illustrating the robustness of our protocol under real experimental conditions. The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science.
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Affiliation(s)
- Peng Xu
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
| | - Su Yi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
- School of Physical Sciences & CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wenxian Zhang
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
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Bai K, Peng Z, Luo HG, An JH. Retrieving Ideal Precision in Noisy Quantum Optical Metrology. PHYSICAL REVIEW LETTERS 2019; 123:040402. [PMID: 31491244 DOI: 10.1103/physrevlett.123.040402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Indexed: 06/10/2023]
Abstract
Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.
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Affiliation(s)
- Kai Bai
- School of Physical Science and Technology & Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
| | - Zhen Peng
- School of Physical Science and Technology & Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
| | - Hong-Gang Luo
- School of Physical Science and Technology & Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Jun-Hong An
- School of Physical Science and Technology & Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China
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Evrard A, Makhalov V, Chalopin T, Sidorenkov LA, Dalibard J, Lopes R, Nascimbene S. Enhanced Magnetic Sensitivity with Non-Gaussian Quantum Fluctuations. PHYSICAL REVIEW LETTERS 2019; 122:173601. [PMID: 31107084 DOI: 10.1103/physrevlett.122.173601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Indexed: 06/09/2023]
Abstract
The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In Gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-Gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of nonclassical states of the electronic spin J=8 of dysprosium atoms, created using light-induced nonlinear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-Gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.
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Affiliation(s)
- Alexandre Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Vasiliy Makhalov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Thomas Chalopin
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Leonid A Sidorenkov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Raphael Lopes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Sylvain Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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28
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Xu XT, Wang ZY, Jiao RH, Yi CR, Sun W, Chen S. Ultra-low noise magnetic field for quantum gases. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:054708. [PMID: 31153239 DOI: 10.1063/1.5087957] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2019] [Accepted: 05/06/2019] [Indexed: 06/09/2023]
Abstract
A ultralow noise magnetic field is essential for many branches of scientific research. Examples include experiments conducted on ultracold atoms, quantum simulations, and precision measurements. In ultracold atom experiments specifically, a bias magnetic field will often serve as a quantization axis and be applied for Zeeman splitting. As atomic states are usually sensitive to magnetic fields, a magnetic field characterized by ultralow noise as well as high stability is typically required for experimentation. For this study, a bias magnetic field is successfully stabilized at 14.5 G, with the root mean square value of the noise reduced to 18.5 μG (1.28 ppm) by placing μ-metal magnetic shields together with a dynamical feedback circuit. Long-time instability is also regulated consistently below 7 μG. The level of noise exhibited in the bias magnetic field is further confirmed by evaluating the coherence time of a Bose-Einstein condensate characterized by Rabi oscillation. It is concluded that this approach can be applied to other physical systems as well.
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Affiliation(s)
- Xiao-Tian Xu
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Zong-Yao Wang
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Rui-Heng Jiao
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Chang-Rui Yi
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Wei Sun
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Shuai Chen
- Shanghai Branch, National Research Center for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
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29
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Sompet P, Szigeti SS, Schwartz E, Bradley AS, Andersen MF. Thermally robust spin correlations between two 85Rb atoms in an optical microtrap. Nat Commun 2019; 10:1889. [PMID: 31015406 PMCID: PMC6478867 DOI: 10.1038/s41467-019-09420-6] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Accepted: 03/11/2019] [Indexed: 11/21/2022] Open
Abstract
The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped 85Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for 85Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation. Spin-changing atomic collisions are important for thermally robust entanglement generation with applications in quantum information. Here the authors demonstrate record high spin state correlations and long spin relaxation times in the collision of two Rb atoms at relatively warm temperatures.
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Affiliation(s)
- Pimonpan Sompet
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.,Max-Planck-Institut für Quantenoptik, 85748, Garching, Germany
| | - Stuart S Szigeti
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.,Department of Quantum Science, Research School of Physics and Engineering, The Australian National University, Canberra, ACT, 2601, Australia
| | - Eyal Schwartz
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Ashton S Bradley
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Mikkel F Andersen
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.
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30
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Masson SJ, Parkins S. Rapid Production of Many-Body Entanglement in Spin-1 Atoms via Cavity Output Photon Counting. PHYSICAL REVIEW LETTERS 2019; 122:103601. [PMID: 30932652 DOI: 10.1103/physrevlett.122.103601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2018] [Indexed: 06/09/2023]
Abstract
We propose a simple and efficient method for generating metrologically useful quantum entanglement in an ensemble of spin-1 atoms that interacts with a high-finesse optical cavity mode. It requires straightforward preparation of N atoms in the m_{F}=0 sublevel, tailoring of the atom-field interaction to give an effective Tavis-Cummings model for the collective spin-1 ensemble, and a photon counting measurement on the cavity output field. The photon number provides a projective measurement of the collective spin length S, which, for the chosen initial state, is heavily weighted around values S≃sqrt[N], for which the corresponding spin states are strongly entangled and exhibit Heisenberg scaling of the metrological sensitivity with N, as quantified by the quantum Fisher information.
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Affiliation(s)
- Stuart J Masson
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Auckland, Private Bag 92109, Auckland, New Zealand
| | - Scott Parkins
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Auckland, Private Bag 92109, Auckland, New Zealand
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31
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Davis EJ, Bentsen G, Homeier L, Li T, Schleier-Smith MH. Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms. PHYSICAL REVIEW LETTERS 2019; 122:010405. [PMID: 31012698 DOI: 10.1103/physrevlett.122.010405] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Indexed: 06/09/2023]
Abstract
We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of 500 μm are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the m_{f}=0 Zeeman state, we observe correlated pair creation in the m_{f}=±1 states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.
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Affiliation(s)
- Emily J Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Gregory Bentsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Lukas Homeier
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Tracy Li
- Department of Physics, Stanford University, Stanford, California 94305, USA
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32
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Yao Q, Zhang J, Yi XF, You L, Zhang W. Uniaxial Dynamical Decoupling for an Open Quantum System. PHYSICAL REVIEW LETTERS 2019; 122:010408. [PMID: 31012664 DOI: 10.1103/physrevlett.122.010408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2018] [Indexed: 06/09/2023]
Abstract
Dynamical decoupling (DD) is an active and effective method for suppressing decoherence of a quantum system from its environment. In contrast to the nominal biaxial DD, this work presents a uniaxial decoupling protocol that requires a significantly reduced number of pulses and a much lower bias field satisfying the "magic" condition. We show this uniaxial DD protocol works effectively in a number of model systems of practical interest, e.g., a spinor atomic Bose-Einstein condensate in stray magnetic fields (classical noise), or an electron spin coupled to nuclear spins (quantum noise) in a semiconductor quantum dot. It requires only half the number of control pulses and a 10-100 times lower bias field for decoupling as normally employed in the above mentioned illustrative examples, and the overall efficacy is robust against rotation errors of the control pulses. The uniaxial DD protocol we propose shines new light on coherent controls in quantum computing and quantum information processing, quantum metrology, and low field nuclear magnetic resonance.
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Affiliation(s)
- Qi Yao
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
| | - Jun Zhang
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
| | - Xiao-Feng Yi
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
| | - Li You
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Wenxian Zhang
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
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33
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Zan X, Liu J, Han J, Wu J, Li Y. Phase diagrams and multistep condensations of spin-1 bosonic gases in optical lattices. Sci Rep 2018; 8:9143. [PMID: 29904172 PMCID: PMC6002366 DOI: 10.1038/s41598-018-27503-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2017] [Accepted: 06/04/2018] [Indexed: 12/03/2022] Open
Abstract
Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the mF = −1 component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component mF = 0 demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.
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Affiliation(s)
- Xiaolei Zan
- Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China
| | - Jing Liu
- Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China
| | - Jinsen Han
- Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China
| | - Jianhua Wu
- Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China.
| | - Yongqiang Li
- Department of Physics, National University of Defense Technology, Changsha, 410073, P. R. China.
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34
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Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms. Proc Natl Acad Sci U S A 2018; 115:6381-6385. [PMID: 29858344 DOI: 10.1073/pnas.1715105115] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.
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35
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Lange K, Peise J, Lücke B, Kruse I, Vitagliano G, Apellaniz I, Kleinmann M, Tóth G, Klempt C. Entanglement between two spatially separated atomic modes. Science 2018; 360:416-418. [PMID: 29700263 DOI: 10.1126/science.aao2035] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 03/22/2018] [Indexed: 02/15/2024]
Abstract
Modern quantum technologies in the fields of quantum computing, quantum simulation, and quantum metrology require the creation and control of large ensembles of entangled particles. In ultracold ensembles of neutral atoms, nonclassical states have been generated with mutual entanglement among thousands of particles. The entanglement generation relies on the fundamental particle-exchange symmetry in ensembles of identical particles, which lacks the standard notion of entanglement between clearly definable subsystems. Here, we present the generation of entanglement between two spatially separated clouds by splitting an ensemble of ultracold identical particles prepared in a twin Fock state. Because the clouds can be addressed individually, our experiments open a path to exploit the available entangled states of indistinguishable particles for quantum information applications.
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Affiliation(s)
- Karsten Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Jan Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Bernd Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Ilka Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Giuseppe Vitagliano
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
| | - Iagoba Apellaniz
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
| | - Matthias Kleinmann
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
- Ikerbasque, Basque Foundation for Science, E-48013 Bilbao, Spain
- Wigner Research Centre for Physics, Hungarian Academy of Sciences, Post Office Box 49, H-1525 Budapest, Hungary
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany.
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36
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Wrubel JP, Schwettmann A, Fahey DP, Glassman Z, Pechkis HK, Griffin PF, Barnett R, Tiesinga E, Lett PD. A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry. PHYSICAL REVIEW. A 2018; 98:10.1103/PhysRevA.98.023620. [PMID: 31093591 PMCID: PMC6513353 DOI: 10.1103/physreva.98.023620] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F = 1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of |F = 1, m = ±1〉 atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1%.
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Affiliation(s)
- J P Wrubel
- Department of Physics, Creighton University, 2500 California Plaza, Omaha, Nebraska 68178, USA
| | - A Schwettmann
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - D P Fahey
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - Z Glassman
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - H K Pechkis
- Department of Physics, California State University, Chico, CA, 95973, USA
| | - P F Griffin
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
- Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK
| | - R Barnett
- Department of Mathematics, Imperial College London, London, United Kingdom, SW7 2AZ
| | - E Tiesinga
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - P D Lett
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
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37
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Masson SJ, Barrett MD, Parkins S. Cavity QED Engineering of Spin Dynamics and Squeezing in a Spinor Gas. PHYSICAL REVIEW LETTERS 2017; 119:213601. [PMID: 29219405 DOI: 10.1103/physrevlett.119.213601] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Indexed: 06/07/2023]
Abstract
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With realistic parameters, the scheme should enable substantial squeezing on time scales much shorter than current experiments with spin-1 Bose-Einstein condensates.
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Affiliation(s)
- Stuart J Masson
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - M D Barrett
- Centre for Quantum Technologies, 3 Science Drive 2, Singapore 117543
- Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Scott Parkins
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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38
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Sperling J, Walmsley IA. Separable and Inseparable Quantum Trajectories. PHYSICAL REVIEW LETTERS 2017; 119:170401. [PMID: 29219464 DOI: 10.1103/physrevlett.119.170401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Indexed: 06/07/2023]
Abstract
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states by comparing the trajectories to their classically correlated counterparts. For this reason, we introduce equations of motions describing the separable propagation of any interacting quantum system, which are derived by requiring separability for all times. The resulting Schrödinger-type equations allow for comparing the trajectories in a separable configuration with the actual behavior of the system and, thereby, identifying inseparable and time-dependent quantum properties. As an example, we study bipartite discrete- and continuous-variable interacting systems. The generalization of our developed technique to multipartite scenarios is also provided.
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Affiliation(s)
- J Sperling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - I A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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39
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Xu P, Sun H, Yi S, Zhang W. Rebuilding of destroyed spin squeezing in noisy environments. Sci Rep 2017; 7:14102. [PMID: 29074937 PMCID: PMC5658406 DOI: 10.1038/s41598-017-14442-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Accepted: 10/10/2017] [Indexed: 11/09/2022] Open
Abstract
We investigate the process of spin squeezing in a ferromagnetic dipolar spin-1 Bose-Einstein condensate under the driven one-axis twisting scheme, with emphasis on the detrimental effect of noisy environments (stray magnetic fields) which completely destroy the spin squeezing. By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments, we faithfully reconstruct the spin squeezing process under realistic experimental conditions. Our noise-resistant method is ready to be employed to generate the spin squeezed state in a dipolar spin-1 Bose-Einstein condensate and paves a feasible way to the Heisenberg-limit quantum metrology.
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Affiliation(s)
- Peng Xu
- School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China
| | - Huanying Sun
- School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China
| | - S Yi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing, 100190, China
| | - Wenxian Zhang
- School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China.
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