1
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Eckner WJ, Darkwah Oppong N, Cao A, Young AW, Milner WR, Robinson JM, Ye J, Kaufman AM. Realizing spin squeezing with Rydberg interactions in an optical clock. Nature 2023; 621:734-739. [PMID: 37648865 DOI: 10.1038/s41586-023-06360-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 06/22/2023] [Indexed: 09/01/2023]
Abstract
Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.
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Affiliation(s)
- William J Eckner
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Nelson Darkwah Oppong
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Alec Cao
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Aaron W Young
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - William R Milner
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - John M Robinson
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Jun Ye
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Adam M Kaufman
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA.
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2
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Bornet G, Emperauger G, Chen C, Ye B, Block M, Bintz M, Boyd JA, Barredo D, Comparin T, Mezzacapo F, Roscilde T, Lahaye T, Yao NY, Browaeys A. Scalable spin squeezing in a dipolar Rydberg atom array. Nature 2023; 621:728-733. [PMID: 37648859 DOI: 10.1038/s41586-023-06414-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 07/07/2023] [Indexed: 09/01/2023]
Abstract
The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems to enhance the precision of measurements beyond the standard quantum limit1,2. To do so, one can reshape the quantum projection noise-a strategy known as squeezing3,4. In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model4) between the constituents to generate the structured entanglement characteristic of spin squeezing5. Here we explore the prediction, motivated by recent theoretical work6-10, that short-range interactions-and in particular, the two-dimensional dipolar XY model-can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to N = 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 ± 0.3 dB (before correcting for detection errors, or roughly -5 ± 0.3 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by roughly 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.
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Affiliation(s)
- Guillaume Bornet
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
| | - Gabriel Emperauger
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
| | - Cheng Chen
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France.
| | - Bingtian Ye
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Maxwell Block
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Marcus Bintz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Jamie A Boyd
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
| | - Daniel Barredo
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
- Nanomaterials and Nanotechnology Research Center (CINN-CSIC), University of Oviedo (UO), El Entrego, Spain
| | - Tommaso Comparin
- Laboratory of Physics, University of Lyon, Ens de Lyon, CNRS, Lyon, France
| | - Fabio Mezzacapo
- Laboratory of Physics, University of Lyon, Ens de Lyon, CNRS, Lyon, France
| | - Tommaso Roscilde
- Laboratory of Physics, University of Lyon, Ens de Lyon, CNRS, Lyon, France
| | - Thierry Lahaye
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
| | - Norman Y Yao
- Department of Physics, Harvard University, Cambridge, MA, USA
- Department of Physics, University of California, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Antoine Browaeys
- Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France
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3
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Hines JA, Rajagopal SV, Moreau GL, Wahrman MD, Lewis NA, Marković O, Schleier-Smith M. Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles. PHYSICAL REVIEW LETTERS 2023; 131:063401. [PMID: 37625064 DOI: 10.1103/physrevlett.131.063401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Revised: 06/08/2023] [Accepted: 06/20/2023] [Indexed: 08/27/2023]
Abstract
We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.
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Affiliation(s)
- Jacob A Hines
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | | | - Gabriel L Moreau
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Michael D Wahrman
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Neomi A Lewis
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Ognjen Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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4
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Steinert LM, Osterholz P, Eberhard R, Festa L, Lorenz N, Chen Z, Trautmann A, Gross C. Spatially Tunable Spin Interactions in Neutral Atom Arrays. PHYSICAL REVIEW LETTERS 2023; 130:243001. [PMID: 37390432 DOI: 10.1103/physrevlett.130.243001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 01/20/2023] [Accepted: 05/16/2023] [Indexed: 07/02/2023]
Abstract
Analog quantum simulations with Rydberg atoms in optical tweezers routinely address strongly correlated many-body problems due to the hardware-efficient implementation of the Hamiltonian. Yet, their generality is limited, and flexible Hamiltonian-design techniques are needed to widen the scope of these simulators. Here we report on the realization of spatially tunable interactions for XYZ models implemented by two-color near-resonant coupling to Rydberg pair states. Our results demonstrate the unique opportunities of Rydberg dressing for Hamiltonian design in analog quantum simulators.
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Affiliation(s)
- Lea-Marina Steinert
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Philip Osterholz
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Robin Eberhard
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Lorenzo Festa
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Nikolaus Lorenz
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Zaijun Chen
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
| | - Arno Trautmann
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 München, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
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5
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Tarabunga PS, Surace FM, Andreoni R, Angelone A, Dalmonte M. Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids. PHYSICAL REVIEW LETTERS 2022; 129:195301. [PMID: 36399759 DOI: 10.1103/physrevlett.129.195301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 09/07/2022] [Accepted: 10/20/2022] [Indexed: 06/16/2023]
Abstract
Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.
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Affiliation(s)
- P S Tarabunga
- The Abdus Salam International Centre for Theoretical Physics (ICTP), strada Costiera 11, 34151 Trieste, Italy
- International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - F M Surace
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - R Andreoni
- The Abdus Salam International Centre for Theoretical Physics (ICTP), strada Costiera 11, 34151 Trieste, Italy
- International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
- Dipartimento di Fisica "G. Occhialini," Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
| | - A Angelone
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - M Dalmonte
- The Abdus Salam International Centre for Theoretical Physics (ICTP), strada Costiera 11, 34151 Trieste, Italy
- International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
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6
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Hollerith S, Srakaew K, Wei D, Rubio-Abadal A, Adler D, Weckesser P, Kruckenhauser A, Walther V, van Bijnen R, Rui J, Gross C, Bloch I, Zeiher J. Realizing Distance-Selective Interactions in a Rydberg-Dressed Atom Array. PHYSICAL REVIEW LETTERS 2022; 128:113602. [PMID: 35363010 DOI: 10.1103/physrevlett.128.113602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2021] [Accepted: 01/24/2022] [Indexed: 06/14/2023]
Abstract
Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.
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Affiliation(s)
- Simon Hollerith
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Kritsana Srakaew
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - David Wei
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Antonio Rubio-Abadal
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Daniel Adler
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 München, Germany
| | - Pascal Weckesser
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Andreas Kruckenhauser
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciencies, Innsbruck, Austria
- Center of Quantum Physics, University of Innsbruck, Innsbruck, Austria
| | - Valentin Walther
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciencies, Innsbruck, Austria
- Center of Quantum Physics, University of Innsbruck, Innsbruck, Austria
| | - Jun Rui
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Christian Gross
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Physikalisches Institut, Eberhard Karls Universität Tübingen, 72076 Tübingen, Germany
| | - Immanuel Bloch
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 München, Germany
| | - Johannes Zeiher
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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7
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Differential clock comparisons with a multiplexed optical lattice clock. Nature 2022; 602:425-430. [PMID: 35173344 DOI: 10.1038/s41586-021-04344-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 12/14/2021] [Indexed: 11/08/2022]
Abstract
Rapid progress in optical atomic clock performance has advanced the frontiers of timekeeping, metrology and quantum science1-3. Despite considerable efforts, the instabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves4,5. Here we implement a 'multiplexed' one-dimensional optical lattice clock, in which spatially resolved strontium atom ensembles are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser and read-out in parallel. In synchronous Ramsey interrogations of ensemble pairs we observe atom-atom coherence times of 26 s, a 270-fold improvement over the measured atom-laser coherence time, demonstrate a relative instability of [Formula: see text] (where τ is the averaging time) and reach a relative statistical uncertainty of 8.9 × 10-20 after 3.3 h of averaging. These results demonstrate that applications involving optical clock comparisons need not be limited by the instability of the local oscillator. We further realize a miniaturized clock network consisting of 6 atomic ensembles and 15 simultaneous pairwise comparisons with relative instabilities below [Formula: see text], and prepare spatially resolved, heterogeneous ensemble pairs of all four stable strontium isotopes. These results pave the way for multiplexed precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, the development of clock-based gravitational wave and dark matter detectors6-12 and new tests of relativity in the lab13-16.
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8
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9
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Teixeira RC, Larrouy A, Muni A, Lachaud L, Raimond JM, Gleyzes S, Brune M. Preparation of Long-Lived, Non-Autoionizing Circular Rydberg States of Strontium. PHYSICAL REVIEW LETTERS 2020; 125:263001. [PMID: 33449789 DOI: 10.1103/physrevlett.125.263001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a 4D metastable level are impervious to autoionization over more than a few millisecond time scale. This makes it possible to trap and laser-cool Rydberg atoms. Moreover, we observe singlet to triplet transitions due to the core optical manipulations, opening the way to a microwave to optical quantum interface.
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Affiliation(s)
- R C Teixeira
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
- Departamento de Física, Universidade Federal de São Carlos, Rodovia Washington Luís, km 235-SP-310, 13565-905 São Carlos, São Paulo, Brazil
| | - A Larrouy
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
| | - A Muni
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
| | - L Lachaud
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
| | - J-M Raimond
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
| | - S Gleyzes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
| | - M Brune
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11, place Marcelin Berthelot, 75005 Paris, France
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10
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Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 2020; 588:408-413. [PMID: 33328666 DOI: 10.1038/s41586-020-3009-y] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 09/17/2020] [Indexed: 11/09/2022]
Abstract
The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology1, simulation2 and information3. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems2,4-7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms8-10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 1016. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel11,12. The result is a relative fractional frequency stability of 5.2(3) × 10-17τ-1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition13 in tailored atom arrays.
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11
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Schulte M, Lisdat C, Schmidt PO, Sterr U, Hammerer K. Prospects and challenges for squeezing-enhanced optical atomic clocks. Nat Commun 2020; 11:5955. [PMID: 33235213 PMCID: PMC7686368 DOI: 10.1038/s41467-020-19403-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 10/02/2020] [Indexed: 11/18/2022] Open
Abstract
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.
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Affiliation(s)
- Marius Schulte
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Appelstrasse 2, 30167, Hannover, Germany.
| | - Christian Lisdat
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
| | - Piet O Schmidt
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
- Institute for Quantum Optics, Leibniz University Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Uwe Sterr
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
| | - Klemens Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Appelstrasse 2, 30167, Hannover, Germany.
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12
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Pezzè L, Smerzi A. Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol. PHYSICAL REVIEW LETTERS 2020; 125:210503. [PMID: 33274961 DOI: 10.1103/physrevlett.125.210503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 09/29/2020] [Indexed: 06/12/2023]
Abstract
We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.
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Affiliation(s)
- Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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13
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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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14
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Borish V, Marković O, Hines JA, Rajagopal SV, Schleier-Smith M. Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas. PHYSICAL REVIEW LETTERS 2020; 124:063601. [PMID: 32109106 DOI: 10.1103/physrevlett.124.063601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Accepted: 01/09/2020] [Indexed: 06/10/2023]
Abstract
We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.
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Affiliation(s)
- V Borish
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - O Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - J A Hines
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - S V Rajagopal
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - M Schleier-Smith
- Department of Physics, Stanford University, Stanford, California 94305, USA
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15
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Kaubruegger R, Silvi P, Kokail C, van Bijnen R, Rey AM, Ye J, Kaufman AM, Zoller P. Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors. PHYSICAL REVIEW LETTERS 2019; 123:260505. [PMID: 31951449 DOI: 10.1103/physrevlett.123.260505] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Indexed: 06/10/2023]
Abstract
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
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Affiliation(s)
- Raphael Kaubruegger
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Pietro Silvi
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Christian Kokail
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Rick van Bijnen
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Adam M Kaufman
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Peter Zoller
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
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16
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Norcia MA, Young AW, Eckner WJ, Oelker E, Ye J, Kaufman AM. Seconds-scale coherence on an optical clock transition in a tweezer array. Science 2019; 366:93-97. [PMID: 31515245 DOI: 10.1126/science.aay0644] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Accepted: 09/03/2019] [Indexed: 11/03/2022]
Abstract
Coherent control of high-quality factor optical transitions in atoms has revolutionized precision frequency metrology. Leading optical atomic clocks rely on the interrogation of such transitions in either single ions or ensembles of neutral atoms to stabilize a laser frequency at high precision and accuracy. We demonstrate a platform that combines the key strengths of these two approaches, based on arrays of individual strontium atoms held within optical tweezers. We report coherence times of 3.4 seconds, single-ensemble duty cycles up to 96% through repeated interrogation, and frequency stability of 4.7 × 10-16 (τ/s)-1/2 These results establish optical tweezer arrays as a powerful tool for coherent control of optical transitions for metrology and quantum information science.
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Affiliation(s)
- Matthew A Norcia
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Aaron W Young
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - William J Eckner
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Eric Oelker
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Jun Ye
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Adam M Kaufman
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA.
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17
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Covey JP, Madjarov IS, Cooper A, Endres M. 2000-Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays. PHYSICAL REVIEW LETTERS 2019; 122:173201. [PMID: 31107094 DOI: 10.1103/physrevlett.122.173201] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
We demonstrate single-atom resolved imaging with a survival probability of 0.99932(8) and a fidelity of 0.99991(1), enabling us to perform repeated high-fidelity imaging of single atoms in tweezers thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in 813.4 nm tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retroreflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below 5 μK, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of 0.996(1) and average state detection fidelity of 0.981(1). Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.
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Affiliation(s)
- Jacob P Covey
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
| | - Ivaylo S Madjarov
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
| | - Alexandre Cooper
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
| | - Manuel Endres
- Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
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18
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Arias A, Lochead G, Wintermantel TM, Helmrich S, Whitlock S. Realization of a Rydberg-Dressed Ramsey Interferometer and Electrometer. PHYSICAL REVIEW LETTERS 2019; 122:053601. [PMID: 30822025 DOI: 10.1103/physrevlett.122.053601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Revised: 12/14/2018] [Indexed: 06/09/2023]
Abstract
We present the experimental realization and characterization of a Ramsey interferometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly excited Rydberg state. We show that the observed interference signals can be used to precisely measure the Rydberg atom-light coupling strength as well as the population and coherence decay rates of the Rydberg-dressed states with subkilohertz accuracy and for Rydberg state fractions as small as one part in 10^{6}. We also demonstrate an application for measuring small, static electric fields with high sensitivity. This provides the means to combine the outstanding coherence properties of Ramsey interferometers based on atomic ground states with a controllable coupling to strongly interacting states, thus expanding the number of systems suitable for metrological applications and many-body physics studies.
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Affiliation(s)
- A Arias
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - G Lochead
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - T M Wintermantel
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - S Helmrich
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - S Whitlock
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
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19
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20
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Bounds AD, Jackson NC, Hanley RK, Faoro R, Bridge EM, Huillery P, Jones MPA. Rydberg-Dressed Magneto-optical Trap. PHYSICAL REVIEW LETTERS 2018; 120:183401. [PMID: 29775327 DOI: 10.1103/physrevlett.120.183401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/05/2018] [Indexed: 06/08/2023]
Abstract
We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7 kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at <1 μK. Simulations show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable long-range interactions.
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Affiliation(s)
- A D Bounds
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - N C Jackson
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - R K Hanley
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - R Faoro
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - E M Bridge
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - P Huillery
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - M P A Jones
- Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
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21
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Wüster S, Corney JF, Rost JM, Deuar P. Quantum dynamics of long-range interacting systems using the positive-P and gauge-P representations. Phys Rev E 2018; 96:013309. [PMID: 29347183 DOI: 10.1103/physreve.96.013309] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 11/07/2022]
Abstract
We provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long-range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. We show that the long-range character of these interactions does not further increase the limitations of these methods, in contrast to the situation for alternatives such as the density matrix renormalization group. Furthermore, stochastic gauge techniques can also successfully extend simulation times in the long-range-interaction case, by making using of parameters that affect the noise properties of trajectories, without affecting physical observables. We derive essential results that significantly aid the use of these methods: estimates of the available simulation time, optimized stochastic gauges, a general form of the characteristic stochastic variance, and adaptations for very large systems. Testing the performance of particular drift and diffusion gauges for nonlocal interactions, we find that, for small to medium systems, drift gauges are beneficial, whereas for sufficiently large systems, it is optimal to use only a diffusion gauge. The methods are illustrated with direct numerical simulations of interaction quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg states in a Bose-Einstein condensate, also without the need for the typical frozen gas approximation. We demonstrate that gauges can indeed lengthen the useful simulation time.
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Affiliation(s)
- S Wüster
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.,Department of Physics, Bilkent University, Ankara 06800, Turkey.,Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462 023, India
| | - J F Corney
- School of Mathematics and Physics, University of Queensland, Brisbane QLD 4072, Australia
| | - J M Rost
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - P Deuar
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Pl-02-668 Warsaw, Poland
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22
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Potirniche ID, Potter AC, Schleier-Smith M, Vishwanath A, Yao NY. Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems. PHYSICAL REVIEW LETTERS 2017; 119:123601. [PMID: 29341658 DOI: 10.1103/physrevlett.119.123601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2016] [Indexed: 06/07/2023]
Abstract
We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.
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Affiliation(s)
- I-D Potirniche
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - A C Potter
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - M Schleier-Smith
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - A Vishwanath
- Department of Physics, University of California, Berkeley, California 94720, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - N Y Yao
- Department of Physics, University of California, Berkeley, California 94720, USA
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23
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Arias A, Helmrich S, Schweiger C, Ardizzone L, Lochead G, Whitlock S. Versatile, high-power 460 nm laser system for Rydberg excitation of ultracold potassium. OPTICS EXPRESS 2017; 25:14829-14839. [PMID: 28789066 DOI: 10.1364/oe.25.014829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 04/07/2017] [Indexed: 06/07/2023]
Abstract
We present a versatile laser system which provides more than 1.5 W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial titanium-sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we perform two-photon spectroscopy on ultracold potassium gases in which we observe an electromagnetically induced transparency resonance corresponding to the 35s1/2 state and verify the long-term stability of the laser system. Additionally, by performing spectroscopy in a magneto-optical trap we observe strong loss features corresponding to the excitation of s, p, d and higher-l states accessible due to a small electric field.
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24
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Zhang YC, Zhou XF, Zhou X, Guo GC, Zhou ZW. Cavity-Assisted Single-Mode and Two-Mode Spin-Squeezed States via Phase-Locked Atom-Photon Coupling. PHYSICAL REVIEW LETTERS 2017; 118:083604. [PMID: 28282155 DOI: 10.1103/physrevlett.118.083604] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2016] [Indexed: 06/06/2023]
Abstract
We propose a scheme to realize the two-axis countertwisting spin-squeezing Hamiltonian inside an optical cavity with the aid of phase-locked atom-photon coupling. By careful analysis and extensive simulation, we demonstrate that our scheme is robust against dissipation caused by cavity loss and atomic spontaneous emission, and it can achieve significantly higher squeezing than one-axis twisting. We further show how our idea can be extended to generate two-mode spin-squeezed states in two coupled cavities. Because of its easy implementation and high tunability, our scheme is experimentally realizable with current technologies.
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Affiliation(s)
- Yong-Chang Zhang
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, 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
| | - Xiang-Fa Zhou
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, 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
| | - Xingxiang Zhou
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, 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
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, 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
| | - Zheng-Wei Zhou
- Key Laboratory of Quantum Information, Chinese Academy of Sciences, 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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25
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Gaul C, DeSalvo BJ, Aman JA, Dunning FB, Killian TC, Pohl T. Resonant Rydberg Dressing of Alkaline-Earth Atoms via Electromagnetically Induced Transparency. PHYSICAL REVIEW LETTERS 2016; 116:243001. [PMID: 27367387 DOI: 10.1103/physrevlett.116.243001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Indexed: 06/06/2023]
Abstract
We develop an approach to generate finite-range atomic interactions via optical Rydberg-state excitation and study the underlying excitation dynamics in theory and experiment. In contrast to previous work, the proposed scheme is based on resonant optical driving and the establishment of a dark state under conditions of electromagnetically induced transparency (EIT). Analyzing the driven dissipative dynamics of the atomic gas, we show that the interplay between coherent light coupling, radiative decay, and strong Rydberg-Rydberg atom interactions leads to the emergence of sizable effective interactions while providing remarkably long coherence times. The latter are studied experimentally in a cold gas of strontium atoms for which the proposed scheme is most efficient. Our measured atom loss is in agreement with the theoretical prediction based on binary effective interactions between the driven atoms.
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Affiliation(s)
- C Gaul
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - B J DeSalvo
- Rice University, Department of Physics and Astronomy and Rice Center for Quantum Materials, Houston, Texas 77251, USA
| | - J A Aman
- Rice University, Department of Physics and Astronomy and Rice Center for Quantum Materials, Houston, Texas 77251, USA
| | - F B Dunning
- Rice University, Department of Physics and Astronomy and Rice Center for Quantum Materials, Houston, Texas 77251, USA
| | - T C Killian
- Rice University, Department of Physics and Astronomy and Rice Center for Quantum Materials, Houston, Texas 77251, USA
| | - T Pohl
- Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
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26
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Bridge EM, Keegan NC, Bounds AD, Boddy D, Sadler DP, Jones MPA. Tunable cw UV laser with <35 kHz absolute frequency instability for precision spectroscopy of Sr Rydberg states. OPTICS EXPRESS 2016; 24:2281-2292. [PMID: 26906804 DOI: 10.1364/oe.24.002281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a solid-state laser system that generates over 200 mW of continuous-wave, narrowband light, tunable from 316.3 nm - 317.7 nm and 318.0 nm - 319.3 nm. The laser is based on commercially available fiber amplifiers and optical frequency doubling technology, along with sum frequency generation in a periodically poled stoichiometric lithium tantalate crystal. The laser frequency is stabilized to an atomic-referenced high finesse optical transfer cavity. Using a GPS-referenced optical frequency comb we measure a long term frequency instability of < 35 kHz for timescales between 10(-3) s and 10(3) s. As an application we perform spectroscopy of Sr Rydberg states from n = 37 - 81, demonstrating mode-hop-free scans of 24 GHz. In a cold atomic sample we measure Doppler-limited linewidths of 350 kHz.
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27
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Davis E, Bentsen G, Schleier-Smith M. Approaching the Heisenberg Limit without Single-Particle Detection. PHYSICAL REVIEW LETTERS 2016; 116:053601. [PMID: 26894711 DOI: 10.1103/physrevlett.116.053601] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Indexed: 06/05/2023]
Abstract
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
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Affiliation(s)
- Emily Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Gregory Bentsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
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28
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Beverland ME, Alagic G, Martin MJ, Koller AP, Rey AM, Gorshkov AV. Realizing exactly solvable SU( N) magnets with thermal atoms. PHYSICAL REVIEW. A 2016; 93:10.1103/PhysRevA.93.051601. [PMID: 31276073 PMCID: PMC6604830 DOI: 10.1103/physreva.93.051601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the S n symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.
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Affiliation(s)
- Michael E Beverland
- Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Gorjan Alagic
- Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Michael J Martin
- Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Andrew P Koller
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ana M Rey
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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