1
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Hartley D, Käding C, Howl R, Fuentes I. Quantum-enhanced screened dark energy detection. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2024; 84:49. [PMID: 38261898 PMCID: PMC10796756 DOI: 10.1140/epjc/s10052-023-12360-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 12/17/2023] [Indexed: 01/25/2024]
Abstract
We propose an experiment based on a Bose-Einstein condensate interferometer for strongly constraining fifth-force models. Additional scalar fields from modified gravity or higher dimensional theories may account for dark energy and the accelerating expansion of the Universe. These theories have led to proposed screening mechanisms to fit within the tight experimental bounds on fifth-force searches. We show that our proposed experiment would greatly improve the existing constraints on these screening models by many orders of magnitude.
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Affiliation(s)
- Daniel Hartley
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christian Käding
- Technische Universität Wien, Atominstitut, Stadionallee 2, 1020 Vienna, Austria
- National Research University Higher School of Economics, 101000 Moscow, Russia
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD UK
| | - Richard Howl
- Department of Physics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX UK
- Quantum Group, Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD UK
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK
| | - Ivette Fuentes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
- Keble College, Oxford, OX1 3PG UK
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2
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Kondappan M, Ivannikov V, Byrnes T. Optical circuit compactification for ultracold atoms. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2024; 95:013004. [PMID: 38265277 DOI: 10.1063/5.0180938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 12/23/2023] [Indexed: 01/25/2024]
Abstract
We develop a modular and compactified optical circuit for the generation of optical beams for cooling, imaging, and controlling ultracold atoms. One of the simplifications that is made in our circuit is to admix the repumping beams to each other optical beams in its dedicated single-mode fiber. We implement our design, characterize the output, and show that the optical power efficiency of the circuit is in the region of 97%, and after fiber coupling, the efficiencies are in the range of 62-85%. Given its compact design and controllable optical sources, this setup should be adaptable to a variety of quantum experiments based on ultracold gases.
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Affiliation(s)
- Manikandan Kondappan
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- New York University Shanghai, 567 West Yangsi Road, Pudong New District, Shanghai 200126, China
| | - Valentin Ivannikov
- New York University Shanghai, 567 West Yangsi Road, Pudong New District, Shanghai 200126, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| | - Tim Byrnes
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU-ECNU Institute of Physics at NYU Shanghai, New York University Shanghai, 567 West Yangsi Road, Pudong New District, Shanghai 200126, China
- Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
- Department of Physics, New York University, New York, New York 10003, USA
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3
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Saha AK, Ray DS, Deb B. Phase diffusion and fluctuations in a dissipative Bose-Josephson junction. Phys Rev E 2023; 107:034141. [PMID: 37073026 DOI: 10.1103/physreve.107.034141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 03/16/2023] [Indexed: 04/20/2023]
Abstract
We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.
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Affiliation(s)
- Abhik Kumar Saha
- School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Deb Shankar Ray
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Bimalendu Deb
- School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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4
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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}$$2\,.\,{5}_{-0.6}^{+0.6}$$\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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5
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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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6
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Masi L, Petrucciani T, Ferioli G, Semeghini G, Modugno G, Inguscio M, Fattori M. Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice. PHYSICAL REVIEW LETTERS 2021; 127:020601. [PMID: 34296908 DOI: 10.1103/physrevlett.127.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 03/17/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.
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Affiliation(s)
- L Masi
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - T Petrucciani
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - G Ferioli
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Semeghini
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Modugno
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - M Fattori
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
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7
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Moan ER, Horne RA, Arpornthip T, Luo Z, Fallon AJ, Berl SJ, Sackett CA. Quantum Rotation Sensing with Dual Sagnac Interferometers in an Atom-Optical Waveguide. PHYSICAL REVIEW LETTERS 2020; 124:120403. [PMID: 32281864 DOI: 10.1103/physrevlett.124.120403] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Revised: 01/07/2020] [Accepted: 03/09/2020] [Indexed: 06/11/2023]
Abstract
We describe a Sagnac interferometer suitable for rotation sensing, implemented using an atomic Bose-Einstein condensate confined in a harmonic magnetic trap. The atom wave packets are split and recombined by standing-wave Bragg lasers, and the trapping potential steers the packets along circular trajectories with a radius of 0.2 mm. Two conjugate interferometers are implemented simultaneously to provide common-mode rejection of noise and to isolate the rotation signal. With interference visibilities of about 50%, we achieve a rotation sensitivity comparable to Earth's rate in about 10 min of operation. Gyroscope operation was demonstrated by rotating the optical table on which the experiment was performed.
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Affiliation(s)
- E R Moan
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - R A Horne
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - T Arpornthip
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Z Luo
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - A J Fallon
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - S J Berl
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - C A Sackett
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
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8
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Compact chip-scale guided cold atom gyrometers for inertial navigation: Enabling technologies and design study. ACTA ACUST UNITED AC 2019. [DOI: 10.1116/1.5120348] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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9
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Polo J, Ahufinger V, Hekking FWJ, Minguzzi A. Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases. PHYSICAL REVIEW LETTERS 2018; 121:090404. [PMID: 30230871 DOI: 10.1103/physrevlett.121.090404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.
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Affiliation(s)
- J Polo
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
| | - V Ahufinger
- Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
| | - F W J Hekking
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
| | - A Minguzzi
- Univ. Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
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10
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Pigneur M, Berrada T, Bonneau M, Schumm T, Demler E, Schmiedmayer J. Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction. PHYSICAL REVIEW LETTERS 2018; 120:173601. [PMID: 29756828 DOI: 10.1103/physrevlett.120.173601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Indexed: 06/08/2023]
Abstract
We present an experimental study on the nonequilibrium tunnel dynamics of two coupled one-dimensional Bose-Einstein quasicondensates deep in the Josephson regime. Josephson oscillations are initiated by splitting a single one-dimensional condensate and imprinting a relative phase between the superfluids. Regardless of the initial state and experimental parameters, the dynamics of the relative phase and atom number imbalance shows a relaxation to a phase-locked steady state. The latter is characterized by a high phase coherence and reduced fluctuations with respect to the initial state. We propose an empirical model based on the analogy with the anharmonic oscillator to describe the effect of various experimental parameters. A microscopic theory compatible with our observations is still missing.
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Affiliation(s)
- Marine Pigneur
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Tarik Berrada
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Marie Bonneau
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Thorsten Schumm
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jörg Schmiedmayer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
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11
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An FA, Meier EJ, Ang'ong'a J, Gadway B. Correlated Dynamics in a Synthetic Lattice of Momentum States. PHYSICAL REVIEW LETTERS 2018; 120:040407. [PMID: 29437415 DOI: 10.1103/physrevlett.120.040407] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Revised: 08/09/2017] [Indexed: 06/08/2023]
Abstract
We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low-energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the added exchange energy between atoms in distinguishable momentum states leads to an effectively attractive, finite-ranged interaction between atoms in momentum space. In this Letter, we observe the onset of self-trapping driven by such interactions in a momentum-space double well, paving the way for more complex many-body studies in tailored MSLs. We consider the types of phenomena that may result from these interactions, including the formation of chiral solitons in zigzag flux lattices.
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Affiliation(s)
- Fangzhao Alex An
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Eric J Meier
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Jackson Ang'ong'a
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| | - Bryce Gadway
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
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12
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Burton WC, Kennedy CJ, Chung WC, Vadia S, Chen W, Ketterle W. Coherence Times of Bose-Einstein Condensates beyond the Shot-Noise Limit via Superfluid Shielding. PHYSICAL REVIEW LETTERS 2016; 117:275301. [PMID: 28084759 DOI: 10.1103/physrevlett.117.275301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate a new way to extend the coherence time of separated Bose-Einstein condensates that involves immersion into a superfluid bath. When both the system and the bath have similar scattering lengths, immersion in a superfluid bath cancels out inhomogeneous potentials either imposed by external fields or inherent in density fluctuations due to atomic shot noise. This effect, which we call superfluid shielding, allows for coherence lifetimes beyond the projection noise limit. We probe the coherence between separated condensates in different sites of an optical lattice by monitoring the contrast and decay of Bloch oscillations. Our technique demonstrates a new way that interactions can improve the performance of quantum devices.
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Affiliation(s)
- William Cody Burton
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Colin J Kennedy
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Woo Chang Chung
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Samarth Vadia
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany
| | - Wenlan Chen
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wolfgang Ketterle
- Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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13
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Abend S, Gebbe M, Gersemann M, Ahlers H, Müntinga H, Giese E, Gaaloul N, Schubert C, Lämmerzahl C, Ertmer W, Schleich WP, Rasel EM. Atom-Chip Fountain Gravimeter. PHYSICAL REVIEW LETTERS 2016; 117:203003. [PMID: 27886486 DOI: 10.1103/physrevlett.117.203003] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Indexed: 06/06/2023]
Abstract
We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-μGal accuracies in miniaturized, robust devices.
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Affiliation(s)
- S Abend
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - M Gebbe
- ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen, Germany
| | - M Gersemann
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - H Ahlers
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - H Müntinga
- ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen, Germany
| | - E Giese
- Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Albert-Einstein-Allee 11, D-89081 Ulm, Germany
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, ON K1N 6N5, Canada
| | - 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
| | - C Lämmerzahl
- ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen, Germany
| | - W Ertmer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - W P Schleich
- Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Albert-Einstein-Allee 11, D-89081 Ulm, Germany
- Texas A&M University Institute for Advanced Study (TIAS), Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
| | - E M Rasel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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14
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Keil M, Amit O, Zhou S, Groswasser D, Japha Y, Folman R. Fifteen years of cold matter on the atom chip: promise, realizations, and prospects. JOURNAL OF MODERN OPTICS 2016; 63:1840-1885. [PMID: 27499585 PMCID: PMC4960518 DOI: 10.1080/09500340.2016.1178820] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Accepted: 03/22/2016] [Indexed: 05/30/2023]
Abstract
Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.
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Affiliation(s)
- Mark Keil
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Omer Amit
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Shuyu Zhou
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - David Groswasser
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Yonathan Japha
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
| | - Ron Folman
- Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
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15
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Cox KC, Greve GP, Weiner JM, Thompson JK. Deterministic Squeezed States with Collective Measurements and Feedback. PHYSICAL REVIEW LETTERS 2016; 116:093602. [PMID: 26991175 DOI: 10.1103/physrevlett.116.093602] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 06/05/2023]
Abstract
We demonstrate the creation of entangled, spin-squeezed states using a collective, or joint, measurement and real-time feedback. The pseudospin state of an ensemble of N=5×10^{4} laser-cooled ^{87}Rb atoms is deterministically driven to a specified population state with angular resolution that is a factor of 5.5(8) [7.4(6) dB] in variance below the standard quantum limit for unentangled atoms-comparable to the best enhancements using only unitary evolution. Without feedback, conditioning on the outcome of the joint premeasurement, we directly observe up to 59(8) times [17.7(6) dB] improvement in quantum phase variance relative to the standard quantum limit for N=4×10^{5} atoms. This is one of the largest reported entanglement enhancements to date in any system.
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Affiliation(s)
- Kevin C Cox
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Graham P Greve
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Joshua M Weiner
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
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16
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Stevenson R, Hush MR, Bishop T, Lesanovsky I, Fernholz T. Sagnac Interferometry with a Single Atomic Clock. PHYSICAL REVIEW LETTERS 2015; 115:163001. [PMID: 26550871 DOI: 10.1103/physrevlett.115.163001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 06/05/2023]
Abstract
The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology.
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Affiliation(s)
- R Stevenson
- School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - M R Hush
- School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra 2600, Australia
| | - T Bishop
- School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - I Lesanovsky
- School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - T Fernholz
- School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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17
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Liu GQ, Zhang YR, Chang YC, Yue JD, Fan H, Pan XY. Demonstration of entanglement-enhanced phase estimation in solid. Nat Commun 2015; 6:6726. [PMID: 25832364 PMCID: PMC4396365 DOI: 10.1038/ncomms7726] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2014] [Accepted: 02/21/2015] [Indexed: 11/09/2022] Open
Abstract
Precise parameter estimation plays a central role in science and technology. The statistical error in estimation can be decreased by repeating measurement, leading to that the resultant uncertainty of the estimated parameter is proportional to the square root of the number of repetitions in accordance with the central limit theorem. Quantum parameter estimation, an emerging field of quantum technology, aims to use quantum resources to yield higher statistical precision than classical approaches. Here we report the first room-temperature implementation of entanglement-enhanced phase estimation in a solid-state system: the nitrogen-vacancy centre in pure diamond. We demonstrate a super-resolving phase measurement with two entangled qubits of different physical realizations: an nitrogen-vacancy centre electron spin and a proximal (13)C nuclear spin. The experimental data shows clearly the uncertainty reduction when entanglement resource is used, confirming the theoretical expectation. Our results represent an elemental demonstration of enhancement of quantum metrology against classical procedure.
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Affiliation(s)
- Gang-Qin Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yu-Ran Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yan-Chun Chang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Jie-Dong Yue
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng Fan
- 1] Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100190, China
| | - Xin-Yu Pan
- 1] Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100190, China
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18
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Auccaise R, Araujo-Ferreira AG, Sarthour RS, Oliveira IS, Bonagamba TJ, Roditi I. Spin squeezing in a quadrupolar nuclei NMR system. PHYSICAL REVIEW LETTERS 2015; 114:043604. [PMID: 25679893 DOI: 10.1103/physrevlett.114.043604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Indexed: 06/04/2023]
Abstract
We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.
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Affiliation(s)
- R Auccaise
- Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti, 4748, 84030-900 Ponta Grossa, Paraná, Brazil
| | - A G Araujo-Ferreira
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - R S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - I S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - T J Bonagamba
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - I Roditi
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
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19
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Integrated Mach-Zehnder interferometer for Bose-Einstein condensates. Nat Commun 2013; 4:2077. [PMID: 23804159 DOI: 10.1038/ncomms3077] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2013] [Accepted: 05/31/2013] [Indexed: 11/09/2022] Open
Abstract
Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach-Zehnder sequence with trapped Bose-Einstein condensates confined on an atom chip. Particle interactions in our Bose-Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors.
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20
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Taşgın ME. Metal nanoparticle plasmons operating within a quantum lifetime. NANOSCALE 2013; 5:8616-8624. [PMID: 23897124 DOI: 10.1039/c3nr02270f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We investigate the dynamics of a plasmonic oscillation over a metal nanoparticle when it is strongly coupled to a quantum emitter (e.g. quantum dot, molecule). We simulate the density matrix evolution for a simple model, a coupled classical-quantum oscillators system. We show that the lifetime of the plasmonic oscillations can be increased several orders of magnitude, up to the decay time of the quantum emitter. This effect shows itself as the narrowing of the plasmon emission band in the spaser (surface plasmon amplification by the stimulated emission of radiation) experiment [Nature, 2009, 460, 1110], where a gold nanoparticle interacts with the surrounding molecules. Enhancement of the plasmonic excitation lifetime enables stimulated emission to overcome the spontaneous one. The enhancement occurs due to the emergence of a phenomenon analogous to electromagnetically induced transparency (EIT). The effect can find applications in many areas of nanoscale physics, such as in quantum information with plasmons and in increasing solar cell efficiency.
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Affiliation(s)
- Mehmet Emre Taşgın
- Department of Electrical and Electronics Engineering, Kırklareli University, 39020 Karahıdır, Kırklareli, Turkey.
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21
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Machluf S, Japha Y, Folman R. Coherent Stern–Gerlach momentum splitting on an atom chip. Nat Commun 2013; 4:2424. [DOI: 10.1038/ncomms3424] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2013] [Accepted: 08/09/2013] [Indexed: 11/09/2022] Open
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22
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Blumkin A, Rinott S, Schley R, Berkovitz A, Shammass I, Steinhauer J. Observing atom bunching by the Fourier slice theorem. PHYSICAL REVIEW LETTERS 2013; 110:265301. [PMID: 23848890 DOI: 10.1103/physrevlett.110.265301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2012] [Revised: 05/24/2013] [Indexed: 06/02/2023]
Abstract
By a novel reciprocal space analysis of the measurement, we report a calibrated in situ observation of the bunching effect in a 3D ultracold gas. The calibrated measurement with no free parameters confirms the role of the exchange symmetry and the Hanbury Brown-Twiss effect in the bunching. Also, the enhanced fluctuations of the bunching effect give a quantitative measure of the increased isothermal compressibility. We use 2D images to probe the 3D gas, using the same principle by which computerized tomography reconstructs a 3D image of a body. The powerful reciprocal space technique presented is applicable to systems with one, two, or three dimensions.
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Affiliation(s)
- A Blumkin
- Department of Physics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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23
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Gattobigio GL, Couvert A, Reinaudi G, Georgeot B, Guéry-Odelin D. Optically guided beam splitter for propagating matter waves. PHYSICAL REVIEW LETTERS 2012; 109:030403. [PMID: 22861829 DOI: 10.1103/physrevlett.109.030403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2012] [Revised: 05/21/2012] [Indexed: 06/01/2023]
Abstract
We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasimonomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45°. We show that depending on the parameters of this X configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter). The splitting regime results from a chaotic scattering dynamics. The existence of these different regimes turns out to be robust against small variations of the parameters of the system. From numerical studies, we also propose a scheme that provides a robust and controlled beam splitter in two channels only.
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Affiliation(s)
- G L Gattobigio
- Laboratoire de Collisions Agrégats Réactivité, CNRS UMR 5589, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France
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24
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Narayana S, Sato Y. Superfluid quantum interference in multiple-turn reciprocal geometry. PHYSICAL REVIEW LETTERS 2011; 106:255301. [PMID: 21770649 DOI: 10.1103/physrevlett.106.255301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2011] [Revised: 05/23/2011] [Indexed: 05/31/2023]
Abstract
We report the observation of superfluid quantum interference in a compact, large-area matter-wave interferometer consisting of a multiple-turn interfering path in reciprocal geometry. Utilizing the Sagnac effect from Earth's rotation in conjunction with a phase shifter made of superfluid heat current, we demonstrate that such a scheme can be extended for sensitive rotation sensing as well as for general interferometry.
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Affiliation(s)
- Supradeep Narayana
- The Rowland Institute at Harvard, Harvard University, Cambridge, Massachusetts 02142, USA
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25
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He QY, Reid MD, Vaughan TG, Gross C, Oberthaler M, Drummond PD. Einstein-Podolsky-Rosen entanglement strategies in two-well Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2011; 106:120405. [PMID: 21517288 DOI: 10.1103/physrevlett.106.120405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Indexed: 05/30/2023]
Abstract
Criteria suitable for measuring entanglement between two different potential wells in a Bose-Einstein condensation are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or a dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen paradox.
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Affiliation(s)
- Q Y He
- ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
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26
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LeBlanc LJ, Bardon AB, McKeever J, Extavour MHT, Jervis D, Thywissen JH, Piazza F, Smerzi A. Dynamics of a tunable superfluid junction. PHYSICAL REVIEW LETTERS 2011; 106:025302. [PMID: 21405237 DOI: 10.1103/physrevlett.106.025302] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2010] [Indexed: 05/30/2023]
Abstract
We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.
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Affiliation(s)
- L J LeBlanc
- Department of Physics, University of Toronto, 60 St. George, Toronto ON, Canada, M5S 1A7
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27
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Faust DK, Reinhardt WP. Analysis of a Bose-Einstein condensate double-well atom interferometer. PHYSICAL REVIEW LETTERS 2010; 105:240404. [PMID: 21231513 DOI: 10.1103/physrevlett.105.240404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2009] [Indexed: 05/30/2023]
Abstract
Motivated by an open theoretical question in Bose-Einstein condensate atom interferometry, we introduce a novel computational method to describe the condensate order parameter in the presence of a central barrier. We are able to follow the full dynamics of the system during the raising of a barrier, from a single macroscopically occupied ground state to a state where imaging shows a split density and, finally, to the observation of a phase-controlled interference pattern. We are able to discriminate between a mean-field and a two-mode state via the Penrose-Onsager criterion. By simulating the first such experiment, where in spite of the observed splitting of the condensate density there is never more than a single macroscopically occupied state, we provide a definitive interpretation of these systems as a novel many-body form of Young's double-slit experiment.
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Affiliation(s)
- Douglas K Faust
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA.
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28
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Baumgärtner F, Sewell RJ, Eriksson S, Llorente-Garcia I, Dingjan J, Cotter JP, Hinds EA. Measuring energy differences by BEC interferometry on a chip. PHYSICAL REVIEW LETTERS 2010; 105:243003. [PMID: 21231523 DOI: 10.1103/physrevlett.105.243003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2010] [Revised: 10/14/2010] [Indexed: 05/30/2023]
Abstract
We investigate the use of a Bose-Einstein condensate trapped on an atom chip for making interferometric measurements of small energy differences. We measure and explain the noise in the energy difference of the split condensates, which derives from statistical noise in the number difference. We also consider systematic errors. A leading effect is the variation of the rf magnetic field in the trap with distance from the wires on the chip surface. This can produce energy differences that are comparable with those due to gravity.
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Affiliation(s)
- Florian Baumgärtner
- Centre for Cold Matter, Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ, UK
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29
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Zezyulin DA, Konotop VV, Alfimov GL. Dissipative double-well potential: nonlinear stationary and pulsating modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056213. [PMID: 21230569 DOI: 10.1103/physreve.82.056213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2010] [Indexed: 05/30/2023]
Abstract
The analysis of nonlinear modes in a complex absorbing double-well potential supported by linear gain is presented. Families of the nonlinear modes and their bifurcations are found numerically by means of the properly modified "shooting" method. Linear stability and dynamics of the modes are studied. It is shown that no stable modes exist in the case of attractive nonlinearity, while stable modes, including nonsymmetric ones, are found when the nonlinearity is repulsive. Varying a control parameter (e.g., the height of barrier between the wells) results in switching from one mode to another. Apart from stationary modes we have found pulsating solutions emergent from unstable modes.
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Affiliation(s)
- Dmitry A Zezyulin
- Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal.
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30
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Hyllus P, Pezzé L, Smerzi A. Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles. PHYSICAL REVIEW LETTERS 2010; 105:120501. [PMID: 20867618 DOI: 10.1103/physrevlett.105.120501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2010] [Revised: 07/23/2010] [Indexed: 05/29/2023]
Abstract
The concepts of separability, entanglement, spin squeezing, and the Heisenberg limit are central in the theory of quantum-enhanced metrology. In the current literature, these are well established only in the case of linear interferometers operating with input quantum states of a known fixed number of particles. This manuscript generalizes these concepts and extends the quantum phase estimation theory by taking into account classical and quantum fluctuations of the particle number. Our analysis concerns most of the current experiments on precision measurements where the number of particles is known only on average.
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Affiliation(s)
- P Hyllus
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy
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31
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Maussang K, Marti GE, Schneider T, Treutlein P, Li Y, Sinatra A, Long R, Estève J, Reichel J. Enhanced and reduced atom number fluctuations in a BEC splitter. PHYSICAL REVIEW LETTERS 2010; 105:080403. [PMID: 20868082 DOI: 10.1103/physrevlett.105.080403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2010] [Indexed: 05/29/2023]
Abstract
We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to -4.9 dB below the atom shot noise level. Fluctuations rise to more than +3.8 dB close to Tc, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the supershot noise fluctuations directly originate from quantum statistics.
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Affiliation(s)
- Kenneth Maussang
- Laboratoire Kastler-Brossel, ENS, Université Pierre et Marie Curie-Paris 6, CNRS, 24 rue Lhomond, 75 231 Paris Cedex 05, France
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32
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Boukobza E, Moore MG, Cohen D, Vardi A. Nonlinear phase dynamics in a driven bosonic Josephson junction. PHYSICAL REVIEW LETTERS 2010; 104:240402. [PMID: 20867282 DOI: 10.1103/physrevlett.104.240402] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2010] [Indexed: 05/29/2023]
Abstract
We study the collective dynamics of a driven two-mode Bose-Hubbard model in the Josephson interaction regime. The classical phase space is mixed, with chaotic and regular components, which determine the dynamical nature of the fringe visibility. For a weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative phase φ between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the intersite potential barrier stabilizes the φ=π "inverted pendulum" coherent state, and protects the fringe visibility.
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Affiliation(s)
- Erez Boukobza
- Department of Chemistry, Ben-Gurion University of the Negev, Post Office Box 653, Beer-Sheva 84105, Israel
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33
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Whitlock S, Ockeloen CF, Spreeuw RJC. Sub-Poissonian atom-number fluctuations by three-body loss in mesoscopic ensembles. PHYSICAL REVIEW LETTERS 2010; 104:120402. [PMID: 20366518 DOI: 10.1103/physrevlett.104.120402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2009] [Indexed: 05/29/2023]
Abstract
We show that three-body loss of trapped atoms leads to sub-Poissonian atom-number fluctuations. We prepare hundreds of dense ultracold ensembles in an array of magnetic microtraps which undergo rapid three-body decay. The shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian, for ensembles comprising 50-300 atoms. The measured relative variance or Fano factor F=0.53+/-0.22 agrees very well with the prediction by an analytic theory (F=3/5) and numerical calculations. These results will facilitate studies of quantum information science with mesoscopic ensembles.
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Affiliation(s)
- S Whitlock
- Van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
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34
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Itah A, Veksler H, Lahav O, Blumkin A, Moreno C, Gordon C, Steinhauer J. Direct observation of a sub-Poissonian number distribution of atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2010; 104:113001. [PMID: 20366471 DOI: 10.1103/physrevlett.104.113001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2009] [Indexed: 05/29/2023]
Abstract
We report single-site resolution in a lattice with tunneling between sites, allowing for an in situ study of stochastic losses. The ratio of the loss rate to the tunneling rate is seen to determine the number fluctuations, and the overall profile of the lattice. Sub-Poissonian number fluctuations are observed. Deriving the lattice beams from a microlens array results in perfect relative stability between beams.
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Affiliation(s)
- Amir Itah
- Department of Physics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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35
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Schleier-Smith MH, Leroux ID, Vuletić V. States of an ensemble of two-level atoms with reduced quantum uncertainty. PHYSICAL REVIEW LETTERS 2010; 104:073604. [PMID: 20366883 DOI: 10.1103/physrevlett.104.073604] [Citation(s) in RCA: 85] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2009] [Revised: 12/02/2009] [Indexed: 05/29/2023]
Abstract
We generate entangled states of an ensemble of 5x10{4} 87Rb atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.
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Affiliation(s)
- Monika H Schleier-Smith
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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36
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Sakmann K, Streltsov AI, Alon OE, Cederbaum LS. Exact quantum dynamics of a bosonic Josephson junction. PHYSICAL REVIEW LETTERS 2009; 103:220601. [PMID: 20366081 DOI: 10.1103/physrevlett.103.220601] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2009] [Revised: 10/21/2009] [Indexed: 05/29/2023]
Abstract
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics such as enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, which is attributed to a quick loss of coherence.
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Affiliation(s)
- Kaspar Sakmann
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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Döring D, Debs JE, Robins NP, Figl C, Altin PA, Close JD. Ramsey interferometry with an atom laser. OPTICS EXPRESS 2009; 17:20661-20668. [PMID: 19997295 DOI: 10.1364/oe.17.020661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F = 1,mF = 0) --> |F = 2,mF = 0) ground state transition of Bose-condensed (87)Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein condensate and propagates through a sequence of two internal state beam splitters, realized via coherent Raman transitions between the two interfering states. We observe Ramsey fringes with a visibility close to 100% and determine the current and the potentially achievable interferometric phase sensitivity. This system is well suited to testing recent proposals for generating and detecting squeezed atomic states.
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Affiliation(s)
- D Döring
- Australian Research Council Centre of Excellence for Quantum-Atom Optics, The Australian National University, ACT 0200, Australia.
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38
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Tuchman AK, Kasevich MA. Phase-slip interferometry for precision force measurements. PHYSICAL REVIEW LETTERS 2009; 103:130403. [PMID: 19905495 DOI: 10.1103/physrevlett.103.130403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2009] [Indexed: 05/28/2023]
Abstract
We demonstrate a novel atom interferometric force sensor based on phase slips in the dynamic evolution of a squeezed-state array of degenerate ;{87}Rb atoms confined in a one-dimensional optical lattice. The truncated Wigner approximation is used to model our observations.
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Affiliation(s)
- Ari K Tuchman
- Entanglement Technologies, Menlo Park, California 94025, USA
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Boukobza E, Chuchem M, Cohen D, Vardi A. Phase-diffusion dynamics in weakly coupled bose-einstein condensates. PHYSICAL REVIEW LETTERS 2009; 102:180403. [PMID: 19518847 DOI: 10.1103/physrevlett.102.180403] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2008] [Indexed: 05/27/2023]
Abstract
We study the phase sensitivity of collisional phase diffusion between weakly coupled Bose-Einstein condensates, using a semiclassical picture of the two-mode Bose-Hubbard model. When weak coupling is allowed, zero relative phase locking is attained in the Josephson-Fock transition regime, whereas a pi relative phase is only locked in Rabi-Josephson point. Our analytic semiclassical estimates agree well with the numerical results.
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Affiliation(s)
- Erez Boukobza
- Department of Chemistry, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
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Fattori M, Roati G, Deissler B, D'Errico C, Zaccanti M, Jona-Lasinio M, Santos L, Inguscio M, Modugno G. Magnetic dipolar interaction in a Bose-Einstein condensate atomic interferometer. PHYSICAL REVIEW LETTERS 2008; 101:190405. [PMID: 19113248 DOI: 10.1103/physrevlett.101.190405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2008] [Indexed: 05/27/2023]
Abstract
We study the role played by the magnetic dipole interaction in the decoherence of a lattice-based interferometer that employs an alkali Bose-Einstein condensate with a tunable scattering length. The different behavior we observe for two different orientations of the dipoles gives us evidence of the anisotropic character of the interaction. The experiment is correctly reproduced by a model we develop only if the long-range interaction between different lattice sites is taken into account. Our model indicates that dipolar interaction can be compensated by a proper choice of the scattering length and that the magnetic dipole interaction should not represent an obstacle for atom interferometry with Bose-Einstein condensates with a tunable interaction.
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Affiliation(s)
- M Fattori
- LENS and Dipartimento di Fisica, Università di Firenze, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy.
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41
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Huang YP, Moore MG. Optimized double-well quantum interferometry with Gaussian squeezed states. PHYSICAL REVIEW LETTERS 2008; 100:250406. [PMID: 18643644 DOI: 10.1103/physrevlett.100.250406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2007] [Indexed: 05/26/2023]
Abstract
A Mach-Zender interferometer with a Gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase interval. We derive the optimal level of squeezing for a given phase interval Deltatheta{0} and particle number N. We then propose an adaptive measurement sequence in which the amount of squeezing is increased with each measurement. With this scheme, any phase on (-Deltatheta{0},Deltatheta{0}) can be measured with a precision of 3.5/N, requiring only 2-4 measurements, provided only that Ntan(Deltatheta{0})<10{40}. In a double-well Bose-Einstein condensate, the optimized input states can be created by adiabatic manipulation of the ground state.
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Affiliation(s)
- Y P Huang
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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43
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Khodorkovsky Y, Kurizki G, Vardi A. Bosonic amplification of noise-induced suppression of phase diffusion. PHYSICAL REVIEW LETTERS 2008; 100:220403. [PMID: 18643407 DOI: 10.1103/physrevlett.100.220403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2008] [Revised: 04/17/2008] [Indexed: 05/26/2023]
Abstract
We study the effect of noise-induced dephasing on collisional phase diffusion in the two-site Bose-Hubbard model. Dephasing of the quasimomentum modes may slow down phase diffusion in the quantum Zeno limit. Remarkably, the degree of suppression is enhanced by a bosonic factor of order N/logN as the particle number N increases.
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Affiliation(s)
- Y Khodorkovsky
- Department of Chemistry, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel
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44
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Widera A, Trotzky S, Cheinet P, Fölling S, Gerbier F, Bloch I, Gritsev V, Lukin MD, Demler E. Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases. PHYSICAL REVIEW LETTERS 2008; 100:140401. [PMID: 18518006 DOI: 10.1103/physrevlett.100.140401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2007] [Indexed: 05/26/2023]
Abstract
We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.
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Affiliation(s)
- Artur Widera
- Johannes Gutenberg-Universität, Institut für Physik, Staudingerweg 7, 55099 Mainz, Germany.
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Scott RG, Judd TE, Fromhold TM. Exploiting soliton decay and phase fluctuations in atom chip interferometry of bose-einstein condensates. PHYSICAL REVIEW LETTERS 2008; 100:100402. [PMID: 18352165 DOI: 10.1103/physrevlett.100.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2007] [Indexed: 05/26/2023]
Abstract
We show that the decay of a soliton into vortices provides a mechanism for measuring the initial phase difference between two merging Bose-Einstein condensates. At very low temperatures, the mechanism is resonant, operating only when the clouds start in antiphase. But at higher temperatures, phase fluctuations trigger vortex production over a wide range of initial relative phase, as observed in recent experiments at MIT. Choosing the merge time to maximize the number of vortices created makes the interferometer highly sensitive to spatially varying phase patterns and hence atomic movement.
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Affiliation(s)
- R G Scott
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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Fattori M, D'Errico C, Roati G, Zaccanti M, Jona-Lasinio M, Modugno M, Inguscio M, Modugno G. Atom interferometry with a weakly interacting Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2008; 100:080405. [PMID: 18352607 DOI: 10.1103/physrevlett.100.080405] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2007] [Indexed: 05/26/2023]
Abstract
We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0.1 a_(0) and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry.
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Affiliation(s)
- M Fattori
- Dipartimento di Fisica, Università di Firenze, and INFM-CNR Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
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Volk M, Whitlock S, Wolff CH, Hall BV, Sidorov AI. Scanning magnetoresistance microscopy of atom chips. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2008; 79:023702. [PMID: 18315300 DOI: 10.1063/1.2839015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Surface based geometries of microfabricated wires or patterned magnetic films can be used to magnetically trap and manipulate ultracold neutral atoms or Bose-Einstein condensates. We investigate the magnetic properties of such atom chips using a scanning magnetoresistive (MR) microscope with high spatial resolution and high field sensitivity. By comparing MR scans of a permanent magnetic atom chip to field profiles obtained using ultracold atoms, we show that MR sensors are ideally suited to observe small variations of the magnetic field caused by imperfections in the wires or magnetic materials which ultimately lead to fragmentation of ultracold atom clouds. Measurements are also provided for the magnetic field produced by a thin current-carrying wire with small geometric modulations along the edge. Comparisons of our measurements with a full numeric calculation of the current flow in the wire and the subsequent magnetic field show excellent agreement. Our results highlight the use of scanning MR microscopy as a convenient and powerful technique for precisely characterizing the magnetic fields produced near the surface of atom chips.
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Affiliation(s)
- M Volk
- ARC Centre of Excellence for Quantum-Atom Optics and Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
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48
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Jo GB, Choi JH, Christensen CA, Lee YR, Pasquini TA, Ketterle W, Pritchard DE. Matter-wave interferometry with phase fluctuating Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2007; 99:240406. [PMID: 18233429 DOI: 10.1103/physrevlett.99.240406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2007] [Indexed: 05/25/2023]
Abstract
Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations; i.e., the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.
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Affiliation(s)
- G-B Jo
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Gritsev V, Demler E, Lukin M, Polkovnikov A. Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics. PHYSICAL REVIEW LETTERS 2007; 99:200404. [PMID: 18233125 DOI: 10.1103/physrevlett.99.200404] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2007] [Revised: 09/11/2007] [Indexed: 05/25/2023]
Abstract
We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.
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Affiliation(s)
- Vladimir Gritsev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Horikoshi M, Nakagawa K. Suppression of dephasing due to a trapping potential and atom-atom interactions in a trapped-condensate interferometer. PHYSICAL REVIEW LETTERS 2007; 99:180401. [PMID: 17995383 DOI: 10.1103/physrevlett.99.180401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2006] [Indexed: 05/25/2023]
Abstract
We propose and demonstrate a novel trapped-condensate interferometer using optical Bragg diffractions in a harmonic magnetic potential, which can realize a long coherence time with low dephasing. Dephasing of wave packets due to the magnetic potential is canceled by setting the interrogation time equal to the oscillation period of the harmonic potential. The harmonic potential also helps to suppress dephasing due to condensate atom-atom interactions. An interference signal with a fringe contrast of 30% is observed at an interrogation time of 58 ms. For a longer interrogation time about 100 ms, the spatial coherence of the condensate is still maintained with low dephasing, although the interference fringe is washed out by external vibrational noise.
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Affiliation(s)
- Munekazu Horikoshi
- Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Japan
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