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Finger F, Rosa-Medina R, Reiter N, Christodoulou P, Donner T, Esslinger T. Spin- and Momentum-Correlated Atom Pairs Mediated by Photon Exchange and Seeded by Vacuum Fluctuations. Phys Rev Lett 2024; 132:093402. [PMID: 38489609 DOI: 10.1103/physrevlett.132.093402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 10/27/2023] [Accepted: 01/23/2024] [Indexed: 03/17/2024]
Abstract
Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this Letter, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single channel or two discernible channels. The scheme is independent of collisional interactions, fast, and tunable. We observe a collectively enhanced production of pairs and probe interspin correlations in momentum space. We characterize the emergent pair statistics and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.
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Affiliation(s)
- Fabian Finger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Rodrigo Rosa-Medina
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Nicola Reiter
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Tobias Donner
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
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2
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Cao JH, Chen F, Liu Q, Mao TW, Xu WX, Wu LN, You L. Detection of Entangled States Supported by Reinforcement Learning. Phys Rev Lett 2023; 131:073201. [PMID: 37656843 DOI: 10.1103/physrevlett.131.073201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Revised: 06/05/2023] [Accepted: 07/14/2023] [Indexed: 09/03/2023]
Abstract
Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30} dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.
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Affiliation(s)
- Jia-Hao Cao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Feng Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Tian-Wei Mao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Wen-Xin Xu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ling-Na Wu
- Center for Theoretical Physics and School of Science, Hainan University, Haikou 570228, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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3
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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. Rep Prog Phys 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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4
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Anders F, Idel A, Feldmann P, Bondarenko D, Loriani S, Lange K, Peise J, Gersemann M, Meyer-Hoppe B, Abend S, Gaaloul N, Schubert C, Schlippert D, Santos L, Rasel E, Klempt C. Momentum Entanglement for Atom Interferometry. Phys Rev Lett 2021; 127:140402. [PMID: 34652182 DOI: 10.1103/physrevlett.127.140402] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 09/03/2021] [Indexed: 06/13/2023]
Abstract
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise is large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers promise unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
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Affiliation(s)
- F Anders
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - A Idel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - P Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - D Bondarenko
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - S Loriani
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - K Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - J Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - M Gersemann
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - B Meyer-Hoppe
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - S Abend
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - N Gaaloul
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Schubert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - D Schlippert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - E Rasel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
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5
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Kim K, Hur J, Huh S, Choi S, Choi JY. Emission of Spin-Correlated Matter-Wave Jets from Spinor Bose-Einstein Condensates. Phys Rev Lett 2021; 127:043401. [PMID: 34355976 DOI: 10.1103/physrevlett.127.043401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 06/16/2021] [Indexed: 06/13/2023]
Abstract
We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of ^{7}Li atoms. Directional atomic beams with |F=1,m_{F}=1⟩ and |F=1,m_{F}=-1⟩ spin states are generated from |F=1,m_{F}=0⟩ state condensates or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states (|F=1,m_{F}=±1⟩) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter- and intraspin-momentum correlation peaks display a high-contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level. Our Letter paves the way to generating macroscopic quantum entanglement with the spin and motional degree of freedom with massive particles. It has a wide range of applications from quantum information science to the fundamental studies of quantum entanglement.
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Affiliation(s)
- Kyungtae Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Junhyeok Hur
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - SeungJung Huh
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Soonwon Choi
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jae-Yoon Choi
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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6
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Qu A, Evrard B, Dalibard J, Gerbier F. Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level. Phys Rev Lett 2020; 125:033401. [PMID: 32745434 DOI: 10.1103/physrevlett.125.033401] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.
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Affiliation(s)
- An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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7
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Gomez P, Martin F, Mazzinghi C, Benedicto Orenes D, Palacios S, Mitchell MW. Bose-Einstein Condensate Comagnetometer. Phys Rev Lett 2020; 124:170401. [PMID: 32412288 DOI: 10.1103/physrevlett.124.170401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 04/07/2020] [Indexed: 06/11/2023]
Abstract
We describe a comagnetometer employing the f=1 and f=2 ground state hyperfine manifolds of a ^{87}Rb spinor Bose-Einstein condensate as colocated magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f=1 and f=2 transverse magnetizations and azimuth angles are independently measured by nondestructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how the magnetometer coherence time can be extended to ∼1 s, by using spin-dependent interactions to inhibit hyperfine relaxing collisions between f=2 atoms. The technique could be used in high sensitivity searches for new physics on submillimeter length scales, precision studies of ultracold collision physics, and angle-resolved studies of quantum spin dynamics.
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Affiliation(s)
- Pau Gomez
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Quside Technologies S.L., C/Esteve Terradas 1, Of. 217, 08860 Castelldefels (Barcelona), Spain
| | - Ferran Martin
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Quside Technologies S.L., C/Esteve Terradas 1, Of. 217, 08860 Castelldefels (Barcelona), Spain
| | - Chiara Mazzinghi
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Daniel Benedicto Orenes
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Silvana Palacios
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Morgan W Mitchell
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA - Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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8
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Davis EJ, Bentsen G, Homeier L, Li T, Schleier-Smith MH. Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms. Phys Rev Lett 2019; 122:010405. [PMID: 31012698 DOI: 10.1103/physrevlett.122.010405] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Indexed: 06/09/2023]
Abstract
We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of 500 μm are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the m_{f}=0 Zeeman state, we observe correlated pair creation in the m_{f}=±1 states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.
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Affiliation(s)
- Emily J Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Gregory Bentsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Lukas Homeier
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Tracy Li
- Department of Physics, Stanford University, Stanford, California 94305, USA
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9
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Wrubel JP, Schwettmann A, Fahey DP, Glassman Z, Pechkis HK, Griffin PF, Barnett R, Tiesinga E, Lett PD. A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry. Phys Rev A (Coll Park) 2018; 98:10.1103/PhysRevA.98.023620. [PMID: 31093591 PMCID: PMC6513353 DOI: 10.1103/physreva.98.023620] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F = 1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of |F = 1, m = ±1〉 atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1%.
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Affiliation(s)
- J P Wrubel
- Department of Physics, Creighton University, 2500 California Plaza, Omaha, Nebraska 68178, USA
| | - A Schwettmann
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, 440 W. Brooks Street, Norman, Oklahoma 73019, USA
| | - D P Fahey
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - Z Glassman
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - H K Pechkis
- Department of Physics, California State University, Chico, CA, 95973, USA
| | - P F Griffin
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
- Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK
| | - R Barnett
- Department of Mathematics, Imperial College London, London, United Kingdom, SW7 2AZ
| | - E Tiesinga
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
| | - P D Lett
- Quantum Measurement Division, National Institute of Standards and Technology, and Joint Quantum Institute, NIST and University of Maryland, 100 Bureau Drive, Gaithersburg, Maryland 20899-8424, USA
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10
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Masson SJ, Barrett MD, Parkins S. Cavity QED Engineering of Spin Dynamics and Squeezing in a Spinor Gas. Phys Rev Lett 2017; 119:213601. [PMID: 29219405 DOI: 10.1103/physrevlett.119.213601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Indexed: 06/07/2023]
Abstract
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With realistic parameters, the scheme should enable substantial squeezing on time scales much shorter than current experiments with spin-1 Bose-Einstein condensates.
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Affiliation(s)
- Stuart J Masson
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - M D Barrett
- Centre for Quantum Technologies, 3 Science Drive 2, Singapore 117543
- Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Scott Parkins
- Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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11
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Abstract
Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA), focus on the role of motion near separatrices, and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as O(1/ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of O[(ln N)2]. We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.
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Affiliation(s)
- R Mathew
- Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, Maryland 20742, USA
| | - E Tiesinga
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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12
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Kruse I, Lange K, Peise J, Lücke B, Pezzè L, Arlt J, Ertmer W, Lisdat C, Santos L, Smerzi A, Klempt C. Improvement of an Atomic Clock using Squeezed Vacuum. Phys Rev Lett 2016; 117:143004. [PMID: 27740781 DOI: 10.1103/physrevlett.117.143004] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Indexed: 06/06/2023]
Abstract
Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10000 atoms by 2.05_{-0.37}^{+0.34} dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum.
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Affiliation(s)
- I Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - K Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - J Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - B Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - L Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - J Arlt
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, DK-8000 Århus C, Denmark
| | - W Ertmer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Lisdat
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - A Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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13
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Linnemann D, Strobel H, Muessel W, Schulz J, Lewis-Swan RJ, Kheruntsyan KV, Oberthaler MK. Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics. Phys Rev Lett 2016; 117:013001. [PMID: 27419565 DOI: 10.1103/physrevlett.117.013001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Indexed: 06/06/2023]
Abstract
We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.
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Affiliation(s)
- D Linnemann
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - H Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - W Muessel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - J Schulz
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - R J Lewis-Swan
- The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia
| | - K V Kheruntsyan
- The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia
| | - M K Oberthaler
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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14
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Anquez M, Robbins BA, Bharath HM, Boguslawski M, Hoang TM, Chapman MS. Quantum Kibble-Zurek Mechanism in a Spin-1 Bose-Einstein Condensate. Phys Rev Lett 2016; 116:155301. [PMID: 27127974 DOI: 10.1103/physrevlett.116.155301] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Indexed: 06/05/2023]
Abstract
The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.
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Affiliation(s)
- M Anquez
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - B A Robbins
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - H M Bharath
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - M Boguslawski
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - T M Hoang
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - M S Chapman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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15
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Peise J, Kruse I, Lange K, Lücke B, Pezzè L, Arlt J, Ertmer W, Hammerer K, Santos L, Smerzi A, Klempt C. Satisfying the Einstein-Podolsky-Rosen criterion with massive particles. Nat Commun 2015; 6:8984. [PMID: 26612105 DOI: 10.1038/ncomms9984] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Accepted: 10/23/2015] [Indexed: 11/11/2022] Open
Abstract
In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology. Continuous-variables EPR states present a resource for applications to quantum information processing and metrology, but these states have been created until now only with photon pairs. Here, the authors report the creation of an EPR-correlated two-mode squeezed states in an ultracold atomic ensemble.
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16
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Abstract
Unstable spinor Bose-Einstein condensates are ideal candidates to create nonlinear three-mode interferometers. Our analysis goes beyond the standard SU(1,1) parametric approach and therefore provides the regime of parameters where sub-shot-noise sensitivities can be reached with respect to the input total average number of particles. Decoherence due to particle losses and finite detection efficiency are also considered.
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Affiliation(s)
- Marco Gabbrielli
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019, Sesto Fiorentino, Italy
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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17
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Peise J, Lücke B, Pezzé L, Deuretzbacher F, Ertmer W, Arlt J, Smerzi A, Santos L, Klempt C. Interaction-free measurements by quantum Zeno stabilization of ultracold atoms. Nat Commun 2015; 6:6811. [PMID: 25869121 DOI: 10.1038/ncomms7811] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Accepted: 03/02/2015] [Indexed: 11/09/2022] Open
Abstract
Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments. The inherent strangeness of quantum mechanics means it is possible to detect objects using single-quantum particles even if they do not interact directly. Peise et al. realize such an ‘interaction-free measurement' by exploiting the quantum Zeno effect in a BEC, obviating the need for single-particle sources.
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18
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Lücke B, Peise J, Vitagliano G, Arlt J, Santos L, Tóth G, Klempt C. Detecting multiparticle entanglement of Dicke states. Phys Rev Lett 2014; 112:155304. [PMID: 24785048 DOI: 10.1103/physrevlett.112.155304] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2014] [Indexed: 06/03/2023]
Abstract
Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wider class of entangled states, including Dicke states. Experimentally, we produce a Dicke-like state using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it contains at least genuine 28-particle entanglement. We infer a generalized squeezing parameter of -11.4(5) dB.
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Affiliation(s)
- Bernd Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Jan Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Giuseppe Vitagliano
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
| | - Jan Arlt
- QUANTOP, Institut for Fysik og Astronomi, Aarhus Universitet, 8000 Århus C, Denmark
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain and IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain and Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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19
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Hume DB, Stroescu I, Joos M, Muessel W, Strobel H, Oberthaler MK. Accurate atom counting in mesoscopic ensembles. Phys Rev Lett 2013; 111:253001. [PMID: 24483741 DOI: 10.1103/physrevlett.111.253001] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2013] [Indexed: 06/03/2023]
Abstract
Many cold atom experiments rely on precise atom number detection, especially in the context of quantum-enhanced metrology where effects at the single particle level are important. Here, we investigate the limits of atom number counting via resonant fluorescence detection for mesoscopic samples of trapped atoms. We characterize the precision of these fluorescence measurements beginning from the single-atom level up to more than one thousand. By investigating the primary noise sources, we obtain single-atom resolution for atom numbers as high as 1200. This capability is an essential prerequisite for future experiments with highly entangled states of mesoscopic atomic ensembles.
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Affiliation(s)
- D B Hume
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
| | - I Stroescu
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
| | - M Joos
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
| | - W Muessel
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
| | - H Strobel
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
| | - M K Oberthaler
- Kirchhoff-Institute for Physics, University of Heidelberg, INF 227, 69120 Heidelberg, Germany
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20
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Hoang TM, Gerving CS, Land BJ, Anquez M, Hamley CD, Chapman MS. Dynamic stabilization of a quantum many-body spin system. Phys Rev Lett 2013; 111:090403. [PMID: 24033006 DOI: 10.1103/physrevlett.111.090403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis.
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Affiliation(s)
- T M Hoang
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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21
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Gerving C, Hoang T, Land B, Anquez M, Hamley C, Chapman M. Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate. Nat Commun 2012; 3:1169. [DOI: 10.1038/ncomms2179] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2012] [Accepted: 09/28/2012] [Indexed: 11/09/2022] Open
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22
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Gross C, Strobel H, Nicklas E, Zibold T, Bar-gill N, Kurizki G, Oberthaler MK. Atomic homodyne detection of continuous-variable entangled twin-atom states. Nature 2011; 480:219-23. [DOI: 10.1038/nature10654] [Citation(s) in RCA: 154] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2011] [Accepted: 10/18/2011] [Indexed: 11/08/2022]
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23
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Abstract
We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of -7 dB (-10 dB corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of 100 μs.
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Affiliation(s)
- Eva M Bookjans
- School of Physics, Georgia Institute of Technology, Atlanta, 30332-0430, USA
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24
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Bookjans EM, Vinit A, Raman C. Quantum phase transition in an antiferromagnetic spinor Bose-Einstein condensate. Phys Rev Lett 2011; 107:195306. [PMID: 22181622 DOI: 10.1103/physrevlett.107.195306] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2011] [Indexed: 05/31/2023]
Abstract
We have experimentally observed the dynamics of an antiferromagnetic sodium Bose-Einstein condensate quenched through a quantum phase transition. Using an off-resonant microwave field coupling the F = 1 and F = 2 atomic hyperfine levels, we rapidly switched the quadratic energy shift q from positive to negative values. At q = 0, the system undergoes a transition from a polar to antiferromagnetic phase. We measured the dynamical evolution of the population in the F = 1, mF = 0 state in the vicinity of this transition point and observed a mixed state of all 3 hyperfine components for q < 0. We also observed the coarsening dynamics of the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud.
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Affiliation(s)
- E M Bookjans
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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25
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Lücke B, Scherer M, Kruse J, Pezzé L, Deuretzbacher F, Hyllus P, Topic O, Peise J, Ertmer W, Arlt J, Santos L, Smerzi A, Klempt C. Twin matter waves for interferometry beyond the classical limit. Science 2011; 334:773-6. [PMID: 21998255 DOI: 10.1126/science.1208798] [Citation(s) in RCA: 97] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Interferometers with atomic ensembles are an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to 10(4) pair-correlated atoms with an interferometric sensitivity -1.61(-1.1)(+0.98) decibels beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers.
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Affiliation(s)
- B Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, 30167 Hannover, Germany
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26
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Scherer M, Lücke B, Gebreyesus G, Topic O, Deuretzbacher F, Ertmer W, Santos L, Arlt JJ, Klempt C. Spontaneous breaking of spatial and spin symmetry in spinor condensates. Phys Rev Lett 2010; 105:135302. [PMID: 21230785 DOI: 10.1103/physrevlett.105.135302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2010] [Indexed: 05/30/2023]
Abstract
Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously formed patterns in the longitudinal magnetization.
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Affiliation(s)
- M Scherer
- Institut für Quantenoptik, Leibniz Universität Hannover, 30167 Hannover, Germany
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27
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Kronjäger J, Becker C, Soltan-Panahi P, Bongs K, Sengstock K. Spontaneous pattern formation in an antiferromagnetic quantum gas. Phys Rev Lett 2010; 105:090402. [PMID: 20868141 DOI: 10.1103/physrevlett.105.090402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2010] [Indexed: 05/29/2023]
Abstract
In this Letter we report on the spontaneous formation of surprisingly regular periodic magnetic patterns in an antiferromagnetic Bose-Einstein condensate (BEC). The structures evolve within a quasi-one-dimensional BEC of 87Rb atoms on length scales of a millimeter with typical periodicities of 20…30 μm, given by the spin healing length. We observe two sets of characteristic patterns which can be controlled by an external magnetic field. We identify these patterns as linearly unstable modes within a mean-field approach and calculate their mode structure as well as time and energy scales, which we find to be in good agreement with observations. These investigations open new prospects for controlled studies of symmetry breaking and complex quantum magnetism in bulk BEC.
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Affiliation(s)
- Jochen Kronjäger
- MUARC, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
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