冷原子物理中SU(1,1)的对称性

张仁; 吕辰威

doi:10.12405/j.issn.2097-1486.2022.02.004

您当前的位置：

首页 >

文章列表页 >

冷原子物理中SU(1,1)的对称性

其他 | 更新时间：2024-11-01

- 冷原子物理中SU(1,1)的对称性
- SU(1,1) symmetry in cold atom physics
- 新兴科学和技术趋势 2022年1卷第2期页码：167-177
- 作者机构：
  
  1.西安交通大学　物理与天文系，陕西　西安　710049
  2.普渡大学　物理学院，印第安纳州　西拉法叶　47907
- 作者简介：
  
  [ "张仁，西安交通大学副教授。2008年本科毕业于河南师范大学，2014年毕业于中国人民大学并获得博士学位。2014—2017年在清华大学高等研究院从事博士后研究。2017年加入西安交通大学至今。张仁的研究兴趣包括冷原子物理中散射问题，非厄米物理，量子动力学理论以及弯曲空间中的量子物理等。张仁在冷原子物理的相互调控方面做出了一系列的工作，提出了“轨道Feshbach共振”，将约束诱导共振应用于调控自旋交换相互作用，提出了量子动力学几何化理论等，多项理论成果得到实验证实。目前，他已在包括Nature Reviews Physics, PRL，Science Bulletin等学术杂志发表论文30余篇。电子邮箱：renzhang@xjtu.edu.cn" ]
- 基金信息：
  
  自然科学基金委面上项目(12074307);科技部重点研发项目(2018YFA0307601)
- DOI：10.12405/j.issn.2097-1486.2022.02.004
  中图分类号： O562
- 纸质出版日期：2022-12，
  
  收稿日期：2022-11-20，
  
  修回日期：2022-12-07，
- 稿件说明：
移动端阅览
张仁, 吕辰威. 冷原子物理中SU(1,1)的对称性[J]. 新兴科学和技术趋势, 2022,1(2):167-177.

ZHANG Ren, LÜ Chenwei. SU(1,1) symmetry in cold atom physics. [J]. Emerging Science and Technology, 2022,1(2):167-177.
张仁, 吕辰威. 冷原子物理中SU(1,1)的对称性[J]. 新兴科学和技术趋势, 2022,1(2):167-177. DOI： 10.12405/j.issn.2097-1486.2022.02.004.

ZHANG Ren, LÜ Chenwei. SU(1,1) symmetry in cold atom physics. [J]. Emerging Science and Technology, 2022,1(2):167-177. DOI： 10.12405/j.issn.2097-1486.2022.02.004.

摘要

对称性在物理的研究中发挥着至关重要的作用。得益于其良好的可操控性，冷原子物理已成为开展量子模拟、量子调控的理想平台。对称性分析也是冷原子物理理论研究中的重要研究手段。在本文中，我们关注冷原子物理中的SU(1，1)对称性。我们首先简介SU(1，1)对称性的基本性质，并回顾冷原子物理中的部分动力学研究进展。随后，我们将讨论SU(1，1)对称性在动力学及其几何化研究中的重要作用。最后，我们展望了SU(1，1)对称性有可能给出的新的研究进展，为冷原子物理研究带来新的活力。

Abstract

Symmetry plays an important role in the physics research. Thanks to its high controllability

cold atoms have been the ideal platform for quantum simulation and quantum control. Symmetry analysis is also one of the important means of study in cold atom physics. This paper focuses on the SU(1

1) symmetry. It briefly introduces the basic properties of the SU(1

1) symmetry

reviews some of the recent advances on quantum dynamics in cold atom physics

and emphasizes the prominent role of SU(1

1) symmetry in the dynamics studies of cold atoms. At last

the author presents the outlook on the possibilities of future research.

关键词

SU(11)对称性冷原子物理玻色气体标度不变费米气体Efimov物理

Keywords

SU(11) symmetrycold atom physicsBose gasscale-invariant Fermi gasEfimov physics

references

YANG C N. Symmetry and physics[M]. Proceedings of the American PhilosophicalSociety,140(3):267-288,1996. doi: 10.1142/9789814449021_0021http://doi.org/10.1142/9789814449021_0021.

NOVAES M. Some basics of su(1, 1)[J]. Revista Brasileira de Ensino de Física, 2004, 26(4): 351-357. doi: 10.1590/S1806-11172004000400008http://doi.org/10.1590/S1806-11172004000400008.

YURKE B, MCCALL S L, KLAUDER J R. SU(2) and SU(1, 1) interferometers[J]. Physical Review A, 1986, 33(6): 4033-4054. doi: 10.1103/PhysRevA.33.4033http://doi.org/10.1103/PhysRevA.33.4033.

CHIN C, GRIMM R, JULIENNE P, et al. Feshbach resonances in ultracold gases[J]. Reviews of Modern Physics, 2010, 82(2): 1225-1286. doi: 10.1103/RevModPhys.82.1225http://doi.org/10.1103/RevModPhys.82.1225.

KÖHLER T, GóRAL K, JULIENNE P S. Production of cold molecules via magnetically tunable Feshbach resonances[J]. Reviews of Modern Physics, 2006, 78(4): 1311-1361. doi: 10.1103/RevModPhys.78.1311http://doi.org/10.1103/RevModPhys.78.1311.

BLOCH I, DALIBARD J, ZWERGER W. Many-Body Physics with Ultracold Gases[J]. 2007. doi: 10.48550/arXiv.0704.3011http://doi.org/10.48550/arXiv.0704.3011.

SCHÄFER F, FUKUHARA T, SUGAWA S, et al. Tools for quantum simulation with ultracold atoms in optical lattices[J]. Nature Reviews Physics, 2020, 2(8): 411-425. doi: 10.1038/s42254-020-0195-3http://doi.org/10.1038/s42254-020-0195-3.

GROSS C, BLOCH I. Quantum simulations with ultracold atoms in optical lattices[J]. Science, 2017, 357(6355): 995-1001. doi: 10.1126/science.aal3837http://doi.org/10.1126/science.aal3837.

LISOWSKI T. Expectation values of squeezing Hamiltonians in the SU(1, 1) coherent states[J]. Journal of Physics A: Mathematical and General, 1992, 25(23): L1295-L1298. doi: 10.1088/0305-4470/25/23/005http://doi.org/10.1088/0305-4470/25/23/005.

BAN M. Decomposition formulas for su(1, 1) and su(2) Lie algebras and their applications in quantum optics[J]. Journal of the Optical Society of America B, 1993, 10(8): 1347. doi: 10.1364/JOSAB.10.001347http://doi.org/10.1364/JOSAB.10.001347.

BALAZS N L, VOROS A. Chaos on the pseudosphere[J]. Physics Reports, 1986, 143(3): 109-240. doi: 10.1016/0370-1573(86)90159-6http://doi.org/10.1016/0370-1573(86)90159-6.

STEINHAUER J, OZERI R, KATZ N, et al. Excitation Spectrum of a Bose-Einstein Condensate[J]. Physical Review Letters, 2002, 88(12): 120407. doi: 10.1103/PhysRevLett.88.120407http://doi.org/10.1103/PhysRevLett.88.120407.

KRAEMER T, MARK M, WALDBURGER P, et al. Evidence for Efimov quantum states in an ultracold gas of caesium atoms[J]. Nature, 2006, 440(7082): 315-318. doi: 10.1038/nature04626http://doi.org/10.1038/nature04626.

ZHAI H. Degenerate quantum gases with spin-orbit coupling: a review[J]. Reports on Progress in Physics, 2015, 78(2): 026001. doi: 10.1088/0034-4885/78/2/026001http://doi.org/10.1088/0034-4885/78/2/026001.

WERNER F, CASTIN Y. Unitary gas in an isotropic harmonic trap: Symmetry properties and applications[J]. Physical Review A, 2006, 74(5): 053604. doi: 10.1103/PhysRevA.74.053604http://doi.org/10.1103/PhysRevA.74.053604.

CHEVY F, BRETIN V, ROSENBUSCH P, et al. Transverse Breathing Mode of an Elongated Bose-Einstein Condensate[J]. Physical Review Letters, 2002, 88(25): 250402. doi: 10.1103/PhysRevLett.88.250402http://doi.org/10.1103/PhysRevLett.88.250402.

PITAEVSKII L P, ROSCH A. Breathing modes and hidden symmetry of trapped atoms in two dimensions[J]. Physical Review A, 1997, 55(2): R853-R856. doi: 10.1103/PhysRevA.55.R853http://doi.org/10.1103/PhysRevA.55.R853.

VOGT E, FELD M, FRÖHLICH B, et al. Scale Invariance and Viscosity of a Two-Dimensional Fermi Gas[J]. Physical Review Letters, 2012, 108(7): 070404. doi: 10.1103/PhysRevLett.108.070404http://doi.org/10.1103/PhysRevLett.108.070404.

GAO C, YU Z. Breathing mode of two-dimensional atomic Fermi gases in harmonic traps[J]. Physical Review A, 2012, 86(4): 043609. doi: 10.1103/PhysRevA.86.043609http://doi.org/10.1103/PhysRevA.86.043609.

HOFMANN J. Quantum Anomaly, Universal Relations, and Breathing Mode of a Two-Dimensional Fermi Gas[J]. Physical Review Letters, 2012, 108(18): 185303. doi: 10.1103/PhysRevLett.108.185303http://doi.org/10.1103/PhysRevLett.108.185303.

HU H, LIU X J. Resonantly interacting p -wave Fermi superfluid in two dimensions: Tan’s contact and the breathing mode[J]. Physical Review A, 2019, 100(2): 023611. doi: 10.1103/PhysRevA.100.023611http://doi.org/10.1103/PhysRevA.100.023611.

ZHANG Y C, ZHANG S. Strongly interacting p-wave Fermi gas in two dimensions: Universal relations and breathing mode[J]. Physical Review A, 2017, 95(2): 023603. doi: 10.1103/PhysRevA.95.023603http://doi.org/10.1103/PhysRevA.95.023603.

TONIOLO U, MULKERIN B C, VALE C J, et al. Dimensional crossover in a strongly interacting ultracold atomic Fermi gas[J]. Physical Review A, 2017, 96(4): 041604. doi: 10.1103/PhysRevA.96.041604http://doi.org/10.1103/PhysRevA.96.041604.

CLARK L W, GAJ A, FENG L, et al. Collective emission of matter-wave jets from driven Bose-Einstein condensates[J]. Nature, 2017, 551(7680): 356-359. doi: 10.1038/nature24272http://doi.org/10.1038/nature24272.

HU J, FENG L, ZHANG Z, et al. Quantum simulation of Unruh radiation[J]. Nature Physics, 2019, 15(8): 785-789. doi: 10.1038/s41567-019-0537-1http://doi.org/10.1038/s41567-019-0537-1.

CHENG Y, SHI Z Y. Many-body dynamics with time-dependent interaction[J]. Physical Review A, 2021, 104(2): 023307. doi: 10.1103/PhysRevA.104.023307http://doi.org/10.1103/PhysRevA.104.023307.

LV C, ZHANG R, ZHOU Q. S U (1, 1) Echoes for Breathers in Quantum Gases[J]. Physical Review Letters, 2020, 125(25): 253002. doi: 10.1103/PhysRevLett.125.253002http://doi.org/10.1103/PhysRevLett.125.253002.

CHEN Y Y, ZHANG P, ZHENG W, et al. Many-body echo[J]. Physical Review A, 2020, 102(1): 011301. doi: 10.1103/PhysRevA.102.011301http://doi.org/10.1103/PhysRevA.102.011301.

SAINT-JALM R, CASTILHO P C M, LE CERF é, et al. Dynamical Symmetry and Breathers in a Two-Dimensional Bose Gas[J]. Physical Review X, 2019, 9(2): 021035. doi: 10.1103/PhysRevX.9.021035http://doi.org/10.1103/PhysRevX.9.021035.

SHI Z Y, GAO C, ZHAI H. Ideal-Gas Approach to Hydrodynamics[J]. Physical Review X, 2021, 11(4): 041031. doi: 10.1103/PhysRevX.11.041031http://doi.org/10.1103/PhysRevX.11.041031.

BETHE H and PEIERLS R.Quantum theory of the diplon[J]. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 1935, 148(863): 146-156. doi: 10.1098/rspa.1935.0010http://doi.org/10.1098/rspa.1935.0010.

HUANG K, YANG C N. Quantum-Mechanical Many-Body Problem with Hard-Sphere Interaction[J]. Physical Review, 1957, 105(3): 767-775. doi: 10.1103/PhysRev.105.767http://doi.org/10.1103/PhysRev.105.767.

DENG S, SHI Z Y, DIAO P, et al. Observation of the Efimovian expansion in scale-invariant Fermi gases[J]. Science, 2016, 353(6297): 371-374. doi: 10.1126/science.aaf0666http://doi.org/10.1126/science.aaf0666.

ZHANG J, YANG X, LV C, et al. Quantum Dynamics of Cold Atomic Gas with $SU(1, 1)$ Symmetry[J]. 2022. doi: 10.48550/arXiv.2201.04304http://doi.org/10.48550/arXiv.2201.04304.

GREENE C H, GIANNAKEAS P, PéREZ-RíOS J. Universal few-body physics and cluster formation[J]. Reviews of Modern Physics, 2017, 89(3): 035006. doi: 10.1103/RevModPhys.89.035006http://doi.org/10.1103/RevModPhys.89.035006.

NAIDON P, ENDO S. Efimov Physics: a review[J]. 2016. doi: 10.48550/arXiv.1610.09805http://doi.org/10.48550/arXiv.1610.09805.

KOLODRUBETZ M, SELS D, MEHTA P, et al. Geometry and non-adiabatic response in quantum and classical systems[J]. Physics Reports, 2017, 697: 1-87. doi: 10.1016/j.physrep.2017.07.001http://doi.org/10.1016/j.physrep.2017.07.001.

LYU C, LV C, ZHOU Q. Geometrizing Quantum Dynamics of a Bose-Einstein Condensate[J]. Physical Review Letters, 2020, 125(25): 253401. doi: 10.1103/PhysRevLett.125.253401http://doi.org/10.1103/PhysRevLett.125.253401.

HAHN E L. Spin Echoes[J]. Physical Review, 1950, 80(4): 580-594. doi: 10.1103/PhysRev.80.580http://doi.org/10.1103/PhysRev.80.580.

CARR H Y, PURCELL E M. Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments[J]. Physical Review, 1954, 94(3): 630-638. doi: 10.1103/PhysRev.94.630http://doi.org/10.1103/PhysRev.94.630.

MERLOTI K, DUBESSY R, LONGCHAMBON L, et al. Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension[J]. Physical Review A, 2013, 88(6): 061603. doi: 10.1103/PhysRevA.88.061603http://doi.org/10.1103/PhysRevA.88.061603.

HOLTEN M, BAYHA L, KLEIN A C, et al. Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas[J]. Physical Review Letters, 2018, 121(12): 120401. doi: 10.1103/PhysRevLett.121.120401http://doi.org/10.1103/PhysRevLett.121.120401.

PEPPLER T, DYKE P, ZAMORANO M, et al. Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases[J]. Physical Review Letters, 2018, 121(12): 120402. doi: 10.1103/PhysRevLett.121.120402http://doi.org/10.1103/PhysRevLett.121.120402.

YIN X Y, HU H, LIU X J. Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases[J]. Physical Review Letters, 2020, 124(1): 013401. doi: 10.1103/PhysRevLett.124.013401http://doi.org/10.1103/PhysRevLett.124.013401.

ELLIOTT E, JOSEPH J A, THOMAS J E. Observation of Conformal Symmetry Breaking and Scale Invariance in Expanding Fermi Gases[J]. Physical Review Letters, 2014, 112(4): 040405. doi: 10.1103/PhysRevLett.112.040405http://doi.org/10.1103/PhysRevLett.112.040405.

HU H, MULKERIN B C, TONIOLO U, et al. Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions[J]. Physical Review Letters, 2019, 122(7): 070401. doi: 10.1103/PhysRevLett.122.070401http://doi.org/10.1103/PhysRevLett.122.070401.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

暂无数据