Measuring Zak phase in room-temperature atoms

Ruosong Mao; Xingqi Xu; Jiefei Wang; Chenran Xu; Gewei Qian; Han Cai; Shi-Yao Zhu; Da-Wei Wang

doi:10.1038/s41377-022-00990-7

Go to Nature Website

Your Location：

Home >

Browse articles >

Measuring Zak phase in room-temperature atoms

Original Articles

- Measuring Zak phase in room-temperature atoms
- Light: Science & Applications Vol. 11, Issue 10, Pages: 2530-2539(2022)
- Affiliations：
  
  1.Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou 310027, China
  2.College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
  3.Hefei National Laboratory, Hefei 230088, China
  4.CAS Center of Excellence in Topological Quantum Computation, 100190 Beijing, China
- Author bio：
  
  Han Cai (hancai@zju.edu.cn)
  Da-Wei Wang (dwwang@zju.edu.cn)
- Funds：
- DOI：10.1038/s41377-022-00990-7
  CLC：
- Published：31 October 2022，
  
  Published Online：09 October 2022，
  
  Received：23 May 2022，
  
  Revised：20 September 2022，
  
  Accepted：21 September 2022
- Accepted：
Scan QR Code
Mao, R. S. et al. Measuring Zak phase in room-temperature atoms. Light: Science & Applications, 11, 2530-2539 (2022).
DOI：

Mao, R. S. et al. Measuring Zak phase in room-temperature atoms. Light: Science & Applications, 11, 2530-2539 (2022). DOI： 10.1038/s41377-022-00990-7.

摘要

Abstract

Cold atoms provide a flexible platform for synthesizing and characterizing topological matter

where geometric phases play a central role. However

cold atoms are intrinsically prone to thermal noise

which can overwhelm the topological response and hamper promised applications. On the other hand

geometric phases also determine the energy spectra of particles subjected to a static force

based on the polarization relation between Wannier-Stark ladders and geometric Zak phases. By exploiting this relation

we develop a method to extract geometric phases from energy spectra of room-temperature superradiance lattices

which are momentum-space lattices of timed Dicke states. In such momentum-space lattices the thermal motion of atoms

instead of being a source of noise

provides effective forces which lead to spectroscopic signatures of the Zak phases. We measure Zak phases directly from the anti-crossings between Wannier-Stark ladders in the Doppler-broadened absorption spectra of superradiance lattices. Our approach paves the way of measuring topological invariants and developing their applications in room-temperature atoms.

关键词

Keywords

references

M. Z. Hasan , C. L. Kane . Colloquium: topological insulators . Rev. Mod. Phys. , 2010 . 82 263 DOI:10.1103/RevModPhys.82.3045http://doi.org/10.1103/RevModPhys.82.3045 .

X. L. Qi , S. C. Zhang . Topological insulators and superconductors . Rev. Mod. Phys. , 2011 . 83 1057 DOI:10.1103/RevModPhys.83.1057http://doi.org/10.1103/RevModPhys.83.1057 .

J. Zak . Berry's phase for energy bands in solids . Phys. Rev. Lett. , 1989 . 62 2747 DOI:10.1103/PhysRevLett.62.2747http://doi.org/10.1103/PhysRevLett.62.2747 .

K. Von Klitzing , G. Dorda , M. Pepper . New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance . Phys. Rev. Lett. , 1980 . 45 494 DOI:10.1103/PhysRevLett.45.494http://doi.org/10.1103/PhysRevLett.45.494 .

D. J. Thouless , M. Kohmoto , M. P. Nightingale , M. den Nijs . Quantized Hall conductance in a two-dimensional periodic potential . Phys. Rev. Lett. , 1982 . 49 405 DOI:10.1103/PhysRevLett.49.405http://doi.org/10.1103/PhysRevLett.49.405 .

F. D. M. Haldane . Model for a quantum Hall effect without landau levels: condensed-matter realization of the "parity anomaly" . Phys. Rev. Lett. , 1988 . 61 2015 DOI:10.1103/PhysRevLett.61.2015http://doi.org/10.1103/PhysRevLett.61.2015 .

N. R. Cooper , J. Dalibard , I. B. Spielman . Topological bands for ultracold atoms . Rev. Mod. Phys. , 2019 . 91 015005 DOI:10.1103/RevModPhys.91.015005http://doi.org/10.1103/RevModPhys.91.015005 .

M. Atala , 等 . Direct measurement of the Zak phase in topological Bloch bands . Nat. Phys. , 2013 . 9 795 DOI:10.1038/nphys2790http://doi.org/10.1038/nphys2790 .

E. J. Meier , 等 . Observation of the topological Anderson insulator in disordered atomic wires . Science , 2018 . 362 929 DOI:10.1126/science.aat3406http://doi.org/10.1126/science.aat3406 .

D. Xie , W. Gou , T. Xiao , B. Gadway , B. Yan . Topological characterizations of an extended Su-Schrieffer-Heeger model . npj Quantum Inf. , 2019 . 5 1 DOI:10.1038/s41534-019-0159-6http://doi.org/10.1038/s41534-019-0159-6 .

P. Hauke , M. Lewenstein , A. Eckardt . Tomography of band insulators from quench dynamics . Phys. Rev. Lett. , 2014 . 113 045303 DOI:10.1103/PhysRevLett.113.045303http://doi.org/10.1103/PhysRevLett.113.045303 .

T. V. Zache , 等 . Dynamical topological transition in the massive Schwinger model with a θ term . Phys. Rev. Lett. , 2019 . 122 050403 DOI:10.1103/PhysRevLett.122.050403http://doi.org/10.1103/PhysRevLett.122.050403 .

M. Aidelsburger , 等 . Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms . Nat. Phys. , 2015 . 11 162 DOI:10.1038/nphys3171http://doi.org/10.1038/nphys3171 .

T. Chalopin , 等 . Probing chiral edge dynamics and bulk topology of a synthetic Hall system . Nat. Phys. , 2020 . 16 1017 DOI:10.1038/s41567-020-0942-5http://doi.org/10.1038/s41567-020-0942-5 .

D. N. Maksimov , E. N. Bulgakov , A. R. Kolovsky . Wannier-Stark states in double-periodic lattices. I. One-dimensional lattices . Phys. Rev. A , 2015 . 91 053631 DOI:10.1103/PhysRevA.91.053631http://doi.org/10.1103/PhysRevA.91.053631 .

W. R. Lee , K. Park . Direct manifestation of topological order in the winding number of the Wannier-Stark ladder . Phys. Rev. B , 2015 . 92 195144 DOI:10.1103/PhysRevB.92.195144http://doi.org/10.1103/PhysRevB.92.195144 .

A. R. Kolovsky . Topological phase transitions in tilted optical lattices . Phys. Rev. A , 2018 . 98 013603 DOI:10.1103/PhysRevA.98.013603http://doi.org/10.1103/PhysRevA.98.013603 .

A. N. Poddubny . Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders . Phys. Rev. B , 2019 . 100 075418 DOI:10.1103/PhysRevB.100.075418http://doi.org/10.1103/PhysRevB.100.075418 .

N. Marzari , A. A. Mostofi , J. R. Yates , I. Souza , D. Vanderbilt . Maximally localized Wannier functions: theory and applications . Rev. Mod. Phys. , 2012 . 84 1419 DOI:10.1103/RevModPhys.84.1419http://doi.org/10.1103/RevModPhys.84.1419 .

R. D. King-Smith , D. Vanderbilt . Thoery of polarization of crystalline solids . Phys. Rev. B , 1993 . 47 1651R DOI:10.1103/PhysRevB.47.1651http://doi.org/10.1103/PhysRevB.47.1651 .

R. Resta . Macroscopic polarization in crystalline dielectrics: the geometric phase approach . Rev. Mod. Phys. , 1994 . 66 899 DOI:10.1103/RevModPhys.66.899http://doi.org/10.1103/RevModPhys.66.899 .

S. Kivelson . Wannier functions in one-dimensional disordered systems: application to fractionally charged solitons . Phys. Rev. B , 1982 . 26 4269 DOI:10.1103/PhysRevB.26.4269http://doi.org/10.1103/PhysRevB.26.4269 .

D. W. Wang , R. B. Liu , S. Y. Zhu , M. O. Scully . Superradiance lattice . Phys. Rev. Lett. , 2015 . 114 043602 DOI:10.1103/PhysRevLett.114.043602http://doi.org/10.1103/PhysRevLett.114.043602 .

L. Chen , 等 . Experimental observation of one-dimensional superradiance lattices in ultracold atoms . Phys. Rev. Lett. , 2018 . 120 193601 DOI:10.1103/PhysRevLett.120.193601http://doi.org/10.1103/PhysRevLett.120.193601 .

C. Mi , 等 . Time-resolved interplay between superradiant and subradiant states in superradiance lattices of Bose-Einstein condensates . Phys. Rev. A , 2021 . 104 043326 DOI:10.1103/PhysRevA.104.043326http://doi.org/10.1103/PhysRevA.104.043326 .

M. O. Scully , E. S. Fry , C. H. Ooi , K. Wódkiewicz . Directed spontaneous emission from an extended ensemble of N atoms: timing is everything . Phys. Rev. Lett. , 2006 . 96 010501 DOI:10.1103/PhysRevLett.96.010501http://doi.org/10.1103/PhysRevLett.96.010501 .

Y. He , 等 . Geometric control of collective spontaneous emission . Phys. Rev. Lett. , 2020 . 125 213602 DOI:10.1103/PhysRevLett.125.213602http://doi.org/10.1103/PhysRevLett.125.213602 .

W. P. Su , J. R. Schrieffer , A. J. Heeger . Solitons in polyacetylene . Phys. Rev. Lett. , 1979 . 42 1698 DOI:10.1103/PhysRevLett.42.1698http://doi.org/10.1103/PhysRevLett.42.1698 .

E. J. Meier , F. A. An , B. Gadway . Observation of the topological soliton state in the Su–Schrieffer–Heeger model . Nat. Commun. , 2016 . 7 13986 DOI:10.1038/ncomms13986http://doi.org/10.1038/ncomms13986 .

S. Coh , D. Vanderbilt . Electric polarization in a Chern insulator . Phys. Rev. Lett. , 2009 . 102 107603 DOI:10.1103/PhysRevLett.102.107603http://doi.org/10.1103/PhysRevLett.102.107603 .

R. Yu , X. L. Qi , A. B. Bernevig , Z. Fang , X. Dai . Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection . Phys. Rev. B , 2011 . 84 075119 DOI:10.1103/PhysRevB.84.075119http://doi.org/10.1103/PhysRevB.84.075119 .

M. Taherinejad , K. F. Garrity , D. Vanderbilt . Wannier center sheets in topological insulators . Phys. Rev. B , 2014 . 89 115102 DOI:10.1103/PhysRevB.89.115102http://doi.org/10.1103/PhysRevB.89.115102 .

W. A. Benalcazar , B. A. Bernevig , T. L. Hughes . Quantized electric multipole insulators . Science , 2017 . 357 61 DOI:10.1126/science.aah6442http://doi.org/10.1126/science.aah6442 .

M. Ezawa . Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices . Phys. Rev. Lett. , 2018 . 120 026801 DOI:10.1103/PhysRevLett.120.026801http://doi.org/10.1103/PhysRevLett.120.026801 .

J. Wang , Y. Zhu , K. J. Jiang , M. S. Zhan . Bichromatic electromagnetically induced transparency in cold rubidium atoms . Phys. Rev. A , 2003 . 68 195144 DOI:10.1103/PhysRevA.68.063810http://doi.org/10.1103/PhysRevA.68.063810 .

S. Glutsch , F. Bechstedt . Interaction of Wannier-Stark ladders and electrical breakdown in superlattices . Phys. Rev. B , 1999 . 60 16584 DOI:10.1103/PhysRevB.60.16584http://doi.org/10.1103/PhysRevB.60.16584 .

H. Koochaki Kelardeh , V. Apalkov , M. I. Stockman . Wannier-Stark states of graphene in strong electric field . Phys. Rev. B , 2014 . 90 085313 DOI:10.1103/PhysRevB.90.085313http://doi.org/10.1103/PhysRevB.90.085313 .

S. Kuang , R. Wan , P. Du , Y. Jiang , J. Gao . Transmission and reflection of electromagnetically induced absorption grating in homogeneous atomic media . Opt. Express , 2008 . 16 15455 DOI:10.1364/OE.16.015455http://doi.org/10.1364/OE.16.015455 .

P. Peng , 等 . Anti-parity-time symmetry with flying atoms . Nat. Phys. , 2016 . 12 1139 DOI:10.1038/nphys3842http://doi.org/10.1038/nphys3842 .

S. Zhang , 等 . Thermal-motion-induced non-reciprocal quantum optical system . Nat. Photon. , 2018 . 12 744 DOI:10.1038/s41566-018-0269-2http://doi.org/10.1038/s41566-018-0269-2 .

D. W. Wang , H. Cai , L. Yuan , S. Y. Zhu , R. B. Liu . Topological phase transitions in superradiance lattices . Optica , 2015 . 2 712 DOI:10.1364/OPTICA.2.000712http://doi.org/10.1364/OPTICA.2.000712 .

Z. Zhang , 等 . Particlelike behavior of topological defects in linear wave packets in photonic graphene . Phys. Rev. Lett. , 2019 . 122 233905 DOI:10.1103/PhysRevLett.122.233905http://doi.org/10.1103/PhysRevLett.122.233905 .

J. Yuan , C. Wu , L. Wang , G. Chen , S. Jia . Observation of diffraction pattern in two-dimensional optically induced atomic lattice . Opt. Lett. , 2019 . 44 4123 DOI:10.1364/OL.44.004123http://doi.org/10.1364/OL.44.004123 .

J. Yuan , 等 . Tunable optical vortex array in a two-dimensional electromagnetically induced atomic lattice . Opt. Lett. , 2021 . 46 4184 DOI:10.1364/OL.432036http://doi.org/10.1364/OL.432036 .

T. Ozawa , 等 . Topological photonics . Rev. Mod. Phys. , 2019 . 91 015006 DOI:10.1103/RevModPhys.91.015006http://doi.org/10.1103/RevModPhys.91.015006 .

L. Yuan , Q. Lin , M. Xiao , S. Fan . Synthetic dimension in photonics . Optica , 2018 . 5 1396 DOI:10.1364/OPTICA.5.001396http://doi.org/10.1364/OPTICA.5.001396 .

D. Yu , B. Peng , X. Chen , X. J. Liu , L. Yuan . Topological holographic quench dynamics in a synthetic frequency dimension . Light Sci. Appl. , 2021 . 10 209 DOI:10.1038/s41377-021-00646-yhttp://doi.org/10.1038/s41377-021-00646-y .

A. Dutt , 等 . A single photonic cavity with two independent physical synthetic dimensions . Science , 2020 . 367 59 DOI:10.1126/science.aaz3071http://doi.org/10.1126/science.aaz3071 .

Y. Li , 等 . Many-body chiral edge currents and sliding phases of atomic spin waves in momentum-space lattice . Phys. Rev. Lett. , 2020 . 124 140401 DOI:10.1103/PhysRevLett.124.140401http://doi.org/10.1103/PhysRevLett.124.140401 .

F. A. An , E. J. Meier , J. Ang'ong'a , B. Gadway . Correlated dynamcis in a synthetic lattice of momentum states . Phys. Rev. Lett. , 2018 . 120 040407 DOI:10.1103/PhysRevLett.120.040407http://doi.org/10.1103/PhysRevLett.120.040407 .

T. Ozawa , I. Carusotto . Anomalous and quantum Hall effects in lossy photonic lattices . Phys. Rev. Lett. , 2014 . 112 133902 DOI:10.1103/PhysRevLett.112.133902http://doi.org/10.1103/PhysRevLett.112.133902 .

H. Cai , 等 . Experimental observation of momentum-space chiral edge currents in room-temperature atoms . Phys. Rev. Lett. , 2019 . 122 023601 DOI:10.1103/PhysRevLett.122.023601http://doi.org/10.1103/PhysRevLett.122.023601 .

Y. He , 等 . Flat-band localization in Creutz superradiance lattices . Phys. Rev. Lett. , 2021 . 126 103601 DOI:10.1103/PhysRevLett.126.103601http://doi.org/10.1103/PhysRevLett.126.103601 .

M. Harb , 等 . Quantum transport modelling of silicon nanobeams using heterogeneous computing scheme . J. Appl. Phys. , 2016 . 119 124304 DOI:10.1063/1.4944649http://doi.org/10.1063/1.4944649 .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰