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Probing Non-Equilibrium Dynamics in Two-Dimensional Quantum Gases

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Abstract

Probing nonequilibrium dynamics in a trapped, inhomogeneous atomic quantum gas is a challenging task because coexisting mass transport and spreading of quantum correlations often make the problem intractable. By removing density inhomogeneity in an atomic quantum gas and employing local control of chemical potential as well as interaction parameters, it is possible to perform quasiparticle control and initiate and probe collective quantum dynamics without or with a controlled mass flow. In this chapter, we introduce our approach toward probing nonequilibrium dynamics with a fully controllable quantum simulator.

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References

  1. E. Altman et al., Quantum simulators: architectures and opportunities. PRX Quantum 2(1), 017003 (2021)

    Google Scholar 

  2. A. Amo et al., Superfluidity of polaritons in semiconductor microcavities. Nat. Phys. 5(11), 805–810 (2009)

    Article  Google Scholar 

  3. D.G. Angelakis, M.F. Santos, S. Bose, Photon-blockade-induced Mott transitions and X Y spin models in coupled cavity arrays. Phys. Rev. A 76(3), 031805 (2007)

    Google Scholar 

  4. N. Arunkumar, A. Jagannathan, J.E. Thomas, Designer spatial control of interactions in ultracold gases. Phys. Rev. Lett. 122(4), 040405 (2019)

    Google Scholar 

  5. F. Arute et al., Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    Article  ADS  Google Scholar 

  6. W.S. Bakr et al., A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462(7269), 74–77 (2009)

    Article  ADS  Google Scholar 

  7. C. Barceló, S. Liberati, M. Visser, A. gravity, Living Rev. Relat. 14(1), 3 (2011)

    Google Scholar 

  8. J.T. Barreiro et al., An open-system quantum simulator with trapped ions. Nature 470(7335), 486–491 (2011)

    Article  ADS  Google Scholar 

  9. D.M. Bauer et al., Combination of a magnetic Feshbach resonance and an optical bound-to-bound transition. Phys. Rev. A 79(6), 062713 (2009)

    Google Scholar 

  10. D.M. Bauer et al., Control of a magnetic Feshbach resonance with laser light. Nat. Phys. 5(5), 339–342 (2009)

    Article  Google Scholar 

  11. V.L. Berezinsky, Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Zh. Eksp. Teor. Fiz. 61, 610 (1972)

    Google Scholar 

  12. H. Bernien et al., Probing many-body dynamics on a 51-atom quantum simulator. Nature 551(7682), 579–584 (2017)

    Article  ADS  Google Scholar 

  13. D.J. Bishop, J.D. Reppy, Study of the superfluid transition in two-dimensional He 4 films. Phys. Rev. Lett. 40(26), 1727 (1978)

    Google Scholar 

  14. R. Blatt, C.F. Roos, Quantum simulations with trapped ions. Nat. Phys. 8(4), 277–284 (2012)

    Article  Google Scholar 

  15. I. Bloch, Ultracold quantum gases in optical lattices. Nat. Phys. 1(1), 23–30 (2005)

    Article  Google Scholar 

  16. I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases. Rev. Modern Phys. 80(3), 885 (2008)

    Google Scholar 

  17. I. Bloch, J. Dalibard, S. Nascimbene, Quantum simulations with ultracold quantum gases. Nat. Phys. 8(4), 267–276 (2012)

    Article  Google Scholar 

  18. D. Blume, C.H. Greene, Fermi pseudopotential approximation: two particles under external confinement. Phys. Rev. A 65(4), 043613 (2002)

    Google Scholar 

  19. N. Bogoliubov, On the theory of superfluidity. J. Phys. 11(1), 23 (1947)

    Google Scholar 

  20. S.N. Bose, Thermal equilibrium of the radiation field in the presence of matter. Z. Phys. 26(1), 178 (1924)

    Google Scholar 

  21. I. Buluta, F. Nori, Quantum simulators. Science 326(5949), 108–111 (2009)

    Article  ADS  Google Scholar 

  22. I. Buluta, S. Ashhab, F. Nori, Natural and artificial atoms for quantum computation. Rep. Progress Phys. 74(10), 104401 (2011)

    Google Scholar 

  23. L.V. Butov, Condensation and pattern formation in cold exciton gases in coupled quantum wells. J. Phys. Condensed Matt. 16(50), R1577 (2004)

    Google Scholar 

  24. T. Byrnes et al., Quantum simulator for the Hubbard model with long-range Coulomb interactions using surface acoustic waves. Phys. Rev. Lett. 99(1), 016405 (2007)

    Google Scholar 

  25. T. Byrnes et al., Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays. Phys. Rev. B 78(7), 075320 (2008)

    Google Scholar 

  26. D.E. Chang et al., Colloquium: quantum matter built from nanoscopic lattices of atoms and photons. Rev. Modern Phys. 90(3), 031002 (2018)

    Google Scholar 

  27. J. Chiaverini, W.E. Lybarger Jr., Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays. Phys. Rev. A 77(2), 022324 (2008)

    Google Scholar 

  28. C. Chin et al., High resolution Feshbach spectroscopy of cesium. Phys. Rev. Lett. 85(13), 2717 (2000)

    Google Scholar 

  29. C. Chin et al., Precision Feshbach spectroscopy of ultracold Cs 2. Phys. Rev. A 70(3), 032701 (2004)

    Google Scholar 

  30. C. Chin et al., Feshbach resonances in ultracold gases. Rev. Modern Phys. 82(2), 1225 (2010)

    Google Scholar 

  31. L. Chomaz et al., Emergence of coherence via transverse condensation in a uniform quasi-two-dimensional Bose gas. Nat. Commun. 6, 6162 (2015)

    Article  ADS  Google Scholar 

  32. S. Chu, Cold atoms and quantum control. Nature 416(6877), 206–210 (2002)

    Article  ADS  Google Scholar 

  33. J.I. Cirac, P. Zoller, Goals and opportunities in quantum simulation. Nat. Phys. 8(4), 264–266 (2012)

    Article  Google Scholar 

  34. R.J. Clark et al., A two-dimensional lattice ion trap for quantum simulation. J. Appl. Phys. 105(1), 013114 (2009)

    Google Scholar 

  35. L.W. Clark et al., Quantum dynamics with spatiotemporal control of interactions in a stable Bose-Einstein condensate. Phys. Rev. Lett. 115(15), 155301 (2015)

    Google Scholar 

  36. P. Coleman, A.J. Schofield., Quantum criticality. Nature 433(7023), 226–229 (2005)

    Google Scholar 

  37. R. Desbuquois et al., Superfluid behaviour of a two-dimensional Bose gas. Nat. Phys. 8(9), 645–648 (2012)

    Article  Google Scholar 

  38. Y. Ding, Radio-Frequency-Controlled Cold Collisions and Universal Properties of Unitary Bose Gases. PhD Thesis. Purdue University, 2017

    Google Scholar 

  39. R.J. Dodd et al., Characterizing the coherence of Bose-Einstein condensates and atom lasers. Optics Express 1(10), 284–292 (1997)

    Article  ADS  Google Scholar 

  40. L.-M. Duan, E. Demler, M.D. Lukin, Controlling spin exchange interactions of ultracold atoms in optical lattices. Phys. Rev. Lett. 91(9), 090402 (2003)

    Google Scholar 

  41. E.E. Edwards et al., Quantum simulation and phase diagram of the transverse-field Ising model with three atomic spins. Phys. Rev. B 82(6), 060412 (2010)

    Google Scholar 

  42. K. Enomoto et al., Optical Feshbach resonance using the intercombination transition. Phys. Rev. Lett. 101(20), 203201 (2008)

    Google Scholar 

  43. U. Fano, Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124(6), 1866 (1961)

    Google Scholar 

  44. F.K. Fatemi, K.M. Jones, P.D. Lett, Observation of optically induced Feshbach resonances in collisions of cold atoms. Phys. Rev. Lett. 85(21), 4462 (2000)

    Google Scholar 

  45. P.O. Fedichev et al., Influence of nearly resonant light on the scattering length in low-temperature atomic gases. Phys. Rev. Lett. 77(14), 2913 (1996)

    Google Scholar 

  46. H. Feshbach, Unified theory of nuclear reactions. Ann. Phys. 5(4), 357–390 (1958)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. R.P. Feynman, Atomic theory of the two-fluid model of liquid helium. Phys. Rev. 94(2), 262 (1954)

    Google Scholar 

  48. R.P. Feynman, Simulating physics with computers. Int. J. Theoret. Phys. 21(6/7), 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  49. R.P. Feynman, Quantum mechanical computers. Optics News 11(2), 11–20 (1985)

    Article  Google Scholar 

  50. R.P. Feynman, M. Cohen, Energy spectrum of the excitations in liquid helium. Phys. Rev. 102(5), 1189 (1956)

    Google Scholar 

  51. D.S. Fisher, P.C. Hohenberg, Dilute Bose gas in two dimensions. Phys. Rev. B 37(10), 4936 (1988)

    Google Scholar 

  52. L.J. Garay et al., Sonic black holes in dilute Bose-Einstein condensates. Phys. Rev. A 63(2), 023611 (2001)

    Google Scholar 

  53. I.M. Georgescu, S. Ashhab, F. Nori, Quantum simulation. Rev. Modern Phys. 86(1), 153 (2014)

    Google Scholar 

  54. R. Gerritsma et al., Quantum simulation of the Klein paradox with trapped ions. Phys. Rev. Lett. 106(6), 060503 (2011)

    Google Scholar 

  55. S. Giorgini, L.P. Pitaevskii, S. Stringari, Anomalous fluctuations of the condensate in interacting Bose gases. Phys. Rev. Lett. 80(23), 5040 (1998)

    Google Scholar 

  56. N. Goldman, J.C. Budich, P. Zoller, Topological quantum matter with ultracold gases in optical lattices. Nat. Phys. 12(7), 639–645 (2016)

    Article  Google Scholar 

  57. A.D. Greentree et al., Quantum phase transitions of light. Nat. Phys. 2(12), 856–861 (2006)

    Article  Google Scholar 

  58. M. Greiner, S. Fölling, Optical lattices. Nature 453(7196), 736–738 (2008)

    Article  ADS  Google Scholar 

  59. M. Greiner et al., Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415(6867), 39–44 (2002)

    Article  ADS  Google Scholar 

  60. G.F. Gribakin, V.V. Flambaum, Calculation of the scattering length in atomic collisions using the semiclassical approximation. Phys. Rev. A 48(1), 546 (1993)

    Google Scholar 

  61. C. Gross, I. Bloch, Quantum simulations with ultracold atoms in optical lattices. Science 357(6355), 995–1001 (2017)

    Article  ADS  Google Scholar 

  62. Z. Hadzibabic, J. Dalibard, Two-dimensional Bose fluids: an atomic physics perspective. La Rivista del Nuovo Cimento 34(6), 389–434 (2011)

    ADS  Google Scholar 

  63. Z. Hadzibabic et al., Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441(7097), 1118–1121 (2006)

    Article  ADS  Google Scholar 

  64. Z. Hadzibabic et al., The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics. New J. Phys. 10(4), 045006 (2008)

    Google Scholar 

  65. M.J. Hartmann, F.G.S.L. Brandao, M.B. Plenio, Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2(12), 849–855 (2006)

    Article  Google Scholar 

  66. T.-L. Ho, Q. Zhou, Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases. Nat. Phys. 6(2), 131–134 (2010)

    Article  Google Scholar 

  67. C. Honerkamp, W. Hofstetter, Ultracold fermions and the SU (N) Hubbard model. Phys. Rev. Lett. 92(17), 170403 (2004)

    Google Scholar 

  68. K. Hueck et al., Two-dimensional homogeneous Fermi gases. Phys. Rev. Lett. 120(6), 060402 (2018)

    Google Scholar 

  69. C.-L. Hung et al., Observation of scale invariance and universality in two-dimensional Bose gases. Nature 470(7333), 236–239 (2011)

    Article  ADS  Google Scholar 

  70. A. Jagannathan et al., Optical control of magnetic Feshbach resonances by closed-channel electromagnetically induced transparency. Phys. Rev. Lett. 116(7), 075301 (2016)

    Google Scholar 

  71. D. Jaksch, P. Zoller, The cold atom Hubbard toolbox. Ann. Phys. 315(1), 52–79 (2005)

    Article  ADS  MATH  Google Scholar 

  72. D. Jaksch et al., Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81(15), 3108 (1998)

    Google Scholar 

  73. J. Javanainen, Spectrum of light scattered from a degenerate Bose gas. Phys. Rev. Lett. 75(10), 1927 (1995)

    Google Scholar 

  74. K.M Jones et al., Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering. Rev. Modern Phys. 78(2), 483 (2006)

    Google Scholar 

  75. P.S. Julienne, F.H. Mies, Collisions of ultracold trapped atoms. JOSA B 6(11), 2257–2269 (1989)

    Article  ADS  Google Scholar 

  76. J. Kasprzak et al., Bose–Einstein condensation of exciton polaritons. Nature 443(7110), 409–414 (2006)

    Article  ADS  Google Scholar 

  77. W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn, Making, probing and understanding Bose-Einstein condensates (1999). Preprint condmat/9904034

    Google Scholar 

  78. K. Kim et al., Quantum simulation of frustrated Ising spins with trapped ions. Nature 465(7298), 590–593 (2010)

    Article  ADS  Google Scholar 

  79. J.M. Kosterlitz, D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C Solid State Phys. 6(7), 1181 (1973)

    Google Scholar 

  80. T.D. Ladd et al., Quantum computers. Nature 464(7285), 45–53 (2010)

    Article  ADS  Google Scholar 

  81. R. Landig et al., Measuring the dynamic structure factor of a quantum gas undergoing a structural phase transition. Nat. Commun. 6(1), 1–6 (2015)

    Article  Google Scholar 

  82. B.P. Lanyon et al., Universal digital quantum simulation with trapped ions. Science 334(6052), 57–61 (2011)

    Article  ADS  Google Scholar 

  83. K. Le Hur, T.M. Rice, Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices. Ann. Phys. 324(7), 1452–1515 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  84. P.A. Lee, N. Nagaosa, X.-G. Wen, Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Modern Phys. 78(1), 17 (2006)

    Google Scholar 

  85. H.J. Lewandowski et al., Simplified system for creating a Bose–Einstein condensate. J. Low Temperat. Phys. 132(5–6), 309–367 (2003)

    Article  ADS  Google Scholar 

  86. M. Lewenstein et al., Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56(2), 243–379 (2007)

    Article  ADS  Google Scholar 

  87. X. Liu et al., Redefining the Quantum Supremacy Baseline with a New Generation Sunway Supercomputer (2021). Preprint arXiv:2111.01066

    Google Scholar 

  88. S. Lloyd, Universal quantum simulators. Science 273, 1073–1078 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  89. P. Makotyn et al., Universal dynamics of a degenerate unitary Bose gas. Nat. Phys. 10(2), 116–119 (2014)

    Article  Google Scholar 

  90. E. Manousakis, A quantum-dot array as model for copper-oxide superconductors: a dedicated quantum simulator for the many-fermion problem. J. Low Temperat. Phys. 126(5–6), 1501–1513 (2002)

    Article  ADS  Google Scholar 

  91. P. Minnhagen, The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films. Rev. Modern Phys. 59(4), 1001 (1987)

    Google Scholar 

  92. M. Naraschewski, R.J. Glauber, Spatial coherence and density correlations of trapped Bose gases. Phys. Rev. A 59(6), 4595 (1999)

    Google Scholar 

  93. S. Nascimbène et al., Exploring the thermodynamics of a universal Fermi gas. Nature 463(7284), 1057–1060 (2010)

    Article  ADS  Google Scholar 

  94. N. Navon et al., The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328(5979), 729–732 (2010)

    Article  ADS  Google Scholar 

  95. N. Navon et al., Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas. Phys. Rev. Lett. 107(13), 135301 (2011)

    Google Scholar 

  96. D.R. Nelson, J.M. Kosterlitz, Universal jump in the superfluid density of two-dimensional superfluids. Phys. Rev. Lett. 39(19), 1201 (1977)

    Google Scholar 

  97. R. Ozeri, L. Khaykovich, N. Davidson, Long spin relaxation times in a single-beam blue-detuned optical trap. Phys. Rev. A 59(3), R1750 (1999)

    Google Scholar 

  98. C.J. Pethick, H. Smith, Bose–Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  99. D.S. Petrov, M. Holzmann, G.V. Shlyapnikov, Bose-Einstein condensation in quasi-2D trapped gases. Phys. Rev. Lett. 84(12), 2551 (2000)

    Google Scholar 

  100. A. Polkovnikov et al., Colloquium: nonequilibrium dynamics of closed interacting quantum systems. Rev. Modern Phys. 83(3), 863 (2011)

    Google Scholar 

  101. V.N. Popov, On the theory of the superfluidity of two-and one-dimensional Bose systems. Teoreticheskaya i Matematicheskaya Fizika 11(3), 354–365 (1972)

    Google Scholar 

  102. A. Posazhennikova, Colloquium: weakly interacting, dilute Bose gases in 2D. Rev. Modern Phys. 78(4), 1111 (2006)

    Google Scholar 

  103. N. Prokof’ev, O. Ruebenacker, B. Svistunov, Critical point of a weakly interacting two-dimensional Bose gas. Phys. Rev. Lett. 87(27), 270402 (2001)

    Google Scholar 

  104. N. Prokof’ev, B. Svistunov, Two-dimensional weakly interacting Bose gas in the fluctuation region. Phys. Rev. A 66(4), 043608 (2002)

    Google Scholar 

  105. A. Rapp et al., Color superfluidity and “baryon” formation in ultracold fermions. Phys. Rev. Lett. 98(16), 160405 (2007)

    Google Scholar 

  106. S.P. Rath et al., Equilibrium state of a trapped two-dimensional Bose gas. Phys. Rev. A 82(1), 013609 (2010)

    Google Scholar 

  107. S. Sachdev, Quantum phase transitions, in Handbook of Magnetism and Advanced Magnetic Materials (Wiley, Hoboken, 2007)

    Google Scholar 

  108. S. Sachdev, B. Keimer, Quantum criticality (2011). Preprint arXiv:1102.4628

    Google Scholar 

  109. M. Saffman, T.G. Walker, K. Mølmer, Quantum information with Rydberg atoms. Rev. Modern Phys. 82(3), 2313 (2010)

    Google Scholar 

  110. A.I. Safonov et al., Observation of quasicondensate in two-dimensional atomic hydrogen. Phys. Rev. Lett. 81(21), 4545 (1998)

    Google Scholar 

  111. J.J. Sakurai, E.D. Commins, Modern Quantum Mechanics (Revised Edition) (Addison-Wesley, Boston, 1995)

    Book  Google Scholar 

  112. P. Schauß et al., Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491(7422), 87–91 (2012)

    Article  ADS  Google Scholar 

  113. P. Schindler et al., Quantum simulation of dynamical maps with trapped ions. Nat. Phys. 9(6), 361–367 (2013)

    Article  Google Scholar 

  114. R. Schmied, J.H. Wesenberg, D. Leibfried, Optimal surface-electrode trap lattices for quantum simulation with trapped ions. Phys. Rev. Lett. 102(23), 233002 (2009)

    Google Scholar 

  115. D. Snoke, Spontaneous Bose coherence of excitons and polaritons. Science 298(5597), 1368–1372 (2002)

    Article  ADS  Google Scholar 

  116. S. Somaroo et al., Quantum simulations on a quantum computer. Phys. Rev. Lett. 82(26), 5381 (1999)

    Google Scholar 

  117. R. Somma et al., Simulating physical phenomena by quantum networks. Phys. Rev. A 65(4), 042323 (2002)

    Google Scholar 

  118. I.B. Spielman, W.D. Phillips, J.V. Porto, Mott-insulator transition in a two-dimensional atomic Bose gas. Phys. Rev. Lett. 98(8), 080404 (2007)

    Google Scholar 

  119. M. Theis et al., Tuning the scattering length with an optically induced Feshbach resonance. Phys. Rev. Lett. 93(12), 123001 (2004)

    Google Scholar 

  120. O. Thomas et al., Experimental realization of a Rydberg optical Feshbach resonance in a quantum many-body system. Nat. Commun. 9(1), 1–6 (2018)

    Article  Google Scholar 

  121. C.H. Tseng et al., Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer. Phys. Rev. A 61(1), 012302 (1999)

    Google Scholar 

  122. S. Tung et al., Observation of the presuperfluid regime in a two-dimensional Bose gas. Phys. Rev. Lett. 105(23), 230408 (2010)

    Google Scholar 

  123. L. Van Hove, Correlations in space and time and Born approximation scattering in systems of interacting particles. Phys. Rev. 95(1), 249 (1954)

    Google Scholar 

  124. A. van Oudenaarden, J.E. Mooij, One-dimensional Mott insulator formed by quantum vortices in Josephson junction arrays. Phys. Rev. Lett. 76(26), 4947 (1996)

    Google Scholar 

  125. J.L. Ville et al., Loading and compression of a single two-dimensional Bose gas in an optical accordion. Phys. Rev. A 95(1), 013632 (2017)

    Google Scholar 

  126. H. Weimer et al., A Rydberg quantum simulator. Nat. Phys. 6(5), 382–388 (2010)

    Article  Google Scholar 

  127. H. Wu, J.E. Thomas, Optical control of Feshbach resonances in Fermi gases using molecular dark states. Phys. Rev. Lett. 108(1), 010401 (2012)

    Google Scholar 

  128. Y. Wu et al., Strong quantum computational advantage using a super conducting quantum processor. Phys. Rev. Lett. 127(18), 180501 (2021)

    Google Scholar 

  129. T. Yamamoto et al., Spectroscopy of superconducting charge qubits coupled by a Josephson inductance. Phys. Rev. B 77(6), 064505 (2008)

    Google Scholar 

  130. R. Yamazaki et al., Submicron spatial modulation of an interatomic interaction in a Bose-Einstein condensate. Phys. Rev. Lett. 105(5), 050405 (2010)

    Google Scholar 

  131. T. Yefsah et al., Exploring the thermodynamics of a two-dimensional Bose gas. Phys. Rev. Lett. 107(13), 130401 (2011)

    Google Scholar 

  132. F. Zambelli et al., Dynamic structure factor and momentum distribution of a trapped Bose gas. Phys. Rev. A 61(6), 063608 (2000)

    Google Scholar 

  133. X. Zhang et al., Exploring quantum criticality based on ultracold atoms in optical lattices. New J. Phys. 13(4), 045011 (2011)

    Google Scholar 

  134. X. Zhang et al., Observation of quantum criticality with ultracold atoms in optical lattices. Science 335(6072), 1070–1072 (2012)

    Article  ADS  Google Scholar 

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    Cheng-An Chen

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Chen, CA. (2022). Introduction. In: Probing Non-Equilibrium Dynamics in Two-Dimensional Quantum Gases. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-031-13355-8_1

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