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Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas


Spin–orbit (SO) coupling leads to numerous phenomena in electron systems. Artificial SO coupling in ultracold neutral atoms provides the opportunity to study such phenomena in bosonic systems, which exhibit superfluidity and various symmetry-breaking condensate phases. In general, a richer structure of symmetry breaking results in a nontrivial finite-temperature phase diagram, but the thermodynamics of the SO-coupled Bose gas at finite temperature remains unknown both in theory and experiment. Here we experimentally determine a new finite-temperature phase transition that is consistent with the transition between the stripe ordered phase and the magnetized phase. We also observe that the magnetic phase and the Bose condensate transitions occur simultaneously as temperature decreases. We determine the entire finite-temperature phase diagram of the SO-coupled Bose gas, thus illustrating the power of quantum simulation.

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Figure 1: Zero-temperature phase diagram and three scenarios for the finite-temperature phase diagram for an SO-coupled Bose gas.
Figure 2: Critical temperature Tc of a spin–orbit coupled Bose gas.
Figure 3: Histogram of condensate magnetization for Ω<Ω1.
Figure 4: Phase transition between the ST condensate and the MG condensate at very low temperatures.
Figure 5: Finite-temperature phase diagram of spin–orbit coupled Bose gas.
Figure 6: Formation of magnetic order for Ω1<Ω<Ω2.


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We acknowledge insightful discussions with C. Chin and T-L. Ho. S. C. thanks B. Zhao for his careful reading of the manuscript. This work has been supported by the NNSF of China, the CAS, the National Fundamental Research Program (under Grant No. 2011CB921300, No. 2011CB921500), NSERC and Tsinghua University Initiative Scientific Research Program.

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Authors and Affiliations



S.C. and J-W.P. planned and supervised the project. S-C.J., J-Y.Z., Z-D.D. and S.C. performed the experiments, L.Z., W.Z., Y-J.D. and H.Z. provided theoretical support, and all the authors contributed to analysis of the data and writing the manuscript.

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Correspondence to Shuai Chen or Jian-Wei Pan.

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The authors declare no competing financial interests.

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Ji, SC., Zhang, JY., Zhang, L. et al. Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas. Nature Phys 10, 314–320 (2014).

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