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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
AAPPS Bulletin Open Access 05 December 2022
Scientific Reports Open Access 16 May 2019
Nature Communications Open Access 22 January 2019
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X-L. & Zhang, S-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Lin, Y-J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).
Wang, P. et al. Spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).
Cheuk, L. M. et al. Spin-injection spectroscopy of a spin–orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).
Zhang, J-Y. et al. Collective dipole oscillation of a spin–orbit coupled Bose–Einstein condensate. Phys. Rev. Lett. 109, 115301 (2012).
Williams, R. A. et al. Synthetic partial waves in ultracold atomic collisions. Science 335, 314–317 (2012).
Qu, C., Hamner, C., Gong, M., Zhang, C. & Engels, P. Observation of Zitterbewegung in a spin–orbit-coupled Bose–Einstein condensate. Phys. Rev. A 88, 021604(R) (2013).
Zhang, L. et al. Stability of excited dressed states with spin–orbit coupling. Phys. Rev. A 87, 011601(R) (2013).
Wang, C., Gao, C., Jian, C-M. & Zhai, H. Spin–orbit coupled spinor Bose–Einstein condensates. Phys. Rev. Lett. 105, 160403 (2010).
Ho, T-L. & Zhang, S. Bose–Einstein condensates with spin–orbit interaction. Phys. Rev. Lett. 107, 150403 (2011).
Li, Y., Pitaevskii, L. P. & Stringari, S. Quantum tricriticality and phase transitions in spin–orbit coupled Bose–Einstein condensates. Phys. Rev. Lett. 108, 225301 (2012).
Wu, C-J., Mondragon-Shem, I. & Zhou, X-F. Unconventional Bose–Einstein condensations from spin–orbit coupling. Chin. Phys. Lett. 28, 097102 (2011).
Jian, C-M. & Zhai, H. Paired superfluidity and fractionalized vortices in systems of spin–orbit coupled bosons. Phys. Rev. B 84, 060508(R) (2011).
Gopalakrishnan, S., Lamacraft, A. & Goldbart, P. M. Universal phase structure of dilute Bose gases with Rashba spin–orbit coupling. Phys. Rev. A 84, 061604(R) (2011).
Ozawa, T. & Baym, G. Stability of ultracold atomic Bose condensates with Rashba spin–orbit coupling against quantum and thermal fluctuations. Phys. Rev. Lett. 109, 025301 (2012).
Cui, X. & Zhou, Q. Enhancement of condensate depletion due to spin–orbit coupling. Phys. Rev. A 87, 031604(R) (2013).
Zheng, W., Yu, Z-Q., Cui, X. & Zhai, H. Properties of Bose gases with Raman-induced spin–orbit coupling. J. Phys. B 46, 134007 (2013).
Sedrakyan, T. A., Kamenev, A. & Glazman, L. I. Composite fermion state of spin–orbit-coupled bosons. Phys. Rev. A 86, 063639 (2012).
Zhu, Q., Zhang, C. & Wu, B. Exotic superfluidity in spin–orbit coupled Bose–Einstein condensates. Europhys. Lett. 100, 50003 (2012).
Martone, G. I., Li, Y., Pitaevskii, L. P. & Stringari, S. Anisotropic dynamics of a spin–orbit coupled Bose–Einstein condensate. Phys. Rev. A 86, 063621 (2012).
Mukerjee, S., Xu, C. & Moore, J. E. Topological defects and the superfluid transition of the s=1 spinor condensate in two dimensions. Phys. Rev. Lett. 97, 120406 (2006).
James, A. J. A. & Lamacraft, A. Phase diagram of two-dimensional polar condensates in a magnetic field. Phys. Rev. Lett. 106, 140402 (2011).
Shi, Y., Lamacraft, A. & Fendley, P. Boson pairing and unusual criticality in a generalized XY model. Phys. Rev. Lett. 107, 240601 (2011).
Spielman, I. B. Raman process and effective gauge potentials. Phys. Rev. A 79, 063613 (2009).
Wheatley, J. C. Experimental properties of superfluid 3He. Rev. Mod. Phys. 47, 415–470 (1975).
de la Cruz, C. et al. Magnetic order close to superconductivity in the iron-based layered LaO1−xFxFeAs system. Nature 453, 899–902 (2008).
Fang, C., Yao, H., Tsai, W-F., Hu, J-P. & Kivelson, S. A. Theory of electron nematic order in LaFeAsO. Phys. Rev. B 77, 224509 (2008).
Xu, C-K., Müller, M. & Sachdev, S. Ising and spin orders in the iron-based superconductors. Phys. Rev. B 78, 020501(R) (2008).
Li, Y., Martone, G. I., Pitaevskii, L. P. & Stringari, S. Superstripes and the excitation spectrum of a spin–orbit-coupled Bose–Einstein condensate. Phys. Rev. Lett. 110, 235302 (2013).
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.
The authors declare no competing financial interests.
About this article
Cite this article
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). https://doi.org/10.1038/nphys2905
This article is cited by
AAPPS Bulletin (2022)
Nature Reviews Physics (2021)
Scientific Reports (2019)
Nature Communications (2019)
Journal of Low Temperature Physics (2019)