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An impurity immersed in a superfluid can move without friction when its velocity is below a critical value. This phenomenon can be explained by the famous Landau criterion, according to which, the critical velocity is determined by the elementary excitation spectrum of the superfluid. Landau critical velocity has been measured in the isotropic superfluid, such as the liquid He-Ⅱ and the Bose-Einstein condensates of dilute atomic gases, where the onset of dissipation is due to the creation of roton and phonon, respectively. The recent realization of synthetic spin-orbit coupling in quantum gas opens up possibilities for the study of novel superfluidity with ultracold atoms. To date, a specific type of spin-orbit coupling, which is generated by a pair of Raman laser beams, has been achieved in a Bose-Einstein condensate of 87Rb experimentally. Remarkably, the excitation spectrum of this system is anisotropic and can be feasibly tuned by the external laser field. While the anisotropic dynamics has been observed experimentally, the critical velocity has not been measured so far. It is a conventional wisdom that in an anisotropic superfluid, the critical velocity is determined by the excitation spectrum in the moving direction of the impurity. However, this is not always the case. In this work, we investigate the motion of a point-like impurity in a spin-orbit-coupled condensate with the spin-dependent interatomic interaction. In the vicinity of the quantum phase transition between the plane-wave (PW) phase and the zero-momentum (ZM) phase, the onset of the dissipation is due to the emission of a phonon, and the Landau critical velocity vc depends on the anisotropic sound velocity. While the sound velocity varies smoothly across the PW-ZM phase transition, the critical velocity in the direction perpendicular to the axis of spin-orbit coupling exhibits a sudden jump at the phase boundary. The value of vc on the PW phase side of the transition is generally smaller than the one on the ZM phase side, and the jump amplitude of vc is an increasing function of the spin-dependent interaction strength. Beyond the critical velocity, the energy dissipation rate of the impurity is explicitly calculated via a perturbation approach. The discontinuity of vc at the phase boundary can be clearly seen from the dissipation curves, which can be measured through the heating of the condensate. Our prediction can be tested in the current experiments with ultracold atoms.
[1] Pitaevskii L P, Stringari S 2016 Bose-Einstein Condensation and Superfluidity (New York: Oxford University Press) pp65-67
[2] Yu Z Q 2017 Phys. Rev. A 95 033618
[3] Goldman N, Juzeliūnas G, hberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401
[4] Zhai H 2015 Rep. Prog. Phys. 78 026001
[5] Lin Y J, Jimnez-Garca K, Spielman I B 2011 Nature 471 83
[6] Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H, Zhang J 2012 Phys. Rev. Lett. 109 095301
[7] Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S, Zwierlein M W 2012 Phys. Rev. Lett. 109 095302
[8] Zhang J Y, Ji S C, Chen Z, Zhang L, Du Z D, Yan B, Pan G S, Zhao B, Deng Y J, Zhai H, Chen S, Pan J W 2012 Phys. Rev. Lett. 109 115301
[9] Khamehchi M A, Zhang Y, Hamner C, Busch T, Engels P 2014 Phys. Rev. A 90 063624
[10] Ji S C, Zhang L, Xu X T, Wu Z, Deng Y, Chen S, Pan J W 2015 Phys. Rev. Lett. 114 105301
[11] Ozawa T, Pitaevskii L P, Stringari S 2013 Phys. Rev. A 87 063610
[12] Zheng W, Yu Z Q, Cui X, Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007
[13] Wu S, Ke Y, Huang J, Lee C 2017 Phys. Rev. A 95 063606
[14] Zhang Y C, Yu Z Q, Ng T K, Zhang S, Pitaevskii L, Stringari S 2016 Phys. Rev. A 94 033635
[15] Ho T L, Zhang S 2011 Phys. Rev. Lett. 107 150403
[16] Li Y, Pitaevskii L P, Stringari S 2012 Phys. Rev. Lett. 108 225301
[17] Martone G I, Li Y, Pitaevskii L P, Stringari S 2012 Phys. Rev. A 86 063621
[18] Yu Z Q 2012 Report of Postdoc Research (Beijing: Tsinghua University) (in Chinese) [余增强 2012 博士后研究报告 (北京: 清华大学)]
[19] Pitaevskii L P, Stringari S 2016 Bose-Einstein Condensation and Superfluidity (New York: Oxford University Press) pp89-91
[20] He L, Yu Z Q 2016 Acta Phys. Sin. 13 131101 (in Chinese) [贺丽, 余增强 2016 13 131101]
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[1] Pitaevskii L P, Stringari S 2016 Bose-Einstein Condensation and Superfluidity (New York: Oxford University Press) pp65-67
[2] Yu Z Q 2017 Phys. Rev. A 95 033618
[3] Goldman N, Juzeliūnas G, hberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401
[4] Zhai H 2015 Rep. Prog. Phys. 78 026001
[5] Lin Y J, Jimnez-Garca K, Spielman I B 2011 Nature 471 83
[6] Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H, Zhang J 2012 Phys. Rev. Lett. 109 095301
[7] Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S, Zwierlein M W 2012 Phys. Rev. Lett. 109 095302
[8] Zhang J Y, Ji S C, Chen Z, Zhang L, Du Z D, Yan B, Pan G S, Zhao B, Deng Y J, Zhai H, Chen S, Pan J W 2012 Phys. Rev. Lett. 109 115301
[9] Khamehchi M A, Zhang Y, Hamner C, Busch T, Engels P 2014 Phys. Rev. A 90 063624
[10] Ji S C, Zhang L, Xu X T, Wu Z, Deng Y, Chen S, Pan J W 2015 Phys. Rev. Lett. 114 105301
[11] Ozawa T, Pitaevskii L P, Stringari S 2013 Phys. Rev. A 87 063610
[12] Zheng W, Yu Z Q, Cui X, Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007
[13] Wu S, Ke Y, Huang J, Lee C 2017 Phys. Rev. A 95 063606
[14] Zhang Y C, Yu Z Q, Ng T K, Zhang S, Pitaevskii L, Stringari S 2016 Phys. Rev. A 94 033635
[15] Ho T L, Zhang S 2011 Phys. Rev. Lett. 107 150403
[16] Li Y, Pitaevskii L P, Stringari S 2012 Phys. Rev. Lett. 108 225301
[17] Martone G I, Li Y, Pitaevskii L P, Stringari S 2012 Phys. Rev. A 86 063621
[18] Yu Z Q 2012 Report of Postdoc Research (Beijing: Tsinghua University) (in Chinese) [余增强 2012 博士后研究报告 (北京: 清华大学)]
[19] Pitaevskii L P, Stringari S 2016 Bose-Einstein Condensation and Superfluidity (New York: Oxford University Press) pp89-91
[20] He L, Yu Z Q 2016 Acta Phys. Sin. 13 131101 (in Chinese) [贺丽, 余增强 2016 13 131101]
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