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Collective excitation of a trapped BoseEinstein condensate with spinorbit coupling
发布者： admin 发布时间：20170316
In recent years, an important breakthrough in cold atom physics is the realization of spinorbit (SO) coupling [15]. The SO coupled Bose gases, which has no analog in conventional solid materials which deal with fermionic systems, present rich manybody quantum phases such as stripe phase [67] and skyrmion lattices [8]. However, despite of the tremendous attention they have attracted, direct evidences of these exotic phases are still lacking. Here, we would like especially point out that striped phase has recently been directly observed in the experiment [8]. However, instead of the two hyperspin states, they used atoms trapped in a double well potential to represent the pseudospin degrees of freedom, which is not exactly the model we considered in this work. Therefore, the main purpose of the present work is to show that different phases of an SO coupled BoseEinstein condensate (BEC) features distinctive collective excitations, which can therefore be used to distinguish various phases. The theoretical model we use here is same with that in Ref.[3], where an effective onedimension twocomponent BEC system is coherently coupled by two Raman beams propagating along the xaxis with vanishing twophoton detuning. The static and dynamic behavior at T=0 are govered by a coupled GrossPitaevskii equations, based on which we then calculate the Bogoliubov spectrum by numerically solving Bogoliubov equations, and one typical spectrum depending on Raman coupling strength is plotted as follows:
Fig. 1 One can observe that there are two important features in this spectrum: a) In striped phase (ST), there are two lowerlying modes whose frequencies are very close to zero. These two modes will be exactly vanishing in thermodynamic limit corresponding to two Goldstone mode spontaneously breaking U(1) gauge symmetry and translational symmetry simultaneously. b) Spectrum exhibits mode softening near the two critical Raman coupling strength where the system changes from one phase to another. In particular, the spinindependent modes, such as dipole and breathing, are soften near the planewave (PW)/ zeromomentum (ZM) phase boundary, while the spindependent modes, such as spin dipole and spin breathing, are soften near the ST/PW phase boundary. In our work, we especially discussed the spindependent dynamics in a quench process. We observed that distinct features in the three phases when a small spin dipole (breathing) perturbation is added into the system. By calculating the elementary transitional strength (see (b), (c) and (d) in Fig. 1), we can always find a dominant in ST and ZM phase which means the spin dipole mode would nearly oscillate in a sinusoidal way (see Fig. 2(b) and (d)). However, in PW phase, a finite perturbation is able to change the BEC from a miscible to an immiscible condition. Such a huge change of the static response to the spin dipole perturbation will finally leads to a complete nonlinear but nontrivial dynamic oscillation as shown in Fig. 2(c). We hope that our work may stimulate more experimental study of the collective excitation properties of SO coupled BEC.
Fig. 2 This work has been published, see http://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.033616. Reference: [1] N. Goldman, G. Juzeliunas, P. Ohberg, and I. B. Spielman, Rep. Prog. Phys. 77, 126401 (2014). [2] H. Zhai, Rep. Prog. Phys. 78, 026001 (2015). [3] Y.J. Lin, K. JimenezGarcia, and I. B. Spielman, Nature (London). 471, 83 (2011). [4] P. Wang, Z.Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Phys. Rev. Lett. 109, 095301 (2012). [5] L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, and M. W. Zwierlein, Phys. Rev. Lett. 109, 095302 (2012). [6] Y. Li, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 108, 225301 (2012). [7] S.C. Ji, J.Y. Zhang, L. Zhang, Z.D. Du, W. Zheng, Y.J. Deng, H. Zhai, S. Chen, and J.W. Pan, Nature Phys. 10, 314 (2014). [8] H. Hu, B. Ramachandhran, H. Pu, and X.J. Liu, Phys. Rev. Lett. 108, 010402 (2012); S. Sinha, R. Nath, and L. Santos, Phys. Rev. Lett. 107, 270401 (2011).

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