Chin. Phys. Lett.  2017, Vol. 34 Issue (9): 090301    DOI: 10.1088/0256-307X/34/9/090301
Sound Wave of Spin–Orbit Coupled Bose–Einstein Condensates in Optical Lattice
Xu-Dan Chai, Zi-Fa Yu, Ai-Xia Zhang, Ju-Kui Xue**
Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070
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Abstract We study the phonon mode excitation of spin–orbit (SO) coupled Bose–Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode, i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.
Received: 02 May 2017      Published: 15 August 2017
PACS:  03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)  
  03.75.Mn (Multicomponent condensates; spinor condensates)  
  67.85.Hj (Bose-Einstein condensates in optical potentials)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11305132, 11274255 and 11475027, and the Scientific Research Project of Gansu Higher Education under Grant No 2016A-005.
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Xu-Dan Chai, Zi-Fa Yu, Ai-Xia Zhang et al  2017 Chin. Phys. Lett. 34 090301
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Xu-Dan Chai
Zi-Fa Yu
Ai-Xia Zhang
Ju-Kui Xue
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