Abstract
We study the ground-state behavior of a Bose-Einstein Condensate (BEC) in a Raman-laser-assisted one-dimensional (1D) optical lattice potential forming a multilayer system. We find that, such system can be described by an effective model with spin-orbit coupling (SOC) of pseudospin (N-1)/2, where N is the number of layers. Due to the intricate interplay between atomic interactions, SOC and laser-assisted tunnelings, the ground-state phase diagrams generally consist of three phases–a stripe, a plane wave and a normal phase with zero-momentum, touching at a quantum tricritical point. More important, even though the single-particle states only minimize at zero-momentum for odd N, the many-body ground states may still develop finite momenta. The underlying mechanisms are elucidated. Our results provide an alternative way to realize an effective spin-orbit coupling of Bose gas with the Raman-laser-assisted optical lattice, and would also be beneficial to the studies on SOC effects in spinor Bose systems with large spin.
Highlights
The realization of Raman-induced artificial gauge fields in ultracold atomic gases[1,2,3,4,5,6,7] provides a well-controllable way to investigate many fundamental phenomena induced by SOC8–11
Within the lowest band of the lattice, the system can be mapped to an effective model with spin-orbit coupling (SOC), where N different layers play a role of a pseudospin (N − 1)/2 coupled to the intralayer motion via the laser-assisted tunneling of atoms between the layers
The one-dimensional optical lattice potential is sufficiently tilted and unlike the typical atom-atom interactions in conventional spinor BEC46, the special type of interactions from on-site repulsions in our system is quite different in the psuedospin representation, and can give rise to peculiar N-dependent phase diagrams with different behaviors: (1) For even N, by tuning the tunneling strength J, the single-particle ground state may change from a single minimal with zero-momentum to double minima with finite momentum, with the corresponding many-body ground states evolving from a normal phase to a robust stripe phase
Summary
The realization of Raman-induced artificial gauge fields in ultracold atomic gases[1,2,3,4,5,6,7] provides a well-controllable way to investigate many fundamental phenomena induced by SOC8–11. Such method provides a powerful and delicate way to manipulate atoms in lattice potential Stimulated by these developments, some authors[24,25] have proposed an alternative and realistic way to realize an effective 2D SOC in bilayer Bose systems based on the laser-assisted tunneling. In such schemes, the prerequisite “internal” states to fabricate SOC are essentially replaced by the Raman-assisted “external” motional states in each layer, providing a new system to investigate the SO coupled BECs. Motivated by the above advances, in this paper, we consider a gas of ultracold scalar bosons subjected to a Raman-assisted 1D optical lattice potential forming a multilayer system. Such unique features reflect the competition and compromise between Raman-assisted tunneling and atomic interactions in this system
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