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Ground states of a Bose-Einstein Condensate in a one-dimensional laser-assisted optical lattice

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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.

No MeSH data available.


Schematic diagram of the Raman-laser-assisted optical lattice.The lattice potential is deep and tilted enough so that the tight-binding approximation can be applied but the direct tunnelings between adjacent sites can be neglected. Two Raman lasers (labeled as red and blue arrows) couple the internal electron ground state /g〉i to an excited state /e〉i and would induce an interlayer transition (see the context for detail). (a). Energy levels with Δ the energy difference between adjacent sites. (b) Momentum relations. k1,2 are the incident momenta of two Raman lasers, δk = k1 − k2 = δkz + δk⊥.
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f1: Schematic diagram of the Raman-laser-assisted optical lattice.The lattice potential is deep and tilted enough so that the tight-binding approximation can be applied but the direct tunnelings between adjacent sites can be neglected. Two Raman lasers (labeled as red and blue arrows) couple the internal electron ground state /g〉i to an excited state /e〉i and would induce an interlayer transition (see the context for detail). (a). Energy levels with Δ the energy difference between adjacent sites. (b) Momentum relations. k1,2 are the incident momenta of two Raman lasers, δk = k1 − k2 = δkz + δk⊥.

Mentions: We consider a three-dimensional ultra-cold Bose gas (e.g. 87Rb) loaded into a one-dimensional optical lattice potential. Such potential are tight enough that the atoms only occupy the lowest energy band of the lattice potential (along z-axis), but move freely in the traverse xy-plane, forming a stacked-disk configuration. Furthermore, we apply a linear gradient potential in z-direction to tilt the lattice, as depicted in Fig. (1). Such global tilt can be achieved by implementing a frequency shift between the lasers for the creating of the lattice potential4748, or by tilting the lattice along the direction of the gravitational field4950. The single-particle Hamiltonian of this system reads:


Ground states of a Bose-Einstein Condensate in a one-dimensional laser-assisted optical lattice
Schematic diagram of the Raman-laser-assisted optical lattice.The lattice potential is deep and tilted enough so that the tight-binding approximation can be applied but the direct tunnelings between adjacent sites can be neglected. Two Raman lasers (labeled as red and blue arrows) couple the internal electron ground state /g〉i to an excited state /e〉i and would induce an interlayer transition (see the context for detail). (a). Energy levels with Δ the energy difference between adjacent sites. (b) Momentum relations. k1,2 are the incident momenta of two Raman lasers, δk = k1 − k2 = δkz + δk⊥.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121596&req=5

f1: Schematic diagram of the Raman-laser-assisted optical lattice.The lattice potential is deep and tilted enough so that the tight-binding approximation can be applied but the direct tunnelings between adjacent sites can be neglected. Two Raman lasers (labeled as red and blue arrows) couple the internal electron ground state /g〉i to an excited state /e〉i and would induce an interlayer transition (see the context for detail). (a). Energy levels with Δ the energy difference between adjacent sites. (b) Momentum relations. k1,2 are the incident momenta of two Raman lasers, δk = k1 − k2 = δkz + δk⊥.
Mentions: We consider a three-dimensional ultra-cold Bose gas (e.g. 87Rb) loaded into a one-dimensional optical lattice potential. Such potential are tight enough that the atoms only occupy the lowest energy band of the lattice potential (along z-axis), but move freely in the traverse xy-plane, forming a stacked-disk configuration. Furthermore, we apply a linear gradient potential in z-direction to tilt the lattice, as depicted in Fig. (1). Such global tilt can be achieved by implementing a frequency shift between the lasers for the creating of the lattice potential4748, or by tilting the lattice along the direction of the gravitational field4950. The single-particle Hamiltonian of this system reads:

View Article: PubMed Central - PubMed

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.

No MeSH data available.