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

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.


The ground state momentum km/λ (a,b), 〈Fz〉 (c,d) and  (e,f) as functions of tunneling J/Eλ for given interactions g2D/Eλ = 0.3 (left panel) and g2D/Eλ = 0.4 (right panel). Here, N = 3 and δz/Eλ = 0.01.
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f6: The ground state momentum km/λ (a,b), 〈Fz〉 (c,d) and (e,f) as functions of tunneling J/Eλ for given interactions g2D/Eλ = 0.3 (left panel) and g2D/Eλ = 0.4 (right panel). Here, N = 3 and δz/Eλ = 0.01.

Mentions: In Fig. (5), we give the phase diagram for N = 3. It is interesting to see that even though the single-particle spectrum is only minimized at the k = 0 state, the system can still be Plane Wave or Stripe phases carrying finite momenta in some regimes. In one hand, the zero-momentum Normal phase is predominant for small g2D. In the other hand, the interaction energy would become significant with the increasing of interactions. As shown in Fig. (6e,f), the density of Normal phase in center layer is relative large. And for sufficient large g2D, an instability to Plane Wave/Stripe phases with more delocalized atomic distribution and finite km (Fig. (6a,b)) would happen, where the increasing of kinetic energies is compensated by the decreasing of interaction energies. Furthermore, similar to the even N case, the Plane Wave phase with a finite 〈Fz〉 ≠ 0 (Fig. (6c,d)) only survives for moderate tunneling strength J, between the Normal and Stripe phases, and ends at a tricritical point.


Ground states of a Bose-Einstein Condensate in a one-dimensional laser-assisted optical lattice
The ground state momentum km/λ (a,b), 〈Fz〉 (c,d) and  (e,f) as functions of tunneling J/Eλ for given interactions g2D/Eλ = 0.3 (left panel) and g2D/Eλ = 0.4 (right panel). Here, N = 3 and δz/Eλ = 0.01.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: The ground state momentum km/λ (a,b), 〈Fz〉 (c,d) and (e,f) as functions of tunneling J/Eλ for given interactions g2D/Eλ = 0.3 (left panel) and g2D/Eλ = 0.4 (right panel). Here, N = 3 and δz/Eλ = 0.01.
Mentions: In Fig. (5), we give the phase diagram for N = 3. It is interesting to see that even though the single-particle spectrum is only minimized at the k = 0 state, the system can still be Plane Wave or Stripe phases carrying finite momenta in some regimes. In one hand, the zero-momentum Normal phase is predominant for small g2D. In the other hand, the interaction energy would become significant with the increasing of interactions. As shown in Fig. (6e,f), the density of Normal phase in center layer is relative large. And for sufficient large g2D, an instability to Plane Wave/Stripe phases with more delocalized atomic distribution and finite km (Fig. (6a,b)) would happen, where the increasing of kinetic energies is compensated by the decreasing of interaction energies. Furthermore, similar to the even N case, the Plane Wave phase with a finite 〈Fz〉 ≠ 0 (Fig. (6c,d)) only survives for moderate tunneling strength J, between the Normal and Stripe phases, and ends at a tricritical point.

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.