Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

doi:10.1007/s11467-022-1180-3

Front. Phys.

2022, Vol. 17

Issue (6) : 61503 https://doi.org/10.1007/s11467-022-1180-3

RESEARCH ARTICLE

Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

Chen Jiao¹, Jun-Cheng Liang¹, Zi-Fa Yu¹, Yan Chen², Ai-Xia Zhang¹, Ju-Kui Xue¹(

)

¹. College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
². School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China

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Abstract

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.

Keywords spin−orbit coupled Bose−Einstein condensates stability collapse dynamics

Corresponding Author(s): Ju-Kui Xue

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Issue Date: 15 August 2022

Cite this article:

Chen Jiao,Jun-Cheng Liang,Zi-Fa Yu, et al. Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics[J]. Front. Phys. , 2022, 17(6): 61503.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1180-3
https://academic.hep.com.cn/fop/EN/Y2022/V17/I6/61503

Fig.1 The energy band of the system as a function of

R

and

s

for different

g

and

g 12

, where

Ω 0 = 2.0

and

ω = 0.1

. (a1−a3) for

k 0 = 1.0

g = − 15

and

g 12 = 180

. (b1−b3) for

k 0 = 2.0

g = 50

and

g 12 = − 150

Fig.2 Quasimomentum

k m

corresponding to the minimum of energy as a function of

Ω 0

for different

g 12

ω

and

χ

, where

g = 10

and

k 0 = 1.0

ω = 0.1

for the left column and

ω = 0.5

for the right column.

Fig.3 Phase diagram in

Ω 0 − k 0

plane for different

g 12

ω

and

χ

, where

g = 10

ω = 0.1

for the left column and

ω = 0.5

for the right column.

Fig.4 The critical RC

Ω c

as a function of

χ

, where

g = 10

and

k 0 = 1

ω = 0.1

for the left column and

ω = 0.5

for the right column.

Fig.5 The critical SO coupling strength

k c

as a function of

χ

, where

g = 10

and

Ω 0 = 2.0

ω = 0.1

for the left column and

ω = 0.5

for the right column.

Fig.6 Stability diagram in

g − g 12

plane with different SO coupling strength (

k 0 = 1.0

for the top row, where

Ω 0 ≥ 2 J 02 (χ) k 02

;

k 0 = 2.0

for the bottom row, where

Ω 0 < 2 J 02 (χ) k 02

.) and

χ

for

ω

=0.1,

Ω 0 = 2.0

and

ω R = 20

. The border of regions is obtained by using the variational calculation (the black solid line) and the complete numerical simulation of the G−P equation acquired from the Hamiltonian Eq. (1) (red dots). A1−A3 and B1−B3 are selected points corresponding to(a1)−(a3) and (b1)−(b3) in Fig.1.

Fig.7 Stability diagram in

χ

−

k 0

plane with different interatomic interactions. Here

ω = 0.1

for the left column and

ω = 0.5

for the right column, and the top row for

g = − 15

g 12 = 180

and the bottom row for

g = 50

g 12 = − 150

Fig.8 The time evolution of the wave packet width for different

χ

with the fixed

Ω 0 = 2.0

. (a1, a2) for

k 0 = 1.0

g = − 15

and

g 12 = 180

χ = 0, 0.5, 1.0

corresponding to A1−A3 as marked inFig.6, respectively. (b1, b2) for

k 0 = 2.0

g = 50

and

g 12 = − 150

χ = 0, 0.5, 1.0

corresponding to B1−B3 as marked inFig.6, respectively. Here the left column for

ω = 0.1

and the right column for

ω = 0.5

Fig.9 The critical collapse time

t c

versus

χ

for different phases by means of the variational method. The vertical black dot lines represent the values of

χ c

. Here the left column for

g = − 15

g 12 = 180

and the right column for

g = 50

g 12 = − 150

Fig.10 (a1−a3) Dynamical evolution of the wave packets corresponding to the cases as marked by A1, A2 and A3 in Fig.6(a1)−(a3).(b1−b3) Dynamical evolution of the wave packets corresponding to the cases as marked by B1, B2 and B3 in Fig.6(b1)−(b3).

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