Quantum tunnelling of a weakly open Bose–Einstein condensate in a double well under periodic driving

Abstract

We analyse the dynamics of a weakly open Bose–Einstein condensate (BEC) with attractive atomic interactions in a double-well potential under periodic driving. We find that the inclusion of weakly dissipative effects can dramatically modify the quantum tunnelling of the periodically driven BEC, and some new interesting dynamical properties arise, including a pitchfork bifurcation that leads to two stable nonsymmetric states by adjusting the dissipative parameters. The numerical results based on the approximate two-mode model are also analysed.

Pseudo-parity–time symmetry in periodically high-frequency driven systems: perturbative analysis

“…A good 2 for (c) ϕ = 0 and (d) ϕ π = 2. Red solid lines are for numerical results obtained from the original model (1), and blue dashed lines are for the second-order perturbative results from equations ( 29) and (30). The other parameters are chosen as…”

“…However, the rotating-wave approximation fails to predict the so-called pseudo- symmetry. Therefore, we should push the asymptotic analysis to the next order ϵ 2 and include the second-order terms ρ ω v A j 2 in equations ( 29)- (30). Diagonalizing equations ( 29) and (30), we give the two eigenvalues as…”

“…Most previous studies focused on the unmodulated  -symmetric systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. However, due to the fact that periodic modulation is an important and effective tool for controlling tunneling dynamics [17][18][19][20][21][22][23][24][25][26][27][28][29][30], recently increasing attention has been paid to the  symmetry of the periodically modulated systems, such as simply  -symmetric dimeric systems [31][32][33][34],  -symmetric kicked rotor models [35], and  -symmetric tight-binding lattices [36].…”

“…Time evolutions from the initial state of = c Upper row: long-time evolution of the time-averaged total probability for (a) ϕ = 0 and (b) ϕ π Lower row: short-time evolution of the total probability = | | + | | ϕ = 0 and (d) ϕ π = Red solid lines are for numerical results obtained from the original model (1), and blue dashed lines are for the second-order perturbative results from equations(29) and(30). The other parameters are chosen as = and ω = 10.…”