Dissipation Induced Coherence of a Two-Mode Bose-Einstein Condensate

We discuss the dynamics of a Bose-Einstein condensate in a double-well trap subject to phase noise and particle loss. The phase coherence of a weakly interacting condensate as well as the response to an external driving show a pronounced stochastic resonance effect: Both quantities become maximal for a finite value of the dissipation rate matching the intrinsic time scales of the system. Even stronger effects are observed when dissipation acts in concurrence with strong interparticle interactions, restoring the purity of the condensate almost completely and increasing the phase coherence significantly.

Figure 1

Contrast $\alpha$ in the quasisteady state in dependence on the tunneling rate $J$ and the dissipation rate $1/T_1$ for $U=0$ and $ϵ=0$.

Figure 2

(a) Average contrast $\alpha$ after $t=1.5\mathrm{s}$ starting from a pure BEC (i.e. a product state) with $s_z=n/2$ and $n(0)=100$ particles in dependence on the tunneling rate $J$ for $T_1=0.5\mathrm{s}$, $ϵ=10{\mathrm{s}}^{-1}$, $U=0.1{\mathrm{s}}^{-1}$. (b) Histogram of the probabilities to measure the relative phase $\varphi$ and the relative population imbalance $s_z/n$ in a single experimental run after $t=1.5\mathrm{s}$ obtained from a MCWF simulation of the many-body dynamics.

Figure 3

(a) Oscillation of the relative population imbalance $s_z/n$ of a weakly driven two-mode BEC for $J_0=1.5{\mathrm{s}}^{-1}$, $T_1=0.5\mathrm{s}$ and $ϵ=0$. (b) Amplitude of the oscillations in dependence on the tunneling rate $J_0$.

Figure 4

Time evolution of the purity $p$ and the contrast $\alpha$ for $J=U=10{\mathrm{s}}^{-1}$, $ϵ=0$, $T_1=0.5\mathrm{s}$. The initial state is a pure BEC with $s_z=n/2$ and $n(0)=100$ particles. The results of a MCWF simulation averaged over 100 runs are plotted as a thin solid line while the mean-field results are plotted as a thick line. The dashed line shows the steady state values for $1/T_1=1/T_2=0$, i.e., without coupling to the environment.

Figure 5

Purity $p$ and contrast $\alpha$ after $t=2\mathrm{s}$ in dependence on the dissipation rate $1/T_1$ calculated within the mean-field approximation for the same parameters as in Fig. 4.