Phase coherence in a driven double-well system

We analyze the dynamics of a molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunneling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum-mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunneling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases.

Figure 1

$⟨{\widehat{J}}_x⟩∕⟨n_j⟩$ versus $u_b∕t_J$ for $\Theta =\pi$ and $t_J=2.5$.

Figure 2

$g_{lr}^{\left(2\right)}$ versus $u_b∕t_J$ for $\Theta =\pi$ and $t_J=2.5$.

Figure 3

Time evolution of $P\left({\varphi }_n\right)$ for $\Theta =\pi$, $t_J=2.5$ and for (a) $u_b∕t_J=0.0032$, (b) $u_b∕t_J=0.5623$, and (c) $u_b∕t_J=56.23$; (d) ${\left(\Delta \varphi \right)}^2$ of the steady state.