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arXiv:0909.0195 · Physical Review A

Interaction-induced dynamical phase locking of Bose-Einstein condensates

Erez Boukobza, Doron Cohen, Amichay Vardi

Published Nov 19, 2009• 8 citations
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Abstract

We show that interactions result in the emergence of a definite relative phase between two initially incoherent Bose-Einstein condensates. The many-realization interference fringe visibility is universal at ${g}_{12}^{(1)}\ensuremath{\sim}1/3$ throughout the Josephson interaction regime as evident from a semiclassical picture. Other types of incoherent preparation yield qualitatively different coherence dynamics.

DOI
10.1103/physreva.80.053619

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We show that interactions result in the emergence of a definite relative phase between two initially incoherent Bose-Einstein condensates. The many-realization interference fringe visibility is universal at g12(1)\ensuremath∼1/3{g}_{12}^{(1)}\ensuremath{\sim}1/3g12(1)​\ensuremath∼1/3 throughout the Josephson interaction regime as evident from a semiclassical picture. Other types of incoherent preparation yield qualitatively different coherence dynamics.
We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between the two condensates. For initially incoherent condensates, we find a universal value for the buildup of coherence in the Josephson regime. In addition, we contrast two seemingly similar on-separatrix coherent preparations, finding striking differences in their convergence to classicality as the number of particles increases.
We study the dynamics of the relative phase following the connection of the two independently formed Bose-Einstein condensates. Dissipation is assumed to be due to the creation of quasiparticles induced by a fluctuating condensate particle number. The coherence between different values of the phase, which is characteristic of the initial Fock state, is quickly lost after the net exchange of a few atoms has taken place. This process effectively measures the phase and marks the onset of a semiclassical regime in which the system undergoes Bloch oscillations around the initial particle number. These fast oscillations excite quasiparticles within each condensate and the system relaxes at a longer time scale until it displays low-energy, damped, Josephson plasma oscillations, eventually coming to a halt when the equilibrium configuration is finally reached.
We study the buildup of quantum coherence between two Bose-Einstein condensates that are initially in mixed states. We consider in detail the two cases where each condensate is initially in a thermal or a Poisson distribution of atom number. Although initially there is no relative phase between the condensates, a sequence of spatial atom detections produces an interference pattern with arbitrary but fixed relative phase. The visibility of this interference pattern is close to one for the Poisson distribution of two condensates with equal counting rates but it becomes a stochastic variable in the thermal case, where the visibility will vary from run to run around an average visibility of $\ensuremath{\pi}/4.$ In both cases, the variance of the phase distribution is inversely proportional to the number of atom detections in the regime where this number is large compared to one but small compared with the total mean number of atoms in the condensates.
We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.