Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Figure 1

Atom number evolution for Fock, crescent, and coherent initial states.

Figure 2

Zero-dimensional predictions for the atomic evolution. The dash-dotted line represents the classical mean-field prediction, the solid line is for an initial Fock state ($8.25\times {10}^5$ trajectories), and the dotted line is for an initial coherent state, as previously shown in Ref. 12 ($3.45\times {10}^5$ trajectories), which is almost indistinguishable from the Fock state.