Fermionic phase space method for exact quantum dynamics

Numerical approaches are an indispensable part of endeavours to understand quantum many-body physics in condensed matter and AMO physics. In particular, there is a need for real-time, dynamical simulations, driven in large part by the progress in the control and flexibility of ultracold atom experiments, which has made the dynamically evolving quantum many-body state directly accessible. For bosons, first-principles phase-space methods have successfully simulated dynamics in experimentally realistic systems [1]. However, these methods are not directly applicable to fermionic systems, which are an increasingly important area of ultracold atoms, often with direct relevance to condensed matter systems. In this work we employ a Gaussian stochastic method based on a generalized phase-space representation of the quantum density operator [2]. We use the method to calculate the dynamics of the production of correlated pairs of fermionic atoms by dissociation of a Bose-Einstein condensate (BEC) of diatomic molecules [3]. This work represents the first application of this fermionic phase-space method to the dynamics of a multimode system of many interacting particles. The Gaussian phase-space method provides an exact solution to quantum dynamics, as long as sampling error can be controlled. It can be viewed as providing the quantum corrections, through additional stochastic terms, to different mean-field approaches. The simulations take a uniform molecular BEC (MBEC) in a coherent state as the initial condition. Assuming sufficiently low densities, we neglect s-wave scattering interactions. The Hamiltonian is then given by