First-principles quantum simulations of many-mode open interacting Bose gases using stochastic gauge methods

Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with no further approximations. Simulations are of a set of stochastic equations that in the limit of many realizations correspond exactly to the full quantum evolution. These are obtained using the stochastic gauge method (derived here), an extension of the positive P phase-space representation. The systems investigated are: 1) Dynamics of spatial correlations in uniform 1D and 2D Bose gases after the rapid appearance of significant two-body collisions (e.g. after entering a Feshbach resonance). 2) Dynamics of stimulated Bose enhancement of scattered atom modes during the collision of two Bose-Einstein condensates with a mean of 150 000 atoms. 3) Dynamics of trapped bosons, where the size of the trap is of the same order as the range of the interparticle potential. 4) Grand canonical thermodynamics of uniform 1D Bose gases for a variety of temperatures and collision strengths. Observables calculated include 1st-3rd order spatial correlation functions (including finite separation) and momentum distributions. The stochastic gauge method is derived, and its application to interacting Bose gases investigated in detail. It is found to improve simulation effectiveness under many conditions, and to be capable of overcoming instability and boundary term problems. Additionally, conditions under which very generalized phase-space represntations can be used to obtain tractable many-body simulations are analysed.