Squeezed and fragmented states of strongly interacting bosons in a   double well. Part II: Quantum Monte Carlo simulations
  We present path integral ground state (PIGS) quantum Monte Carlo calculations for the ground state ($T = 0$) properties of repulsively interacting bosons in a three-dimensional external double well potential over a range of interaction strengths and potential parameters. We focus our calculations on ground state number statistics and the one-body density matrix in order to understand the level of squeezing and fragmentation that the system exhibits as a function of interaction strength. We compare our PIGS results to both a two-mode model and a recently-proposed eight-mode model. For weak interactions, the various models agree with the numerically exact PIGS simulations. However, the models fail to correctly predict the amount of squeezing and fragmentation exhibited by the PIGS simulations for strong interactions. One novel and somewhat surprising result from our simulations involves the relationship between squeezing and interaction strength: rather than a monotonic relationship between these quantities, we find that for certain barrier heights the squeezing increases as a function of interaction strength until it reaches a maximum, after which it decreases again. We also see a similar relationship between fragmentation and interaction strength. We discuss the physical mechanisms that account for this behavior and the implications for the design of atom interferometers, which can use squeezed states to reduce measurement uncertainty. 
Joel C. Corbo, Jonathan L. DuBois, K. Birgitta Whaley
cond-mat.quant-gas quant-ph