Comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates

Abstract

We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics-the positive-P representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strengths of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions, which can be problematic for the positive-P method. We find that the truncated Wigner method mostly agrees with the positive-P simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.

Quantum dynamics in the bosonic Josephson junction

“…Phase-space methods [25] have been extensively applied for the numerical simulation of quantum and thermal fluctuation effects in BECs [26][27][28][29][30][31][32][33][34][35][36][37][38]. Such methods utilize the semiclassical propagation of phase-space distributions with quantum fluctuations emulated via stochastic noise terms, and using a cloud of initial conditions that reflects the uncertainty of the initial quantum wave packet.…”

Role of spatial inhomogeneity in dissociation of trapped molecular condensates

“…The dashed and the dash-dotted curves are, respectively, for the cases that include only molecule-molecule and moleculeatom interactions (the case with only atom-atom interactions was studied in [42]), while the dotted curve corresponds to the inclusion of all three types of s-wave scattering terms.…”

“…As discussed in Ref. [42], the most reliable method in this situation is the truncated Wigner approach, which produces stochastic equations that remain stable for much longer simulation durations than the positive-P equations. The Wigner equations in the present case are…”

“…We treat these effects explicitly using two alternative phase-space representation techniques: first-principles simulations using the positive-P method [74] and a truncated Wigner approximation [75,76]. Owing to the fact that these phase-space methods are currently well established for bosonic fields (see, e.g., [39,40,42,46,47,77,78]), we restrict our study only to dissociation into bosonic atoms. Development of similar techniques for fermions is under way [41,43], but they are so far limited to treating homogeneous systems and therefore are not adopted yet to the present problem of dissociation of spatially inhomogeneous molecular condensates.…”

“…In the short-time limit, the converted fraction of molecules into constituent atoms is small and one can employ the undepleted molecular-field approximation, which was successfully used in theoretical descriptions of parametric down-conversion in quantum optics [38]. Even though a less restrictive description of dissociation dynamics can be accomplished via state-of-the-art numerical techniques, such as the first-principles simulations using the positive-P and Gaussian representations [39][40][41][42][43], the truncated Wigner function approach [42], the Hartree-FockBogoliubov method [37,42,44], and a generalized GrossPitaevskii (GP) equation [45], the main motivation of the present work is to obtain approximate analytic results which are less computationally expensive and have the intrinsic appeal of analytic simplicity. By comparing these results with the numerical ones, one can verify their accuracy and the range of validity in different parameter regimes.…”