Nonequilibrium kinetic theory for trapped binary condensates

Abstract

We derive a non-equilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation of timescale argument of kinetic theory, the dynamics of the condensates of the multi-component system are shown to be described by dissipative Gross-Pitaevskii equations, self-consistently coupled to corresponding Quantum Boltzmann equations for the non-condensate atoms: on top of the usual mean field contributions, our scheme identifies a total of 8 distinct collisional processes, whose dynamical interplay is expected to be responsible for the system's equilibration. In order to provide their first characterization, we perform a detailed numerical analysis of the role of trap frequency and geometry on collisional rates for experimentally accessible mixtures of 87 Rb-41 K and 87 Rb-85 Rb, discussing the extent to which the system may approach the hydrodynamic regime with regard to some of those processes as a guide for future experimental investigations of ultracold Bose gas mixtures.

Time-of-flight expansion of binary Bose–Einstein condensates at finite temperature

“…The finite temperature dynamics of a partially-condensed system is well described in the context of a 'two-gas' model ('Zaremba-Nikuni-Griffin', or 'ZNG' model [46,47]), consisting of a BEC and a thermal cloud. Here we follow our earlier work [48][49][50] which appropriately generalized this to a binary mixture in such a way that both BECs and both thermal clouds are coupled within and between the mixture components through both meanfield and collisional interactions. In order to probe expansion dynamics, we limit our discussion here to the collisionless limit of the above theory: in this limit, each BEC is described by a generalized Gross-Pitaevskii equation (GPE),…”

“…The experimental scenario is simulated as follows. The initial equilibrium states are obtained in the usual way [48][49][50]52]. At time t=0, the atoms are released from the trap (i.e.…”

“…The comparison of our experimental data with the full simulation in the preceding sections has shown that it is vital to appropriately include the initial gravitational sag between the two species. The role of trap sag has previously been theoretically investigated in [30,31], while the effect of temperature has been considered in [27,42,[48][49][50]. Figure 7 provides a more complete analysis of the effect of the sag on the COM position of the expanded partially condensed 39 K cloud.…”

Phase separation and dynamics of two-component Bose-Einstein condensates

“…To address the role of temperature in such dynamics, we use the two-component generalization of the ZNG model, which has been previously demonstrated to pass the stringent test of the undamped Kohn mode, essential for a correct modeling of collective modes [43]. Our kinetic model [37] describes the self-consistent coupling of two BECs, each coupled to their own thermal cloud, and additionally includes coupling between the thermal clouds. This approach enables us to consider the relative importance of damping arising from mean-field coupling (U j c , U j n ) and thermal-condensate (C ..…”

“…The aim of this article is fourfold: (i) to demonstrate that for a trapped binary mixture, = 0 is generally no longer the optimal criterion for the transition boundary; (ii) to characterize the full phase diagram (see Fig. 1) based on the identification of a new parameter; (iii) to propose measurements of the frequency and damping rates of induced dipole oscillations as a universal experimental tool for mapping out the phase diagram; and (iv) to demonstrate the importance of thermal effects on the dynamics, by providing a numerical implementation of a fully self-consistent finite-temperature model for binary mixtures [37]. This extends the successful Zaremba-Nikuni-Griffin (ZNG) model [38] to two components.…”