Ultracold quantum gases provide a unique setting for studying and understanding the properties of interacting quantum systems. Here, we investigate a multi-component system of $^{87}$Rb--$^{39}$K Bose-Einstein condensates (BECs) with tunable interact
ions both theoretically and experimentally. Such multi-component systems can be characterized by their miscibility, where miscible components lead to a mixed ground state and immiscible components form a phase-separated state. Here we perform the first full simulation of the dynamical expansion of this system including both BECs and thermal clouds, which allows for a detailed comparison with experimental results. In particular we show that striking features emerge in time-of-flight for BECs with strong interspecies repulsion, even for systems which were separated in situ by a large gravitational sag. An analysis of the center of mass positions of the BECs after expansion yields qualitative agreement with the homogeneous criterion for phase-separation, but reveals no clear transition point between the mixed and the separated phases. Instead one can identify a transition region, for which the presence of a gravitational sag is found to be advantageous. Moreover we analyze the situation where only one component is condensed and show that the density distribution of the thermal component also show some distinct features. Our work sheds new light on the analysis of multi-component systems after time-of-flight and will guide future experiments on the detection of miscibility in these systems.
The non-equilibrium dynamics of trapped ultracold atomic gases, or mixtures thereof, is an extremely rich subject. Despite 20 years of studies, and remarkable progress mainly on the experimental front, numerous open question remain, related to the gr
owth, relaxation and thermalisation of such systems, and there is still no universally-accepted theory for their theoretical description. In this paper we discuss one of the state-of-the-art kinetic approaches, which gives an intuitive picture of the physical processes happening at the microscopic scale, being broadly applicable both below and above the critical region (but not within the critical region itself). Specifically, the Zaremba-Nikuni-Griffin (ZNG) scheme provides a self-consistent description of the coupling between the condensate and the thermal atoms, including the collisions between these two subsystems. It has been successfully tested against experiments in various settings, including collective modes (e.g. monopole, dipole and quadrupole modes), topological excitations (solitons and vortices) and surface evaporative cooling. Here, we show that it can capture two important aspects of non- equilibrium dynamics for both single-component and two-component BECs: the Kohn mode (the undamped dipole oscillation independent of interactions and temperature) and (re)thermalization leading to condensate growth following sudden evaporation. Our simulations, performed in a spherically-symmetric trap reveal (i) an interesting two-stage dynamics and the emergence of a prominent monopole mode in the evaporative cooling of a single component Bose gas, and (ii) the long thermalization time associated with the sympathetic cooling of a realistic two-component mixture. Related open questions arise about the mechanisms and the nature of thermalization in such systems, where further controlled experiments are needed for benchmarking.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled se
tting. In a homogeneous system, the transition between mixed and separated phases is fully characterised by a `miscibility parameter, based on the ratio of intra- to inter-species interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
