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 setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies 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.
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 setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies 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.
The effects of miscibility in interacting two-component classical fluids are relevant in a broad range of daily applications. When considering quantum systems, two-component Bose–Einstein condensates provide a well-controlled platform where the miscible–immiscible phase transition can be completely characterized. In homogeneous systems, this phase transition is governed only by the competition between intra- and inter-species interactions. However, in more conventional experiments dealing with trapped gases, the pressure of the confinement increases the role of the kinetic energy and makes the system more miscible. In the most general case, the miscibility phase diagram of unbalanced mixtures of different atomic species is strongly modified by the atom number ratio and the different gravitational sags. Here, we numerically investigate the ground-state of a 23Na–39K quantum mixture for different interaction strengths and atom number ratios considering realistic experimental parameters. Defining the spatial overlap between the resulting atomic clouds, we construct the phase diagram of the miscibility transition which could be directly measured in real experiments.
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.
In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.
We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors phase mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as $L\ensuremath{\rightarrow}0$ ($L\ensuremath{\rightarrow}\ensuremath{\infty}$) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length ${\ensuremath{\xi}}_{\mathrm{ho}}$ plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the g's.
The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the $^{23}\mathrm{Na}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixture and the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.
We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature Tc is studied using a leading-order large-N approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above Tc where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above Tc where no condensate is present this dynamical transition should still be observable in experiments.