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arXiv:cond-mat/9809061 · Physical Review Letters

Dynamics of Two Interacting Bose-Einstein Condensates

Alice Sinatra, Peter O. Fedichev, Yvan Castin, Jean Dalibard, Georgy V. Shlyapnikov

Published Jan 11, 1999• 59 citations
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Abstract

We analyze the dynamics of two trapped interacting Bose-Einstein condensates in the absence of thermal cloud and identify two regimes for the evolution: a regime of slow periodic oscillations and a regime of strong nonlinear mixing leading to the damping of the relative motion of the condensates. We compare our predictions with an experiment recently performed at JILA.

DOI
10.1103/physrevlett.82.251

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We analyze the dynamics of two trapped interacting Bose-Einstein condensates in the absence of thermal cloud and identify two regimes for the evolution: a regime of slow periodic oscillations and a regime of strong nonlinear mixing leading to the damping of the relative motion of the condensates. We compare our predictions with an experiment recently performed at JILA.
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.
Motivated by recent experiments studyingthe dynamics ofconfigurations bearing a small number of vortices inatomic Bose-Einstein condensates (BECs), weillustrate that such systems can be accurately described byordinary differential equations (ODEs) incorporating the precessionand interaction dynamics ofvortices inharmonic traps.This dynamics is tackled in detail at the ODE level, both forthe simpler case of equal charge vortices,and for the more complicated(yet also experimentally relevant) case of opposite charge vortices.In the former case, we identify the dynamics as being chieflyquasi-periodic (although potentially periodic), while in thelatter, irregular dynamics may ensuewhen suitableexternal drive of the BEC cloud is also considered. Our analytical findings arecorroborated by numerical computations of the reduced ODE system.
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.
The dynamics of two-component Bose-Einstein condensates in rotating traps is investigated. In the Thomas-Fermi limit, equations of motion are derived showing multiple static solutions for a vortex-free condensate. Dynamic stability analysis of these solutions and comparison to truncated Wigner simulations enable us to identify the regimes for which vortex states will occur. In addition, our analysis predicts center-of-mass oscillations that are induced by interspecies interactions and affect each component separately. For attractive interspecies interactions, these oscillations lead to a stable symmetry-broken state.