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WORLD SCIENTIFIC eBooks

Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates

David S. Hall, M. R. Matthews, J. R. Ensher, Carl Wieman, Eric Cornell

Published Jan 1, 2008• 8 citations
Publisher

Abstract

We present studies of the time-evolution of a twocomponent system of Bose-Einstein condensates (BEC) in the |F = 1, m f = -1 and |2, 1 spin states of 87 Rb.The two condensates are created with a well-defined relative phase and complete spatial overlap.In subsequent evolution they undergo complex relative motions that tend to preserve the total density profile.The motions quickly damp out, leaving the condensates in a steady state with a nonnegligible (and adjustable) overlap region.

DOI
10.1142/9789812813787_0071

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We present studies of the time-evolution of a twocomponent system of Bose-Einstein condensates (BEC) in the |F = 1, m f = -1 and |2, 1 spin states of 87 Rb.The two condensates are created with a well-defined relative phase and complete spatial overlap.In subsequent evolution they undergo complex relative motions that tend to preserve the total density profile.The motions quickly damp out, leaving the condensates in a steady state with a nonnegligible (and adjustable) overlap region.
We describe the first experiments that study in a controlled way the dynamics of distinguishable and interpenetrating bosonic quantum fluids. We work with a two-component system of Bose-Einstein condensates in the $|{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1〉$ and ∣2,1〉|2,1〉∣2,1〉 spin states of 87Rb{}^{87}\mathrm{Rb}87Rb. The two condensates are created with complete spatial overlap, and in subsequent evolution they undergo complex relative motions that tend to preserve the total density profile. The motions quickly damp out, leaving the condensates in a steady state with a non-negligible (and adjustable) overlap region.
We study the spin-mixing dynamics of an f=1f=1f=1 spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.
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 have observed and characterized the nonequilibrium spatial dynamics of a two-component 87 Rb Bose–Einstein condensate (BEC) that is controllable switched back and forth between the miscible and immiscible phases of the phase separation transition by changing the internal states of the 87 Rb atoms. The subsequent evolution exhibits large scale oscillations of the spatial structure that involve component mixing and separation. We show that the larger total energy of the miscible system results in a higher oscillation frequency. This investigation introduces a new technique to control the miscibility and the spatial degrees of freedom in atomic BECs.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.
The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of | F = 1, m f = 1〉 and |2, 1〉 internal spin states of 87 Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, −1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.