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arXiv:1511.01624 · Physical Review A

Bouncing motion and penetration dynamics in multicomponent Bose-Einstein condensates

Yujiro Eto, Masahiro O. Takahashi, Keita Nabeta, Ryotaro Okada, Masaya Kunimi, Hiroki Saito, Takuya Hirano

Published Mar 8, 2016• 20 citations
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Abstract

We investigate the dynamic properties of bouncing and penetration in colliding binary and ternary Bose-Einstein condensates comprised of different Zeeman or hyperfine states of $^{87}\mathrm{Rb}$. Through the application of magnetic field gradient pulses, two- or three-component condensates in an optical trap are spatially separated and then made to collide. The subsequent evolutions are classified into two categories: repeated bouncing motion and mutual penetration after damped bounces. We experimentally observed mutual penetration for immiscible condensates, bouncing between miscible condensates, and domain formation for miscible condensates. From numerical simulations of the Gross-Pitaevskii equation, we find that the penetration time can be tuned by slightly changing the atomic interaction strengths.

DOI
10.1103/physreva.93.033615

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We investigate the dynamic properties of bouncing and penetration in colliding binary and ternary Bose-Einstein condensates comprised of different Zeeman or hyperfine states of 87Rb^{87}\mathrm{Rb}87Rb. Through the application of magnetic field gradient pulses, two- or three-component condensates in an optical trap are spatially separated and then made to collide. The subsequent evolutions are classified into two categories: repeated bouncing motion and mutual penetration after damped bounces. We experimentally observed mutual penetration for immiscible condensates, bouncing between miscible condensates, and domain formation for miscible condensates. From numerical simulations of the Gross-Pitaevskii equation, we find that the penetration time can be tuned by slightly changing the atomic interaction strengths.
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.
We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with different magnetic moments: the two condensates are initially created with the same density profile, but are trapped into different magnetic potentials, whose minima are vertically displaced by a distance much larger than the initial size of both condensates. Then the two condensates begin to perform collective oscillations, undergoing a complex evolution, characterized by collisions between the two condensates. We investigate the effects of their mutual interaction on the center-of-mass oscillations and on the time evolution of the aspect ratios. Our theoretical analysis provides a useful insight into the recent experimental observations by Maddaloni et al. [Phys. Rev. Lett. 85, 2413 (2000)].
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 examine the dynamics associated with the miscibility-immiscibility transition of trapped two-species Bose-Einstein condensates (TBECs) of dilute atomic gases in the presence of vortices. In particular, we consider TBECs of Rb hyperfine states and Rb-Cs mixture. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupies the edges at phase separation. But suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the interspecies interactions to drive the TBECs from miscible to immiscible phase, and use the time-dependent Gross-Pitaevskii equation to probe the phenomenon of phase separation. We also examine the effects of higher charged vortex to phase separation.
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.