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arXiv:1701.06683 · Physical Review Letters

Dynamics of Fragmented Condensates and Macroscopic Entanglement

Aurel Bulgac, Shi Jin

Published Jul 31, 2017• 23 citations
arXivHTMLPDF

Abstract

The relative phase of the order parameters in the collision of two condensates can influence the outcome of their collision in the case of weak coupling. With increasing interaction strength, however, the initially independent phases of the two order parameters in the colliding partners quickly become phase locked, as the strong coupling favors an overall phase rigidity of the entire condensate, and upon their separation the emerging superfluid fragments become entangled.

DOI
10.1103/physrevlett.119.052501

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The relative phase of the order parameters in the collision of two condensates can influence the outcome of their collision in the case of weak coupling. With increasing interaction strength, however, the initially independent phases of the two order parameters in the colliding partners quickly become phase locked, as the strong coupling favors an overall phase rigidity of the entire condensate, and upon their separation the emerging superfluid fragments become entangled.
Bose-Einstein condensates (BEC) serve as a model system for the study of decoherence and dephasing processes. We denote ‘dephasing’ as the loss of overall common phase due to the coherent evo lution of the macroscopic wavefunction of the BEC. In contrast, ‘decoherence’ in this case is the coupling of the macroscopic wavefunction state to a continuum of initially unoccupied momentum excitations via collisions. Decoherence is driven by the fluctuations in th ese momentum modes and is irreversible on the timescales larger than the so -called ‘memory time’ of the continuum [1].
We study the phase separation in three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin F=1F=1F=1 ferromagnetic Bose-Einstein condensate upon an increase of the strength of spin-orbit (SO) coupling ${p}_{x}{\mathrm{\ensuremath{\Sigma}}}_{z}$ above a critical value, where px{p}_{x}px​ is the linear momentum and ${\mathrm{\ensuremath{\Sigma}}}_{z}$ is the zzz component of the spin-1 matrix. The bright vector solitons are demonstrated to be mobile and dynamically stable. The collision between two such vector solitons is found to be elastic at all velocities with the conservation of density of each vector soliton. The two colliding vector solitons repel at small separation and at very small colliding velocity, they come close and bounce back with the same velocity without ever encountering each other. This repulsion produced by SO coupling is responsible for the phase separation in a vector soliton for large strengths of SO coupling. The collision dynamics is found to be completely insensitive to the relative phase of the colliding solitons. However, in the absence of SO coupling, at very small velocity, the two colliding vector solitons attract each other and form a vector soliton molecule and the collision dynamics is sensitive to the relative phase as in scalar solitons. The present investigation is carried out through a numerical solution and an analytic variational approximation of the underlying mean-field Gross-Pitaevskii equation.
Abstract The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped in a one-dimensional asymmetric double-well potential is studied by solving the many-body Schrödinger equation numerically accurately. We examine how the gradual loss of symmetry of the confining trap affects the macroscopic quantum tunneling dynamics of the system between the two wells. In an asymmetric double well, the two wells are not equivalent anymore, say, the left well is deeper than the right one. Accordingly, we analyze the dynamics by initially preparing the condensate in both the left and the right wells. The dynamics of the system is characterized by the time evolution of a few physical quantities of increasing many-body complexity, namely, the survival probability, depletion and fragmentation, and the many-particle position and momentum variances. In particular, we have examined the frequencies and amplitudes of the oscillations of the survival probabilities, the time scale for the development of fragmentation and its degree, and the growth and oscillatory behavior of the many-particle position and momentum variances. There is an overall suppression of the oscillations of the survival probabilities in an asymmetric double well, except for resonant values of asymmetry for which the one-body ground state energy in the right well matches with one of the one-body excited states in the left well, thereby resulting in resonantly enhanced tunneling from the right well ground state. Overall, depending on whether the condensate is initially prepared in the left or right well, the repulsive inter-atomic interactions affect the survival probabilities differently. For a sufficiently strong repulsive interaction, the system is found to become fragmented. The degree of fragmentation depends both on the asymmetry of the trap and the initial well in which the condensate is prepared in a non-trivial manner. Furthermore, we show that the phenomenon of resonantly enhanced tunneling can be accompanied by a large degree of fragmentation (depletion) for the strong (weak) interaction. The many-particle position and momentum variances follow the density oscillations of the system in the asymmetric double well and bears prominent signatures of the degree of depletion or fragmentation, depending on the strength of the interactions. These quantities further exhibit a fine structure signifying a breathing-mode oscillation. Finally, a universality of fragmentation for systems made of different numbers of particles but the same interaction parameter is also found and its dependence on the asymmetry is investigated. The phenomenon is robust despite the asymmetry of the junction and admits a macroscopically-large fragmented condensate characterized by a diverging many-particle position variance. This is as far as one can get from the dynamics of the density in the junction.