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Bulletin of the American Physical Society

Controllable friction of dark solitons in Bose-Fermi mixtures

Hilary M. Hurst, Dmitry K. Efimkin, Victor M. Galitski

Published Mar 13, 2017• 0 citations
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Abstract

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose gas and a non-interacting, degenerate Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton by treating it as a particle with negative mass, and calculate its friction coefficient. Surprisingly, the amount of friction depends on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We compare our results to experimental regimes and conclude that tunable friction has measurable physical consquences in experiments with Bose-Fermi mixtures.

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We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose gas and a non-interacting, degenerate Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton by treating it as a particle with negative mass, and calculate its friction coefficient. Surprisingly, the amount of friction depends on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We compare our results to experimental regimes and conclude that tunable friction has measurable physical consquences in experiments with Bose-Fermi mixtures.
We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers.
Solitons, spatially-localized, mobile excitations resulting from an interplay between nonlinearity and dispersion, are ubiquitous in physical systems from water channels and oceans to optical fibers and Bose-Einstein condensates (BECs). For the first time, we observed and controlled the Brownian motion of solitons. We launched long-lived dark solitons in highly elongated 87Rb^{87}\rm{Rb}87Rb BECs and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one-dimension (1-D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1-D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.
The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.
Generation and properties of dark solitons are studied in detail by means of numerical simulation of quasi one-dimensional heteronuclear two-component Bose-Einstein condensates in syntonic potential.Dark solitons are only induced in one of the condensate components by modulational instability with instantaneous conversion of repulsive interspecies interaction to attraction.Solitons pass through each other periodically in syntonic potential.In addition,the number of dark solitons is affiliated with ratio of particle mass and ratio of particles numbers.
We investigate the dynamics of a binary mixture of Bose-Einstein condensates in the impurity limit -- where one component is dilute enough to be treated like an impurity -- and confined to two dimensions. Using the mean-field coupled Gross-Pitaevskii equations, we find that the binary mixture supports the formation of stable symbiotic dark-bright solitons when the inter- and intra-component interactions are repulsive. We further study the interaction between solitons and observe that the solitons undergo merging and repulsion depending on the relative phase between the bright component of the composite structure.