Kinetic theory of dark solitons with tunable friction

Abstract

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.

A direct derivation of the dark soliton excitation energy

“…This soliton energy form has been successfully applied to numerous studies of dark soliton dynamics in external potentials, yielding good agreement with experiments [11][12][13][14][15][16][22][23][24]; see also the pertinent two-component generalization to the dark-bright soliton [25][26][27][28][29][30]. The energy is also a key element for more exotic topics such as the negative mass of the dark soliton [17][18][19]. However, this crucial renormalized energy was suggested in a somewhat vague way, namely, it was stated that "the soliton part of the total Hamiltonian (the system energy) may be defined as Eq.…”

“…One theme of research in this broad field is to study the effective nonlinear dynamics of the dark solitons, highlighting the particle aspect of these solitary waves. In order to discuss the effective mass and related kinetic dynamics of dark solitons [10][11][12][13][14][15][16][17][18][19], it is essential to characterize the excitation energy of a dark soliton. Importantly, this energy also serves as a starting point for investigating dynamics of dark soliton filaments and surfaces in higher dimensions [20,21].…”

Soliton diffusion in a Bose-Einstein condensate: A signature of the analogue Hawking radiation

“…We see that for small τ , D(ζ DS ) ∝ τ , in accordance with the Einstein relation for Brownian motion [55]; however for larger τ , D(ζ DS ) ∝ τ 3 , that is, the dark soliton displays a nonlinear time-variance of its position, which can be regarded as a nonlinear Brownian motion. Furthermore, in contrast with the Einstein relation where the diffusion coefficient ∝ 1/γ, here D(ζ DS ) ∝ γ since the dark soliton has a negative mass [43,44].…”

“…Among diverse types of solitons discovered in many branches of physics, matter wave solitons in atomic BECs have been broadly studied [29][30][31][32][33][34][35][36][37][38][39][40]. Their diffusion has also been explored recently in various settings [41][42][43][44].…”

Control of anomalous diffusion of a Bose polaron

“…To this end, we treat the Bose Polaron problem within an open quantum system framework. The open quantum system approach has been used recently in the context of ultracold quantum gases to study the diffusion of an impurity and two impurities in a BEC [35][36][37], for the movement of a bright soliton in a superfluid in one dimension [38], see also [39][40][41]). On the other hand, the effect of contact interactions, dipole-dipole interactions and disorder on the diffusion properties of 1D dipolar two-component condensates were studied in [42], identifying again the conditions for subdiffusion.…”