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Chinese Physics B

Propagation of dark soliton interacting with domain wall in two immiscible Bose–Einstein condensates*

Lang Zheng, Yi‐Cai Zhang, Chaofei Liu

Published Sep 18, 2019• 4 citations
Publisher

Abstract

Reflection and transmission are two behaviors of wave propagating to an interface. The immiscible binary mixtures of Bose–Einstein condensates can form the symmetry-breaking state, in which the domain wall on the center can serve as the interface. In this study, we explore in detail the propagation of a dark soliton interacting with the domain wall in the harmonic trap. We find that the low-energy dark soliton is easy to form the transmission and the high-energy dark soliton trends to reflect from the domain wall. Both reflection and transmission of dark soliton on the domain wall induce the sound radiation. But the sound radiation in the reflection derives from the collective oscillation of condensates, and it in the transmission comes not only from the collective oscillation, but also from the condensate filling in the dark soliton.

DOI
10.1088/1674-1056/ab457e

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Reflection and transmission are two behaviors of wave propagating to an interface. The immiscible binary mixtures of Bose–Einstein condensates can form the symmetry-breaking state, in which the domain wall on the center can serve as the interface. In this study, we explore in detail the propagation of a dark soliton interacting with the domain wall in the harmonic trap. We find that the low-energy dark soliton is easy to form the transmission and the high-energy dark soliton trends to reflect from the domain wall. Both reflection and transmission of dark soliton on the domain wall induce the sound radiation. But the sound radiation in the reflection derives from the collective oscillation of condensates, and it in the transmission comes not only from the collective oscillation, but also from the condensate filling in the dark soliton.
We theoretically investigate the one-dimensional dynamics of a dark soliton in a two-component immiscible mixture of Bose-Einstein condensates with repulsive interactions. We analyze the reflection and transmission of a soliton when it propagates through the domain wall, and we show that a dark-bright soliton can be dynamically generated by the interaction of the dark soliton with the domain wall, outside the regime of parameters where stationary solutions are known to exist. The dynamics of this dark-bright soliton is harmoniclike, with a numerical frequency that is in good agreement with the predictions of a semianalytical model.
Abstract We numerically investigate the collision dynamics of a dark soliton with a domain wall in an immiscible, two-component Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. The role of the inter-species interaction strength δ=g12/g11\delta = g_{12}/g_{11}δ=g12​/g11​ and the soliton's initial displacement Δx\Delta_xΔx​ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a penetrationregimepenetration regimepenetrationregime, where the soliton decays into vortex pairs that cross the interface, and a non−penetrationregimenon-penetration regimenon−penetrationregime, where the soliton's energy is dissipated at the interface through sound emission and vortex annihilation. We present a phase diagram that maps these outcomes across the (δ,Δx)(\delta, \Delta_x)(δ,Δx​) parameter space. Furthermore, within the non-penetration regime, we identify a complex excited state characterized by the combination of component breakup in one component and vortex formation in the other. This work provides the systematic study of dark soliton-domain wall interactions in a 2D phase-separated binary BEC, offering new insights into interfacial dynamics and non-equilibrium transport in multi-component quantum fluids.
The creation and interaction of dark solitons in a two-component Bose-Einstein condensate is investigated. For a miscible case, the interaction of dark solitons in different components is studied. Various possible scenarios are presented, including the formation of a soliton-soliton bound pair. We also analyze the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when it exceeds a critical velocity. For lower velocities multiple reflections within the domain are observed, where the soliton is evaporated and accelerated after each reflection until it finally escapes from the domain.
A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the coexisting soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter time scale than other dissipation mechanisms. Thus, we propose that small realistic modifications to existing experimental setups could enable the experimental observation of this decay channel.
The creation, interaction, observation and stability of dark solitons in two-component condensates are investigated. As a first scenario, we consider the case of miscible components, analysing the creation of solitons in different components via phase-imprinting, and the soliton-soliton interaction in different situations, which include the formation of a soliton-soliton binary system and free single solitons accompanied by a filling of the other component. The different regimes of interaction are analysed numerically, and compared with a variational calculation. The observability of the solitons and their stability are also analysed. In a second scenario, we study the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when exceeding a critical velocity.
Motivated by the experimental development of quasihomogeneous Bose-Einstein condensates confined in boxlike traps, we study numerically the dynamics of dark solitons in such traps at zero temperature. We consider the cases where the side walls of the box potential rise either as a power law or a Gaussian. While the soliton propagates through the homogeneous interior of the box without dissipation, it typically dissipates energy during a reflection from a wall through the emission of sound waves, causing a slight increase in the soliton's speed. We characterize this energy loss as a function of the wall parameters. Moreover, over multiple oscillations and reflections in the boxlike trap, the energy loss and speed increase of the soliton can be significant, although the decay eventually becomes stabilized when the soliton equilibrates with the ambient sound field.