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Chinese Physics B

Interfacial Dynamics of a Dark Soliton in a Two-Dimensional Phase-Separated Bose-Einstein Condensate

Chan Ye, Chen Jiao, Qi Wang, Tao Yang

Published Jan 14, 2026• 0 citations
Publisher

Abstract

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 $\delta = g_{12}/g_{11}$ and the soliton's initial displacement $\Delta_x$ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a $penetration regime$, where the soliton decays into vortex pairs that cross the interface, and a $non-penetration regime$, 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 $(\delta, \Delta_x)$ 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.

DOI
10.1088/1674-1056/ae37fd

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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.
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.
We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a 87Rb^{87}\mathrm{Rb}87Rb BEC.
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.
We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.
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.