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arXiv:cond-mat/0010232 · Physical Review Letters

Dark Solitons in a Two-Component Bose-Einstein Condensate

Patrik Öhberg, Luis Santos

Published Apr 2, 2001• 177 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.86.2918

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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.
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.
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.
In this thesis, we have studied the behavior of two-component dark-bright solitons in multicomponent Bose-Einstein condensates (BECs) analytically and numerically in different situations. We utilized various analytical methods including the variational method and perturbation theory. By imprinting a linear phase on the bright component only, we were able to impart a velocity relative to the dark component and thereby we obtain an internal oscillation between the two components. We find that there are two modes of the oscillation of the dark-bright soliton. The first one is the famous Goldstone mode. This mode represents a moving dark-bright soliton without internal oscillation and is related to the continuous translational symmetry of the underlying equations of motion in the uniform potential. The second mode is the oscillation of the two components relative to each other. We compared the results obtained from the variational method with numerical simulations and found that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments. Also, we studied the binding energy and found a critical value for the breakup of the dark-bright soliton. Building on these results, we have studied another situation where we have the dark-bright soliton oscillate in a harmonic potential. We found for weak trapping the internal modes are nearly independent of center of mass motion of the dark-bright soliton. In contrast, in tighter traps the internal modes couple strongly to the center of mass motion, showing that for dark-bright solitons in a harmonic potential the center of mass and relative degrees of freedom are not independent. We found this result is robust against noise in the initial condition and should, therefore, be experimentally observable. In addition, we have studied the interaction between a moving dark-bright soliton in a uniform background with internal oscillation and a fixed impurity, modeled by a delta function potential. The interaction excites different modes in the system. Our analytical model capture two of these modes: the relative oscillation between the two components, as well as the in-sync oscillation of the widths. The numerical simulations allow further internal modes like out-of-sync oscillations of the soliton widths and even shape deformations of various kinds. We identify regions in parameter space for the transmission, reflection and inelastic scattering of the dark-bright soliton by the potential barrier. We have studied the velocity of dark-bright solitons described with an ansatz that uses one center of mass variable to represent the position of the two components. We found for a dark-bright soliton the maximum velocity is limited by the relative number of atoms in the bright component as compared to the size of the hole or density notch created by the dark component. Above this critical velocity the dark-bright soliton develops internal oscillations, and eventually unbinds and breaks apart.
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 investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.
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.