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Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation

Kevrekidis, Panos, G. C. Katsimiga, Georgios M. Koutentakis, S. I. Mistakidis, Peter Schmelcher

Published Jan 1, 2016• 46 citations
OpenAlex

Abstract

The dynamics of dark bright solitons beyond the mean-eld approximation is investigated. Werst examine the case of a single dark-bright soliton and its oscillations within a parabolic trap.Subsequently, we move to the setting of collisions, comparing the mean-eld approximation to thatinvolving multiple orbitals in both the dark and the bright component. Fragmentation is presentand signicantly aects the dynamics, especially in the case of slower solitons and in that of loweratom numbers. It is shown that the presence of fragmentation allows for bipartite entanglementbetween the distinguishable species. Most importantly the interplay between fragmentation andentanglement leads to the decay of each of the initial mean-eld dark-bright solitons into fast andslow fragmented dark-bright structures. A variety of excitations including dark-bright solitons inmultiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-brightsoliton complexes can also be observed to arise spontaneously in the beyond mean-eld dynamics.

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The dynamics of dark bright solitons beyond the mean-eld approximation is investigated. Werst examine the case of a single dark-bright soliton and its oscillations within a parabolic trap.Subsequently, we move to the setting of collisions, comparing the mean-eld approximation to thatinvolving multiple orbitals in both the dark and the bright component. Fragmentation is presentand signicantly aects the dynamics, especially in the case of slower solitons and in that of loweratom numbers. It is shown that the presence of fragmentation allows for bipartite entanglementbetween the distinguishable species. Most importantly the interplay between fragmentation andentanglement leads to the decay of each of the initial mean-eld dark-bright solitons into fast andslow fragmented dark-bright structures. A variety of excitations including dark-bright solitons inmultiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-brightsoliton complexes can also be observed to arise spontaneously in the beyond mean-eld dynamics.
The dynamics of dark–bright (DB) solitons beyond the mean-field approximation is investigated. We first examine the case of a single DB soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the splitting of each of the parent mean-field DB solitons, placed off-center within the parabolic trap, into a fast and a slow daughter solitary wave. The latter process is in direct contrast to the predictions of the mean-field approximation. A variety of excitations including DB solitons in multiple (concurrently populated) orbitals is observed. Dark–antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics.
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
In the present work, we explore the potential of spin-orbit (SO) coupled Bose-Einstein condensates to support multi-component solitonic states in the form of dark-bright (DB) solitons. In the case where Raman linear coupling between components is absent, we use a multiscale expansion method to reduce the model to the integrable Mel'nikov system. The soliton solutions of the latter allow us to reconstruct approximate traveling DB solitons for the reduced SO coupled system. For small values of the formal perturbation parameter, the resulting waveforms propagate undistorted, while for large values thereof, they shed some dispersive radiation, and subsequently distill into a robust propagating structure. After quantifying the relevant radiation effect, we also study the dynamics of DB solitons in a parabolic trap, exploring how their oscillation frequency varies as a function of the bright component mass and the Raman laser wavenumber.
In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions,motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. Inparticular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interactionbetween two dark-bright solitons in a homogeneous environment beyond the integrable regime, by consideringgeneral inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case wherethe bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponentialinstability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter givesrise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of thebound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations andmonitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.
We analyze the dynamics of two-component vector solitons, namely, dark-bright solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to multicomponent Bose-Einstein condensates. The variational approximation is based on a hyperbolic tangent (hyperbolic secant) for the dark (bright) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright solitons. Analytical calculations are performed for same-width components in the vector soliton, and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it to be proportional to the intercomponent coupling interaction and numerically demonstrate the breakup or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely, the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the number of atoms in the bright component is required to be less than the number of atoms displaced by the dark soliton in the other component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright solitons in 87Rb^{87}\mathrm{Rb}87Rb we find that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments.
In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter- and intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the intercomponent interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter gives rise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of the bound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations and monitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.