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arXiv:2011.02613 · New Journal of Physics

Soliton trains after interaction quenches in Bose mixtures

André Cidrim, Luca Salasnich, Tommaso Macrì

Published Jan 15, 2021• 19 citations

Abstract

Abstract We investigate the quench dynamics of a two-component Bose mixture and study the onset of modulational instability, which leads the system far from equilibrium. Analogous to the single-component counterpart, this phenomenon results in the creation of trains of bright solitons. We provide an analytical estimate of the number of solitons at long times after the quench for each of the two components based on the most unstable mode of the Bogoliubov spectrum, which agrees well with our simulations for quenches to the weak attractive regime when the two components possess equal intraspecies interactions and loss rates. We also explain the significantly different soliton dynamics in a realistic experimental homonuclear potassium mixture in terms of different intraspecies interaction and loss rates. We investigate the quench dynamics of the particle number of each component estimating the characteristic time for the appearance of modulational instability for a variety of interaction strengths and loss rates. Finally we evaluate the influence of the beyond-mean-field contribution, which is crucial for the ground-state properties of the mixture, in the quench dynamics for both the evolution of the particle number and the radial width of the mixture. In particular, even for quenches to strongly attractive effective interactions we do not observe the dynamical formation of solitonic droplets.

DOI: 10.1088/1367-2630/abdbe2

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Abstract We investigate the quench dynamics of a two-component Bose mixture and study the onset of modulational instability, which leads the system far from equilibrium. Analogous to the single-component counterpart, this phenomenon results in the creation of trains of bright solitons. We provide an analytical estimate of the number of solitons at long times after the quench for each of the two components based on the most unstable mode of the Bogoliubov spectrum, which agrees well with our simulations for quenches to the weak attractive regime when the two components possess equal intraspecies interactions and loss rates. We also explain the significantly different soliton dynamics in a realistic experimental homonuclear potassium mixture in terms of different intraspecies interaction and loss rates. We investigate the quench dynamics of the particle number of each component estimating the characteristic time for the appearance of modulational instability for a variety of interaction strengths and loss rates. Finally we evaluate the influence of the beyond-mean-field contribution, which is crucial for the ground-state properties of the mixture, in the quench dynamics for both the evolution of the particle number and the radial width of the mixture. In particular, even for quenches to strongly attractive effective interactions we do not observe the dynamical formation of solitonic droplets.

We investigate numerically the dynamics of paired bright solitons induced by the modulational instability of two-component Bose-Einstein condensates. We derive the analytic gain spectrum by the modulational instability in terms of the interspecies and intraspecies scattering constants and classify the region where the instability occurs. The constraints on the interspecies and intraspecies scattering constants for the existence of the paired bright solitons are found. Using numerical simulations, it is shown that the paired bright solitons induced by the modulational instability exhibit complicated dynamical behaviors depending on the sign and strength of the interspecies and intraspecies scattering constants. - PACS numbers: 03.75.Fi, 05.30.Jp, 32.80Pj, 67.90.+z

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.

Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of inter- and intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.

Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.

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.

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.