Brownian motion of solitons in a Bose-Einstein condensate

Dynamical instability of 3D stationary and traveling planar dark solitons

Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional (3D) Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Motivated by numerous experimental efforts, including our own herein, we use fully 3D numerical simulations to explore the existence, stability, and evolution dynamics of planar dark solitons. This also allows us to examine their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.

Systematic vector solitary waves from their linear limits in one-dimensional n-component Bose-Einstein condensates

We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multidimensional space of the chemical potentials. The Bogoliubov-de Gennes spectral analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical SU(n)-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.

Classification of dark solitons via topological vector potentials

Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.

Machine-learning enhanced dark soliton detection in Bose-Einstein condensates

Most data in cold-atom experiments comes from images, the analysis of which is limited by our preconceptions of the patterns that could be present in the data. We focus on the well-defined case of detecting dark solitons-appearing as local density depletions in a Bose-Einstein condensate (BEC)-using a methodology that is extensible to the general task of pattern recognition in images of cold atoms. Studying soliton dynamics over a wide range of parameters requires the analysis of large datasets, making the existing human-inspection-based methodology a significant bottleneck. Here we describe an automated classification and positioning system for identifying localized excitations in atomic BECs utilizing deep convolutional neural networks to eliminate the need for human image examination. Furthermore, we openly publish our labeled dataset of dark solitons, the first of its kind, for further machine learning research.

Random walks of trains of dissipative solitons

The propagation of light pulses in dual-core nonlinear optical fibers is studied using a model proposed by Sakaguchi and Malomed. The system consists of a supercritical complex Ginzburg-Landau equation coupled to a linear equation. Our analysis includes single standing and walking solitons as well as walking trains of 3, 5, 6, and 12 solitons. For the characterization of the different scenarios, we used ensemble-averaged square displacement of the soliton trajectories and time-averaged power spectrum of the background waves. Power law spectra, indicative of turbulence, were found to be associated with random walks. The number of solitons (or their separations) can trigger anomalous random walks or totally suppress the background waves.

Anomalous diffusion of discrete solitons driven by evolving disorder

Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.

Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates

Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.

Transient diffusion and two-regime localization of discrete breatherlike excitations in nonlinear Schrödinger lattice with disorder

We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales (t≲10^{3}). For longer timescales (t up to 10^{5}), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.

Measurement-induced dynamics and stabilization of spinor-condensate domain walls

Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.

Probing non-locality of interactions in a Bose-Einstein condensate using solitons

We consider a Bose-Einstein condensate (BEC) with non-local inter-particle interactions. The local Gross-Pitaevskii (GP) equation is valid for the gas parameter [Formula: see text], but for [Formula: see text], the BEC is described by a modified GP equation (MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter (ν) on the stability of the solitons using the Vakhitov-Kolokolov (VK) stability criterion. We show that these soliton solutions are stable according to the VK criterion. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.

Collective Modes of a Soliton Train in a Fermi Superfluid

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.

Kinetic theory of dark solitons with tunable friction

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers.