Matter-wave Solitons Research Articles

Pattern formations and their active manipulation in a Rydberg noisy-dressed Bose-Einstein condensate.

We investigate the formation and manipulation of spatial patterns and their structural phase transitions by examining the effects of laser linewidth on the dynamics of Rydberg noise-dressed Bose-Einstein condensates (RnD BECs). We discover that the homogeneous matter wave can transition into various types of self-organized patterns, which are manipulated by tuning the laser linewidth, control field intensity, and atomic density. Remarkably, the system exhibits stable nonlocal matter-wave solitons, vortices, and soliton molecules under specific laser linewidths.

Effective spin dynamics of spin-orbit coupled matter-wave solitons in optical lattices

We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.

Transfer of solitons and half-vortex solitons via adiabatic passage

We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024

Quantum soliton-trains of strongly correlated impurities in Bose-Einstein condensates

Strongly correlated impurities immersed in a Bose-Einstein condensate (BEC) can form a periodic structure of tightly localized single atoms due to competing inter and intraspecies interactions, leading to a self-organized pinned state. In this work, we show numerically that the impurities in the self-pinned state form a soliton-train, as a consequence of a BEC-mediated attractive self-interaction and ordering due to the exclusion principle. The dynamics of the impurities possess the characteristics of bright matter-wave soliton trains as often seen in classical fields; however, in the few impurities cases, the detailed nature of collisions is determined by their quantum statistics. Published by the American Physical Society 2024

Weakly nonlocal matter-wave droplets and soliton trains engineering in a Bose-Einstein condensate

We propose a comprehensive analysis of the modulational instability (MI) phenomenon in one-dimensional Bose-Einstein condensate (BEC) in the context of mutually symmetric components in the binary mixture. The proposed model considers weak nonlocal cubic mean-field and quadratic beyond mean-field interactions arising from quantum fluctuations. The instability regions are analyzed using linear stability analysis of a continuous wave, considering maximum perturbation wavenumber and growth rate. The regions for quantum droplets (QDs) and solitons are identified by varying the nonlocality parameter. Numerical simulations confirm analytical predictions, revealing that nonlocality influences the formation of various QD profiles and instability time. Furthermore, solitonic patterns exhibit nonlocality-dependent behavior. Our study opens new doors to a better characterization of QDs in binary mixtures in the presence of higher-order beyond mean-field effects.

Mixed localized matter wave solitons in Bose–Einstein condensates with time-varying interatomic interaction and a time-varying complex harmonic trapping potential

We study the generation of mixed localized matter wave solitons in the quasi-one-dimensional Gross–Pitaevskii equation with a complex potential (model equation) that describes the dynamics of Bose–Einstein condensates trapped in an harmonic potential when the loss/gain of condensate atoms is taken into account. Performing a modified lens-type transformation, the integrability condition is derived and the model equation is converted to a Kundu-like nonlinear Schrödinger equation. Through the linear stability analysis, the phenomenon of the modulational instability is analyzed and the criterion of the modulational instability is established. Based on the generalized perturbation (n,N−n)−fold Darboux transformation, new mixed localized wave solutions are presented and used for analyzing the generation of mixed matter-wave solitons in Bose–Einstein condensates with two-body interatomic interactions. We show that mixed localized waves generated with these exact solutions can change from a strong interaction to a weak interaction by choosing the parameters such as the similarity parameters, the spectrum parameter, or the seed solution parameter. Our results show that the spectrum parameter is useful for generating interesting structures which are beneficial to understanding the complex physical phenomena in Bose–Einstein condensates with atomic gain/loss.

Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients

Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients

Atomic soliton transmission and induced collapse in scattering from a narrow barrier

We report systematic numerical simulations of the collision of a bright matter-wave soliton made of Bose-condensed alkali-metal atoms through a narrow potential barrier by using the three-dimensional Gross–Pitaevskii equation. In this way, we determine how the transmission coefficient depends on the soliton impact velocity and the barrier height. Quite remarkably, we also obtain the regions of parameters where there is the collapse of the bright soliton induced by the collision. We compare these three-dimensional results with the ones obtained by three different one-dimensional nonlinear Schrödinger equations. We find that a specifically modified nonpolynomial Schrödinger equation is able to accurately assess the transmission coefficient even in a region in which the usual nonpolynomial Schrödinger equation collapses. In particular, this simplified but very effective one-dimensional model takes into account the transverse width dynamics of the soliton with an ordinary differential equation coupled to the partial differential equation of the axial wave function of the Bose–Einstein condensate.

Ring Bose-Einstein condensate in a cavity: Chirality detection and rotation sensing

Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, , in real-time, and with minimal destruction by using a cavity driven with optical fields carrying orbital angular momentum []. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing. Published by the American Physical Society 2024

Cavity optomechanical detection of persistent currents and solitons in a bosonic ring condensate

We present numerical simulations of the cavity optomechanical detection of persistent currents and bright solitons in an atomic Bose-Einstein condensate confined in a ring trap. This paper describes a technique that measures condensate rotation , in real time, and with minimal destruction, in contrast to currently used methods, all of which destroy the condensate completely. For weakly repulsive interatomic interactions, the analysis of persistent currents extends our previous few-mode treatment of the condensate [P. Kumar ] to a stochastic Gross-Pitaevskii simulation. For weakly attractive atomic interactions, we present the first analysis of optomechanical detection of matter-wave soliton motion. We provide optical cavity transmission spectra containing signatures of the condensate rotation, sensitivity as a function of the system response frequency, and atomic density profiles quantifying the effect of the measurement backaction on the condensate. We treat the atoms at a mean-field level and the optical field classically, account for damping and noise in both degrees of freedom, and investigate the linear as well as nonlinear response of the configuration. Our results are consequential for the characterization of rotating matter waves in studies of atomtronics, superfluid hydrodynamics, and matter-wave soliton interferometry. Published by the American Physical Society 2024

Quantum scattering treatment on the time-domain diffraction of a matter-wave soliton

Quantum scattering treatment on the time-domain diffraction of a matter-wave soliton

One-Dimensional Gap Soliton Molecules and Clusters in Optical Lattice-Trapped Coherently Atomic Ensembles via Electromagnetically Induced Transparency

In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.

Direct creation of interacting quasi-one-dimensional Bose–Einstein condensate through fast evaporative cooling

Preparation of atomic Bose–Einstein condensate (BEC) with tunable interactions in a quasi-one-dimensional (quasi-1D) optical trap is essential for both the observation of bright matter-wave solitons and the quantum simulation based on the discrete atomic momentum states. However, the quasi-1D BEC has been obtained by a complex process, which includes the creation of a three-dimensional BEC and its adiabatic transform into a quasi-1D trap. Here, we report the direct creation of a quasi-1D BEC of 133Cs atoms by the fast evaporative cooling of ultracold atoms prepared by the degenerated Raman sideband cooling. We produce the pure BEC of up to 5.5×104 atoms in a quasi-1D optical trap with an evaporative time of 6 s. We demonstrate the anisotropic expansion of the atomic cloud after the release from the quasi-1D trap and study the dependence of both the phase space density and the temperature on the number of atoms in the trap during the evaporative cooling. Our study facilitates the promising applications of quasi-1D interacting atomic gases.

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

Massive particle interferometry with lattice solitons

We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG-based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms.

Quantum Squeezing of Matter-Wave Solitons in Bose-Einstein Condensates

We investigate the quantum squeezing of matter-wave solitons in atomic Bose–Einstein condensates. By calculating quantum fluctuations of the solitons via solving the Bogoliubov–de Gennes equations, we show that significant quantum squeezing can be realized for both bright and dark solitons. We also show that the squeezing efficiency of the solitons can be enhanced and manipulated by atom–atom interaction and soliton blackness. The results reported here are beneficial not only for understanding quantum property of matter-wave solitons, but also for promising applications of Bose-condensed quantum gases.

Matter-wave gap solitons and vortices of dense Bose–Einstein condensates in Moiré optical lattices

Optical lattices provide a key enabling and controllable platform for exploring new physical phenomena and implications of degenerate quantum gases both in the quantum and nonlinear regimes. Based on the Gross–Pitaevskii/nonlinear Schrödinger equation with competing cubic–quintic nonlinearity, we show, numerically and theoretically, the nonlinear localization of dense Bose–Einstein condensates (BECs) in a novel two-dimensional twisted periodic potential called Moiré optical lattices which, in essence, build a bridge between the perfect optical lattices and aperiodic ones. Our theory reveals that the Moiré optical lattices display a wider second gap and flat-band feature, and support two kinds of localized matter-wave structures like gap solitons and topological states (gap vortices) with vortex charge s=1, all populated inside the finite gaps of the linear Bloch-wave spectrum. We demonstrate, by means of linear-stability analysis and direct perturbed evolutions, that these localized structures have wide stability regions, paving the way for studying flat-band and Moiré physics in shallow optical lattices and for finding robust coherent matter waves therein. The twisted periodic structures can be readily implemented with currently available optical-lattice technique in BECs and nonlinear optics experiments where the results predicted here are observable.

Matter-wave solitons in an array of spin-orbit-coupled Bose-Einstein condensates.

We investigate matter-wave solitons in a binary Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, loaded in a one-dimensional (1D) deep optical lattice and a three-dimensional anisotropic magnetic trap, which creates an array of elongated sub-BECs with transverse tunneling. We show that the system supports 1D continuous and discrete solitons localized in the longitudinal (along the array) and the transverse (across the array) directions, respectively. In addition, such solitons are always unpolarized in the zero-momentum state but polarized in finite-momentum states. We also show that the system supports stable two-dimensional semidiscrete solitons, including single- and multiple-peaked ones, localized in both the longitudinal and transverse directions. Stability diagrams for single-peaked semidiscrete solitons in different parameter spaces are identified. The results reported here are beneficial not only for understanding the physical property of SO-coupled BECs but also for generating new types of matter-wave solitons.

Fundamental and multipole gap solitons in spin-orbit-coupled Bose-Einstein condensates with parity-time-symmetric Zeeman lattices

Our results demonstrate that fundamental and tripole matter-wave gap solitons can be stable in spin-orbit-coupled Bose-Einstein condensates (SOC-BECs) in one-dimensional (1D) parity-time (PT)-symmetric Zeeman lattices with attractive interactions. The solitons are found to be in a semi-infinite gap and both the components are complex. The real and imaginary parts of two components of these solitons respectively are even and odd functions. The peak numbers of the second component are twice that of the first component. We analyze the linear stability for the matter-wave gap solitons and the correctness is confirmed by the soliton evolutions. Moreover, the strength of spin-orbit (SO) coupling cannot change the critical threshold of the PT-symmetric Zeeman lattices.

Bright matter-wave bound soliton molecules in spin-1 Bose–Einstein condensates with non-autonomous nonlinearities

This work deals with matter-wave bright soliton molecules in spin-1 Bose–Einstein condensates described by three-component Gross–Pitaevskii equations with non-autonomous nonlinearities that can be tuned by Feshbach resonance management. Notably, it portrays the possibility to generate bright bound soliton molecules with the help of an exact analytic solution under a controlled velocity resonance mechanism. Results show that these soliton molecules experience the effects of time-varying nonlinearities and modulate themselves during propagation by keeping their stable properties. Significantly, the chosen periodic and kink-like nonlinearities expose the snaking, bending, compression, and amplification of multi-structured soliton molecules along with appreciable changes in their amplitude, velocity, width, and oscillations of the molecule profiles. The present results will add significant knowledge to a complete understanding beyond the known interaction dynamics of matter-wave bright solitons in spinor condensates.