The ring dark solitons in spin-1 $^{23}$Na and $^{87}$Rb Bose-Einstein condensates are studied numerically in the framework of the time-dependent Gross-Pitaevskii equations. By simulating the phase engineering technique in real experiments, we explore the roles of the parameters characterizing the far-off resonant laser pulse which can be used to generate the ring dark solitons. The variations of these parameters have dramatic effect on the lifetime and the decay profiles of the ring dark solitons. If only one ring dark soliton is generated in one component of the condensate, ring dark solitons in other components are inclined to be induced, resulting in a coexistence state composed of interdependent ring dark solitons coming from different components of the condensate. Ring dark solitons in this coexistence state exhibit dynamical oscillations for hundreds of milliseconds. By studying the lifetime and decaying profiles of ring dark solitons, we explore the similarities and differences of $^{23}$Na and $^{87}$Rb condensates. Besides, taking into account the fact that the center of the ring may not be coincide with that of the trap, we study the dynamics and decaying profiles of the off-centered ring dark solitons in the presence of symmetry breaking effect.
We propose a protocol for the simultaneous controlled creation of multiple concentric ring dark solitons in a toroidally trapped Bose-Einstein condensate. The decay of these solitons into a vortex-antivortex necklace shows revivals of the soliton structure, but eventually becomes an example of quantum turbulence.
Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families of exact spin soliton solutions for non-integrable cases in spin-1 Bose-Einstein Condensates. The whole particle density is uniform for the spin solitons, which is in sharp contrast to the previously reported solitons of integrable models. The spectrum stability analysis and numerical simulation indicate the spin solitons can exist stably. The spin …
Synthetic spin-tensor-momentum coupling has recently been proposed to realize in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different. We contribute the difference to the different symmetries.
We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we prove that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we dis…
A simple and efficient method to create gap solitons is proposed in a spin-orbit-coupled spin-1 Bose-Einstein condensate. We find that a free expansion along the spin-orbit coupling dimension can generate two moving gap solitons, which are identified from a generalized massive Thirring model. The dynamics of gap solitons can be controlled by adjusting spin-orbit coupling parameters.
We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a non-zero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments rev…
We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. This connection establishes a relationship between the GPE soliton and the magnetic soliton of an easy-plane ferromagnet, where the BEC density relates to the square of the in-plane magnetization of the system. This mapping between well known solitons in two distinct physical systems provides an intuitive understanding of various characteristi…
We study numerically the dynamics of quantized vortices and solitons induced by an oscillating potential inside a trapped Bose-Einstein condensate. The dynamics of the topological defects is much different from the case for a linear uniform object; the metamorphosis between vortices and solitons is characteristic of the dynamics. We discuss how vortices are nucleated by an oscillating potential.
We discuss scattering between a bright soliton and a soliton dimer in coupled quasi-one-dimensional dipolar Bose-Einstein condensates. The dimer is formed by each soliton from both tubes due to the attractive inter-layer dipole-dipole interaction. The dipoles within each tube repel each other, and a stable, bright soliton is stabilized via attractive contact interactions. In general, the scattering is inelastic, transferring the kinetic energy into internal modes of both soliton dimer and single soliton. Our studies reveal rich scattering scenarios, including dimer-soliton repulsion at small i…
We study bright solitons in a Bose-Einstein condensate with a spin-orbit coupling that has been realized experimentally. Both stationary bright solitons and moving bright solitons are found. The stationary bright solitons are the ground states and possess well-defined spin-parity, a symmetry involving both spatial and spin degrees of freedom; these solitons are real valued but not positive definite, and the number of their nodes depends on the strength of spin-orbit coupling. For the moving bright solitons, their shapes are found to change with velocity due to the lack of Galilean invariance i…
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 …
The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usu…
Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even non-interacting wave packets.
By solving the three-dimensional Gross-Pitaevskii equation we generate two-dimensional axially-symmetric and anisotropic dipolar Bose-Einstein condensate bright solitons, for repulsive atomic interaction, stabilized by only a weak one-dimensional optical lattice (OL) aligned along and perpendicular, respectively, to the dipole polarization direction. In the former case vortex solitons can also be created. We show that it is possible to make a stable array of small interacting axially-symmetric dipolar solitons put on alternate OL sites. Further, we demonstrate the elastic nature of the collisi…
The hydrodynamics of quantized vortices and solitons in an atomic Bose-Einstein condensate excited by an oscillating potential are studied by numerically solving the two-dimensional Gross-Pitaevskii equation. The oscillating potential keeps nucleating vortex dipoles, whose impulses alternatively change their direction synchronously with the oscillation of the potential. This leads to synergy dynamics of vortices and solitons which have not been previously reported in quantum fluids.
Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark soliton excitations that show periodic density dynamics in real space. In addition to the density feature, solitons also carry a localized pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.
We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.
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 wavefunction, improving upon previous techniques which on…
We describe oblique half-solitons, a new type of topological defects in a two dimensional spinor Bose Einstein condensate. A realistic protocol based on the optical spin Hall effect is proposed toward their generation within an exciton-polariton system.
Considering a periodically oscillating harmonic potential, we explore the dynamics properties of bright solitons in a Bose-Einstein condensate. It is found that under a slower oscillating potential, soliton movement exhibits a nonperiodic oscillation while it is hardly affected under a fast oscillating potential. Furthermore, the head-on and/or "chase" collisions of two solitons have been obtained, which can be controlled by the oscillating frequency of potential.
Formation of oblique solitons by a flow of polariton condensate past an obstacle is considered. The flow is non-uniform due to a finite life-time of polaritons what changes drastically the conditions of formation of oblique solitons compared with the atomic condensate case. The theory shows that the polariton solitons can be generated by a subsonic flow in agreement with the recent experiment [A. Amo {\it et al.}, Science, {\bf 332,} 1167 (2011)]. Geometric form of oblique solitons and other their parameters are calculated analytically and analytical results are confirmed by numerical simulati…
We show that the presence of soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficient enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also r…
We reveal that Hopf solitons can be stabilized in rotating atomic Bose-Einstein condensate. The Hopfion is a matter-wave vortex complex which carries two independent winding numbers. Such a topological solitonic structure results from a superfluid flow of atoms simultaneously quantized in poloidal and toroidal directions. In the framework of a dissipative mean-field model we observe different unstable evolution scenarios of the Hopfions. We demonstrate energetic and dynamical stability of the Hopf solitons under experimentally feasible conditions.
A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An idealized double well geometry is shown to yield perfect energy transfer and complete periodic identity reversal of the two solitons. Two experimentally relevant geometries are analyzed which should enable the observation of this long-range interaction.
We study solitary waves of polarization (magnetic solitons) in a two-component Bose gas with slightly unequal repulsive intra- and interspin interactions. In experimentally relevant conditions we obtain an analytical solution which reveals that the width and the velocity of magnetic solitons are explicitly related to the spin healing length and the spin sound velocity of the Bose mixture, respectively. We calculate the profiles, the energy and the effective mass of the solitons in the absence of external fields and investigate their oscillation in a harmonic trap where the oscillation period i…
We study the dynamical properties of bright-bright solitons in two species Bose-Einstein condensates with the repulsive interspecies interactions under the external harmonic potentials by using a variational approach combined with numerical simulation. It is found that the interactions between bright-bright solitons vary from repulsive to attractive interactions with the increasing of their separating distances. And the bright-bright solitons can be localized at equilibrium positions, different from the periodic oscillation of bright soliton in the single species condensates. Especially, a thr…
Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross-Pitaevskii equation and good q…
A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the co-existing soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter t…
Experiments on ultra-cold attractive Bose-Einstein Condensates (BECs) have demonstrated that at low dimensions atomic clouds can form localized objects, propagating for long times without significant changes in their shapes and attributed to bright matter-wave solitons, which are coherent objects. We consider the dynamics of bright soliton trains from the perspective of many-boson physics. The fate of matter-wave soliton trains is actually to quickly loose their coherence and become macroscopically fragmented BECs. The death of the coherent matter-wave soliton trains gives birth to fragmented …
We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary time evolution of the Gross-Pitaevskii equation. The dipoles are completely polarized along one direction in the 2D plane so as to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive interactions: a plane wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons…
In a cigar shaped Bose-Einstein condensate, explicit solutions of the coupled mean-field equations, describing defect-grey soliton dynamics are obtained, demonstrating the coexistence of grey soliton and a localized defect. Unlike the case of dark soliton, where the defect trapping center has vanishing superfluid density, the moving grey soliton necessarily possesses a finite superfluid component at the defect location. The wave vector of the impurity is controlled by the velocity of the grey soliton, which has an upper bound. It is found that the presence of the impurity lowers the speed of t…
We discuss the comment [ arXiv:1102.2943] by E. Kozik about "Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates [arXiv:1007.4441]".
We report explicitly a novel family of exact PT-symmetric solitons and further study their spontaneous PT symmetry breaking, stabilities and collisions in Bose-Einstein condensates trapped in a PT-symmetric harmonic trap and a Hermite-Gaussian gain/loss potential. We observe the significant effects of mean-field interaction by modifying the threshold point of spontaneous PT symmetry breaking in Bose-Einstein condensates. Our scenario provides a promising approach to study PT-related universal behaviors in non-Hermitian quantum system based on the manipulation of gain/loss potential in Bose-Ein…
We describe a protocol to prepare solitons in a quasi-1d box-trapped Bose-Einstein condensate using only a quench of the isotropic s-wave scattering length. A quench to exactly four times the initial 1d coupling strength creates one soliton at each boundary of the box, which then propagate in a uniform background density and collide with one another. No nonsolotonic excitations are created during the quench. The procedure is robust against imperfections in the scattering length ramp rate and a mismatch of the final scattering length.
We study theoretically the emission of dark solitons induced by a moving defect in a nonresonantly pumped exciton-polariton condensate. The number of created dark solitons per unit of time is found to be strongly dependent on the pump power. We relate the observed dynamics of this process to the oscillations of the drag force experienced by the condensate. We investigate the stability of the polariton quantum fluid and present various types of dynamics depending on the condensate and moving obstacle parameters. Furthermore, we provide analytical expressions for dark soliton dynamics using the …
Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of different type are considered. The general properties of the stationary states are investigated variationally and numerically, and the stability regions of the soliton-soliton pairs are determined.
The stability of dark solitons generated by a supersonic flow of a Bose-Einstein condensate past a concave corner (or a wedge) is studied. It is shown that solitons in the dispersive shock wave generated at the initial moment of time demonstrate a snake instability during their evolution to stationary curved solitons. Time of decay of soliton to vortices agrees very well with analytical estimates of the instability growth rate.
We give explicit connections of quantum one-hole excited states to classical solitons for the one-dimensional Bose gas with repulsive short-range interactions. We call the quantum states connected to classical solitons the quantum soliton states. We show that the matrix element of the canonical field operator between quantum soliton states with $N-1$ and $N$ particles is given by a dark soliton of the Gross-Pitaevskii equation in the weak coupling case. We suggest that the matrix element corresponds to the order parameter of BEC in the quantum soliton state. The result should be useful in the …
We present families of beating dark-dark solitons in spin-orbit (SO) coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are characterized by two different spatial and temporal scales, which are identified by a multiscale expansion method. The solitons are "beating" ones, as they perform density oscillations with a characteristic frequency, relevant to Zitterbewegung (ZB). We find that spin oscillations may occur, depending on the parity of each soliton branch, which consequently lead to Z…
We develop an analytical description of static ferrodark solitons, the $\mathbb{Z}_2$ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed ansatzes show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities and nematic currents of ferrodark solitons are also discussed. The $\mathbb{Z}_2$ topological defects in the mass superfluid order, dar…
Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states of different nature: bright solitons and quantum liquid droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We develop a simple theoretical model to show that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bi-stable region. We experimentally measure their spin composition, extract their density for a broad range of parameters and map out the b…
We study the possibility of using dark soliton in quasi one dimensional Bose Einstein condensates to produce two level system (qubits) by exploiting the intrinsic nonlinear and the coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the soliton and investigate the emission rate of the qubits in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being by the dark soliton "death" due to quantum evaporation.
We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of…
We demonstrate a stable, mobile, dipolar or nondipolar three-dimensional matter-wave soliton in the vortex core of a uniform nondipolar condensate. All intra- and inter-species contact interactions can be repulsive for a strongly dipolar soliton. For a weakly dipolar or nondipolar soliton, the intra-species contact interaction in the soliton should be attractive for the formation of a compact soliton. The soliton can propagate with a constant velocity along the vortex core without any deformation. Two such solitons undergo a quasi-elastic collision at medium velocities. We illustrate the findi…
We study the quantum reflection of a two-dimensional disk-shaped Bose-Einstein condensate with a dark-soliton excitation by a square potential barrier. For the giving geometry, the dark-soliton initially located at the centre of the condensate cloud survive long enough for investigating the reflection process. We show the time evolution of the reflection probability with respect to various width of the barrier. The asymptotic value of the reflection probability is decreased by the existence of a dark-soliton, and is highly sensitive to the initial orientation of the dark-soliton which also aff…
By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without c…
We discuss how to construct stable multidimensional extensions of one-dimensional dark solitons, the so-called soliton stripes, in two-species Bose-Einstein condensates in the immiscible regime. We show how using a second component to fill the core a dark soliton stripe leads to reduced instabilities while propagating in homogeneous media. We also discuss how in the presence of a trap arbitrarily long-lived dark soliton stripes can be constructed by increasing the filling of the dark stripe core. Numerical evidences of the robustness of the dark soliton stripes in collision scenarios are also …
We study center-of-mass oscillations of a dipolar Bose-Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose-Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose-Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced, if the parameters of the condensate are chosen properly. This provides a …
We investigate non-degenerate bound state solitons systematically in multi-component Bose-Einstein condensates, through developing Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound eigen-states in the self-induced effective quantum wells, in sharp contrast to the bright soliton and dark soliton reported before (which usually correspond to ground state and free eigen-state respectively). We further demonstrate that the bound state solitons with nodes are induced by incoherent inter…
We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose--Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities in the core. The order of phase transitions between different solitons and the critical behaviour of relevant continuous transitions are pro…
We examine the stability and dynamics of a family of crossed dark solitons in a harmonically confined Bose-Einstein condensate in two dimensions. Working in a regime where the fundamental snake instability is suppressed, we show the existence of an instability which leads to an interesting collapse and revival of the initial state for the fundamental case of two crossed solitons. The instability originates from the singular point where the solitons cross, and we characterise it by examining the Bogoliubov spectrum. Finally, we extend the treatment to systems of higher symmetry.
Static and dynamic properties of matter-wave solitons in dense Bose-Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross-Pitaevskii equation shows good agreement, thereby validating the proposed approach.
We theoretically investigate the dynamics of two dark solitons in a polariton condensate under nonresonant pumping, based on driven dissipative Gross-Pitaevskii equations coupled to the rate equation. In particular, the analytical expression of the effective potential between two dark solitons is given. The resulting equation of motion captures how the open-dissipative character of a polariton Bose-Einstein condensate affects the properties of dynamics of two-dark soliton, i.e., two-dark soliton relax by blending with the background at a finite time. We further simulate the relative motion of …
We suggest and study the stable disk- and cigar-shaped gap solitons of a dipolar Bose-Einstein condensate of $^{52}$Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) breathing oscillation of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a moving lattice along axial $z$ direction demonstrates the stab…
The truncated Wigner and positive-P phase-space representations are used to study the dynamics of a one-dimensional Bose gas. This allows calculations of the breathing quantum dynamics of higher-order solitons with 10^{3}-10^{5} particles, as in realistic Bose-Einstein condensation (BEC) experiments. Although classically stable, these decay quantum mechanically. Our calculations show that there are large nonlocal correlations. These also violate the Cauchy-Schwarz inequality, showing the presence of nonclassical quantum entanglement.
This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher-dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.
