We demonstrate exotic stable quasi-two-dimensional solitons in a Rashba or a Dresselhaus spin-orbit (SO) coupled hyperfine spin-1 ($F=1$) trap-less antiferromagnetic Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, the solitons are of the $(-1,0,+1)$ or $(+1,0,-1)$ type with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, where the numbers in the parentheses denote angular momentum in spin components $F_z= +1,0,-1$, respectively. For intermediate SO coupling, the solitons have multi-ring structure maintaining the above-mentioned vortices in respective components. For larger SO coupling, superlattice solitons with a square-lattice structure in total density are found in addition to stripe solitons with stripe pattern in component densities with no periodic modulation in total density.
We consider a parametrically forced Bose-Einstein condensate in the combined presence of an optical lattice and harmonic oscillator potential in the mean field approach. A spatial symmetry broken Bose-condensed phase in non-inertial and inertial frame yields a stripe phase in the presence of both cubic and quintic nonlinearities. We show that existence of such stripe phase solely depends on the interplay between the quintic nonlinearity and lattice potential. Furthermore, we observe that a time-dependent harmonic oscillator frequency destroys such stripe ordering. A linear stability analysis o…
We consider an attractive quasi-one dimensional spin-orbit coupled Bose-Einstein condensate (SOC BEC) confined in a periodic potential produced by the combination of linear and nonlinear optical lattices, and study the effects of squeezing a stripe soliton by varying the inter-atomic interaction in the nonlinear lattice. It is observed that the nodes on the soliton arising entirely due to the effect of spin-orbit coupling tend to disappear as we increase the squeezing effect to finally get a stable fundamental soliton. This leads us to conclude that external pressure can reduce the effect of s…
The recent experimental realization of spin-orbit coupling for ultracold atomic gases opens a new avenue for engineering solitons with internal spatial structures through tuning atomic band dispersions. However, the types of the resulting stripe solitons in a spin-1/2 Bose-Einstein condensate (BEC) have been limited to dark-dark or bright-bright with the same density profiles for different spins. Here we propose that general types of stripe solitons, including magnetic stripe (e.g., dark-bright) and localized stripe waves (neither bright nor dark), could be realized in a spin-1 BEC with widely…
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 report on a theoretical study of a ring-shaped Bose-Einstein condensate with Raman-induced spin-orbital-angular-momentum coupling. We analyze the structure of the ground-state of the system depending different physical parameters and reveal a peculiar fine structure within the stripe phase on the phase diagram. We demonstrate the existence of the predicted stripe sub-phases within a wide range of physical parameters, their traceability through physical observables, and compare the results with several commonly used variational approximations. We also show that predicted sub-phases of the st…
We study numerically the structure of a vortex lattice in two-component Bose-Einstein condensates with equal atomic masses and equal intra- and inter-component coupling strengths. The numerical simulations of the Gross-Pitaevskii equation show that the quantized vortices form uncertain lattice configurations accompanying the vortex stripes, honeycomb lattices, and their complexes. This is a result of the degeneracy of the system for the SU(2) symmetric operation, which makes a continuous transformation between the above structures. In terms of the pseudospin representation, the complex lattice…
A weakly interacting, spin-orbit coupled, ultracold, dilute Bose gas on a two-dimensional square lattice with an external Zeeman field is studied. We explore the plane and stripe wave phases of the system involving nonzero condensate momenta, which occur when the Zeeman field is below a critical value. Their excitation spectra are found using Bogoliubov theory and by two different routes. The validity of each method to obtain the excitation spectrum is discussed, and it is found that projection on the lowest single-particle band is an excellent approximation in the plane wave phase, while it i…
Traveling supersolid stripe patterns in spin-orbit-coupled Bose-Einstein condensates
CNR NANOTEC, Institute of Nanotechnology（意大利国家研究委员会纳米技术研究所）；Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；University of Amsterdam（阿姆斯特丹大学）
We predict that spatially modulated Zeeman splitting resulting in the formation of Zeeman lattice can be used for creation of localized self-sustained excitations in spinor polariton condensates with dominant repulsive interactions. In such lattices, the phenomenon of TE-TM splitting, playing the role of effective spin-orbit interaction, leads to the emergence of the stripe phase and formation of stable gap-stripe solitons with complex intrinsic structure resulting from the presence of two characteristic spatial scales, one of which is set by the period of Zeeman lattice, while other is set by…
The coupled dynamics of the atom and photon fields in optical ring cavities with two counter-propagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is e…
We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. In recent works, it was concluded that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result cruci…
In the present work we examine the statics and dynamics of multiple parallel dark soliton stripes in a two-dimensional Bose-Einstein condensate. Our principal goal is to study the effect of the interaction between the stripes on the transverse instability of the individual stripes. We use a recently developed adiabatic invariant formulation to derive a quasi-analytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. The cases of two-, three- and four-stripe states are studied in detail. We subsequently test our pred…
Quantized vortices are the prototypical feature of superfluidity. Pervasive in all natural systems, vortices are yet to be observed in dipolar quantum gases. Here, we exploit the anisotropic nature of the dipole-dipole interaction of a dysprosium Bose-Einstein condensate to induce angular symmetry breaking in an otherwise cylindrically symmetric pancake-shaped trap. Tilting the magnetic field towards the radial plane deforms the cloud into an ellipsoid through magnetostriction, which is then set into rotation. At stirring frequencies approaching the radial trap frequency, we observe the genera…
In the present work, we develop an adiabatic invariant approach for the evolution of quasi-one-dimensional (stripe) solitons embedded in a two-dimensional Bose-Einstein condensate. The results of the theory are obtained both for the one-component case of dark soliton stripes, as well as for the considerably more involved case of the two-component dark-bright (alias "filled dark") soliton stripes. In both cases, analytical predictions regarding the stability and dynamics of these structures are obtained. One of our main findings is the determination of the instability modes of the waves as a fu…
Recently, stripe phases in spin-orbit coupled Bose-Einstein condensates (BECs) have attracted much attention since they are identified as supersolid phases. In this paper, we exploit experimentally reachable parameters and show theoretically that annular stripe phases with large stripe spacing and high stripe contrast can be achieved in spin-orbital-angular-momentum coupled (SOAMC) BECs. In addition to using Gross-Pitaevskii numerical simulations, we develop a variational ansatz that captures the essential interaction effects to first order, which are not present in the ansatz employed in prev…
Supersolidity - a coexistence of superfluidity and crystalline or amorphous density variations - has been vividly debated ever since its conjecture. While the initial focus was on helium-4, recent experiments uncovered supersolidity in ultra-cold dipolar quantum gases. Here, we propose a new self-bound supersolid phase in a binary mixture of Bose gases with short-range interactions, making use of the non-trivial properties of spin-orbit coupling. We find that a first-order phase transition from a self-bound supersolid stripe phase to a zero-minimum droplet state of the Bose gas occurs as a fun…
Soon after its theoretical prediction, striped-density states in the presence of synthetic spin-orbit coupling were realized in Bose-Einstein condensates of ultracold neutral atoms [J.-R. Li et al., Nature \textbf{543}, 91 (2017)]. The achievement opens avenues to explore the interplay of superfluidity and crystalline order in the search for supersolid features and materials. The system considered is essentially made of two linearly coupled Bose-Einstein condensates, that is a pseudo-spin-$1/2$ system, subject to a spin-dependent gauge field $σ_z \hbar k_\ell$. Under these conditions the strip…
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…
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 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 …
Mass-anisotropy driven stripe pattern formation and directional modulational instability in polariton condensate
Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）；Indian Institute of Technology Gandhinagar（印度理工学院甘地纳加尔分校）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Physics, Virginia Tech（弗吉尼亚理工大学物理系）
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.
The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling. This phase has been recently found experimentally [J.~Li \textit{et al.}, Nature (London) \textbf{543}, 91 (2017)]. In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes…
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.
While a spin-orbit-coupled spin-1 Bose-Einstein condensate has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin-orbit-coupled spin-1 Bose-Einstein condensate. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin-orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of r…
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…
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…
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.
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…
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…
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…
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.
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 soliton…
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 …
In this letter we consider the dynamic behaviors of spin-orbit coupled Bose condensates realized in recent experiments. We show that there exists an interaction induced ac Hall response which is absent in a non-interacting system. This condensate has two distinct equilibrium phases known as the plane wave phase and the stripe phase. In the plane wave phase, we show that an ac longitudinal current will induce an ac radial current in the transverse direction, and vice versa, as a cooperation effect of spin-velocity locking and spin-dependent interaction. In the stripe phase, we show that the dom…
We propose a method to analytically solve the one-dimensional coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. In a uniform external potential, the Hamiltonian comprises the kinetic energy, the linear and the quadratic Zeeman energies. Several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates. These solutions are general that contain neither approximations nor constraints on the system parameters.
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.
It is a common view that rotational motion in a superfluid can exist only in the presence of quantized vortices. However, in our numerical studies on the merging of two concentric Bose-Einstein condensates with axial symmetry in two-dimensional space, we observe the emergence of a spiral dark soliton when one condensate has a non-zero initial angular momentum. This spiral dark soliton enables the transfer of angular momentum between the condensates and allows the merged condensate to rotate even in the absence of quantized vortices. We examine the flow field around the soliton and reveal that …
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…
We present a comprehensive analysis of the form and interaction of dipolar bright solitons across the full parameter space afforded by dipolar Bose-Einstein condensates, revealing the rich behaviour introduced by the non-local nonlinearity. Working within an effective one-dimensional description, we map out the existence of the soliton solutions and show three collisional regimes: free collisions, bound state formation and soliton fusion. Finally, we examine the solitons in their full three-dimensional form through a variational approach; along with regimes of instability to collapse and runaw…
We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a variational approximation and a numerical solution. Plots of chemical potential and root mean square (rms) size of solitons are obtained for the quasi-one-dimensional model of three different dipolar condensates of 52Cr, 168Er and 164Dy atoms. The results achieved are in good agreement with those produced by the full three-dimensional mean-field model of the …
Significant experimental progress has been made recently for observing long-sought supersolid-like states in Bose-Einstein condensates, where spatial translational symmetry is spontaneously broken by anisotropic interactions to form a stripe order. Meanwhile, the superfluid stripe ground state was also observed by applying a weak optical lattice that forces the symmetry breaking. Despite of the similarity of the ground states, here we show that these two symmetry breaking mechanisms can be distinguished by their collective excitation spectra. In contrast to gapless Goldstone modes of the \text…
Supersolidity is an intriguing concept. It combines the property of superfluid flow with the long-range spatial periodicity of solids, two properties which are often mutually exclusive. The original discussion of quantum crystals and supersolidity focuses on solid Helium-4 where it was predicted that vacancies could form dilute weakly interacting Bose-Einstein condensates. In this system, direct observation of supersolidity has been elusive. The concept of supersolidity was then generalized to include other superfluid systems which break the translational symmetry of space. One of such systems…
