We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space, due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system, and study their stability. In most cases, the VA provides good accuracy, and correctly predicts the stability by means of the Vakhitov-Kolokolov (VK)\ criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI, and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes.
Thermal effects on density-modulated phases in a dipolar Bose--Einstein condensate
College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；Key Laboratory of Aerospace Information Materials and Physics (Nanjing University of Aeronautics and Astronautics), MIIT（工业和信息化部航空航天信息材料与物理重点实验室（南京航空航天大学））
The experimental realization of time dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one dimensional two components lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of exotic hidden magnetic phases. The magnetism, characterized solely by string-like nonlocal order parameters, manifests itself both in the charge and, noticeably, in the spin degrees of freedom. Such behavior is enlighten by…
We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einstein condensate (BEC) soliton with a notch in the central plane formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BEC, where one can have a dark-in-bright soliton coupled to a bright solit…
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.
We demonstrate robust, stable, mobile two-dimensional (2D) dipolar ring-dark-in-bright (RDB) Bose-Einstein condensate (BEC) solitons for repulsive contact interaction, subject to a harmonic trap along the $y$ direction perpendicular to the polarization direction $z$. Such a RDB soliton has a ring-shaped notch (zero in density) imprinted on a 2D bright soliton free to move in the $x-z$ plane. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The possibility of creating the RDB soliton by phase imprinting is demonstrated. …
We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to the 1D OL trap can have both repulsive and attractive contact interactions. The dark-in-bright solitons are the excited states of the bright solitons. The solitons, when subject to a small perturbation, exhibit sustained breathing oscillation. The dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium vel…
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 demonstrate stable, robust, bright dipolar Bose-Einstein condensate (BEC) solitons, moving in a direction perpendicular to the polarization direction, formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. Upon small perturbation the solitons are found to exhibit sustained breathing oscillation. The findings are illustrated by numerical simulation using the 3D mean-field Gross-Pitaevskii equation and a reduced 2D model in three and two spatial dimensions …
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…
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 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…
We study the formation of stable bright solitons in quasi-one-dimensional (quasi-1D) spin-orbit- (SO-) and Rabi-coupled two pseudospinor dipolar Bose-Einstein condensates (BECs) of 164 Dy atoms in the presence of repulsive contact interactions. As a result of the combined attraction-repulsion effect of both interactions and the addition of SO and Rabi couplings, two kinds of ground states in the form of self-trapped bright solitons can be formed, a plane-wave soliton (PWS) and a stripe soliton (SS). These quasi-1D solitons cannot exist in a condensate with purely repulsive contact interactions…
We investigate the coherent collision of anisotropic quasi-two-dimensional bright solitons in dipolar Bose-Einstein condensates. Our analysis is based on the extended Gross-Pitaevskii equation, and we use the split-operator method for the grid calculations and the time-dependent variational principle with an ansatz of coupled Gaussian functions to calculate the time evolution of the ground state. We compare the results of both approaches for collisions where initially the solitons are in the repelling side-by-side configuration and move towards each other with a specific momentum. We change th…
We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed in Phys. Rev. Lett. 100, 090406 (2008). A challenging feature of the expected solitons is their strong inherent anisotropy, due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended Gross-Pitaevskii equa…
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 …
The dynamics of a two-soliton molecule bouncing on the reflecting atomic mirror under the effect of gravity has been studied by analytical and numerical methods. The analytical description is based on the variational approximation. In numerical simulations, we observe the resonance oscillations of the two-soliton's center-of-mass position and width, induced by modulated atomic mirror. Theoretical predictions are verified by numerical simulations of the nonlocal Gross-Pitaevskii equation (GPE) and qualitative agreement between them is found. Hamiltonian dynamic system for a dipolar Bose-Einstei…
We consider a bilayer system of two-dimensional Bose-Einstein-condensed dipolar dark excitons (upper layer) and bright ones (bottom layer). We demonstrate that the interlayer interaction leads to a mixing between excitations from different layers. This mixing leads to the appearance of a second spectral branch in the spectrum of bright condensate. The excitation spectrum of the condensate of dark dipolar excitons then becomes optically accessible during luminescence spectra measurements of the bright condensate, which allows one to probe its kinetic properties. This approach is relevant for ex…
Stabilizing vortex solitons with high values of the topological charge, S, is a challenging issue in optics, studies of Bose-Einstein condensates (BECs) and other fields. To develop a new approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, $V(r)\sim \cos (2r+δ)$, with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions (DDIs). Two radial lattices are considered, with $δ=0$ and $π$, i.e., a potential maximum or mini…
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a pancake confinement at $T=0$ K and study the effect of quantized vorticity on the phases that can be realized depending upon the ratio between dipolar and short-range interaction. By increasing this ratio the system undergoes a spontaneous density modulation in the form of an ordered arrangement o…
The bright, dark and grey solitons are well-known soliton solutions of the Gross-Pitaevskii equation for the attractive and repulsive BEC. We consider solitons in the dipolar BEC of the fully polarized particles, speaking of the dipolar BEC we mean both the magnetized BEC and the electrically polarized BEC. We show that these two types of the dipolar BEC reveal different behavior of the collective excitations. This is related to the fact that the electric and the magnetic fields satisfy to the different pairs of the Maxwell equation set. Thus we consider them independently. We obtain exact ana…
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 demonstrate fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction the first species may spatially separate from the second species thus forming a demixed configuration, which can be spatially-symmetric or symmetry-broken. In the spatially-symmetric case, one of the the species occupies the central region, whereas the other species separates into two equal parts and stay predominantly out of…
We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimen…
The possibility of generating stable anisotropic solitons in dipolar Bose-Einstein condensates (BECs) leads to a different scenario not possible in a nondipolar BEC with contact interaction. We study the statics and dynamics of anisotropic bright solitons in quasi-two-dimensional BECs consisting of polarized dipolar atoms.We study the collision dynamics of two such solitons at different velocities for different angles between the polarization and collision directions. The collision is found to be quasi elastic at large velocities. At small velocities the collision is inelastic leading to the f…
Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions suppo…
We numerically study the breathing dynamics induced by collision between bright solitons in the one-dimensional Bose-Einstein condensates with strong dipole-dipole interaction. This breathing phenomenon is closely related to the after-collision short-lived attraction of solitons induced by the dipolar effect. The initial phase difference of solitons leads to the asymmetric dynamics after collision, which is manifested on their different breathing amplitude, breathing frequency, and atom number. We clarify that the asymmetry of breathing frequency is directly induced by the asymmetric atom numb…
Solitons in the extended hydrodynamic model of the dipolar Bose-Einstein condensate with quantum fluctuations are considered. This model includes the continuity equation for the scalar field of concentration, the Euler equation for the vector field of velocity, the pressure evolution equation for the second rank tensor of pressure, and the evolution equation for the third rank tensor. Large amplitude soliton solution caused by the dipolar part of quantum fluctuations is found. It appears as the bright soliton. Hence, it is the area of compression of the number of particles. Moreover, it exists…
We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $\sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons…
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 consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solit…
The interaction between two bright solitons in a dipolar Bose-Einstein condensate (BEC) has been investigated aiming at finding the regimes when they form a stable bound state, known as soliton molecule. To study soliton interactions in BEC we employed a method similar to that used in experimental investigation of the interaction between solitons in optical fibers. The idea consists in creating two solitons at some spatial separation from each other at initial time $t_0$, and then measuring the distance between them at a later time $t_1 > t_0$. Depending on whether the distance between soliton…
The formation of a dense Bose-Einstein condensate in dark spin states of two-dimensional dipolar excitons is shown to be driven by a dynamical transition to the long-lived dark states. The condensate is stabilized by strong dipole-dipole interactions up to densities high enough for a dark quantum liquid to form. The persistence of dark condensation was observed in recent experiments. A model describing the non-equilibrium dynamics of externally driven coupled dark and bright condensates reproduces the step-like dependence of the exciton density on the pump power or on temperature. This unique …
Confinement-controlled pattern selection in a finite population-imbalanced dipolar Bose-Einstein condensate
College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT（工业和信息化部航空航天信息材料与物理重点实验室）；School of Physics and Zhejiang Institute of Modern Physics, Zhejiang University（浙江大学物理系及现代物理研究所）；Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University（浙江大学浙江省量子技术与器件重点实验室）
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional (1D) flat-top fundamental and multipole solitons, two-dime…
We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that …
We introduce an effectively one-dimensional (1D) model of a bosonic gas of particles carrying collinear dipole moments which are induced by an external polarizing field with the strength periodically modulated along the coordinate, which gives rise to an effective nonlocal nonlinear lattice in the condensate. The existence, shape and stability of bright solitons, appearing in this model, are investigated by means of the variational approximation and numerical methods. The mobility of solitons and interactions between them are studied too.
We study matter-wave bright solitons in spin-orbit (SO) coupled Bose-Einstein condensates (BECs) with attractive interatomic interactions. We use a multiscale expansion method to identify solution families for chemical potentials in the semi-infinite gap of the linear energy spectrum. Depending on the linear and spin-orbit coupling strengths, the solitons may resemble either standard bright nonlinear Schrödinger solitons or exhibit a modulated density profile, reminiscent of the stripe phase of SO-coupled repulsive BECs. Our numerical results are in excellent agreement with our analytical find…
The possible phases and the nano-scale particle correlations of two-dimensional interacting dipolar particles is a long-sought problem in many-body physics. Here we observe a spontaneous condensation of trapped two-dimensional dipolar excitons with internal spin degrees of freedom from an interacting gas into a high density, closely packed liquid state made mostly of dark dipoles. Another phase transition, into a bright, highly repulsive plasma is observed at even higher excitation powers. The dark liquid state is formed below a critical temperature $T_c \approx 4.8K$, and it is manifested by …
Smooth time-dependent control of dipolar Bose-Einstein condensates
University of the Basque Country UPV/EHU（巴斯克国立大学）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基奎科学基金会）；CSIC（西班牙国家科学研究委员会）；Instituto de Ciencia de Materiales de Madrid (ICMM)（马德里材料科学研究所）；Donostia International Physics Center DIPC（圣塞巴斯蒂安国际物理中心）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；University College Cork（科克大学学院）
The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas with dipole-dipole (DD) interactions is reported. The governing equation is taken as the quintic nonlinear Schrödinger equation (NLSE) with the nonlocal cubic term accounting for the DD attraction. In different regions of the parameter space (the dipole moment and atom number), matter-wave solitons feature flat-top or compacton-like shapes. For the flat-top states, the NLSE with the local cubic-quintic (CQ) nonlinearity is shown to be a good approximation. Specific dynamical effects are studied assuming that the stre…
We demonstrate the existence of one and two-dimensional bright solitons in the Bose-Einstein condensate with repulsive dipole-dipole interactions induced by a combination of dc and ac polarizing fields, oriented perpendicular to the plane in which the BEC is trapped, assuming that the strength of the fields grows in the radial ($r$) direction faster than $r^{3}$. Stable tightly confined 1D and 2D fundamental solitons, twisted solitons in 1D, and solitary vortices in 2D are found in a numerical form. The fundamental solitons remain robust under the action of an expulsive potential, which is ind…
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multi-atom Schrödinger equation, we discover that such systems can exhibit not only the well known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly…
We consider quantum phase transitions in a system of bright dipolar excitons which can form bound pairs (dipolar biexcitons). We assume a narrow resonance in the interaction of excitons with opposite spins. At sufficiently large density a resonant exciton superfluid transforms into a superfluid of biexcitons. The transition may be either of the first or the second kind. The average relative momenta of excitons in the pairs being beyond the light cone, the transition should be accompanied by reduction of the photoluminescence intensity. Effective magnetic fields due to the long-range exchange s…
Several new features arise in the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. Thi…
We describe the behavior of a repulsively interacting Bose-Einstein condensate of indirect dipolar exciton gas in a double quantum well (QW) system under external static or dynamic electric fields at finite temperatures. Electrostatic perturbation is considered to be created by an impurity atom or shot-range defect of QW fluctuation. The screening of this defect potential by an exciton condensate is studied. We find asymptotic spatial dependence of the screened potential and analyse its dependence on the temperature and exciton concentration. It is shown that the asymptotic of the screened pot…
Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long range dipolar interactions on a two-leg ladder. Using two complimentary variational approaches, valid for weak interactions, we find rich physics driven by the long range forces. Generically, long range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. Nearest neighbor interactions produce a novel interleg charge density wave phase, where the total density remains uniform, but the density on each leg of…
Using time dependent nonlinear (s-wave scattering length) coupling between the components of a weakly interacting two component Bose-Einstein condensate (BEC), we show the possibility of matter wave switching (fraction of atoms transfer) between the components via shape changing/intensity redistribution (matter redistribution) soliton interactions. We investigate the exact bright-bright N-soliton solution of an effective one-dimensional (1D) two component BEC by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. In particular, we show that the effective 1D c…
