Two-component Bose-Einstein Condensates Research Articles

Ground States of Two-Component Bose–Einstein Condensates with Josephson Junction: The Endpoint Cases

Ground States of Two-Component Bose–Einstein Condensates with Josephson Junction: The Endpoint Cases

2D Skyrmion topological charge of spin textures with arbitrary boundary conditions: a two-component spinorial BEC as a case study

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

Parallel finite-element codes for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

We present and distribute a parallel finite-element toolbox written in the free software FreeFEM for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions. The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFEM with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method. Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFEM with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states. Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox's results with known theoretical and numerical findings that have been reported in the literature. Program summaryProgram Title: FFEM_BdG_ddm_toolbox.zipCPC Library link to program files:https://doi.org/10.17632/w9hg964wpb.1Licensing provisions: GPLv3Programming language:FreeFEM (v 4.12) free software (www.freefem.org)Nature of problem: Among the plethora of configurations that may exist in Gross-Pitaevskii (GP) equations modeling one or two-component Bose-Einstein condensates, only the ones that are deemed spectrally stable (or even, in some cases, weakly unstable) have high probability to be observed in realistic ultracold atoms experiments. To investigate the spectral stability of solutions requires the numerical study of the linearization of GP equations, the latter commonly known as the Bogoliubov-de Gennes (BdG) spectral problem. The present software offers an efficient and reliable tool for the computation of eigenvalues (or modes) of the BdG problem for a given two- or three-dimensional GP configuration. Then, the spectral stability (or instability) can be inferred from its spectrum, thus predicting (or not) its observability in experiments.Solution method: The present toolbox in FreeFEM consists of the following steps. At first, the GP equations in two (2D) and three (3D) spatial dimensions are discretized by using P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. For a given configuration of interest, mesh adaptivity in FreeFEM is deployed in order to reduce the size of the problem, thus reducing the toolbox's execution time. Then, stationary states of the GP equations are obtained by a Newton method whose backbone involves the use of a reliable and efficient linear solver judiciously selected from the PETSc1 library. Upon identifying stationary configurations, to trace branches of such solutions a parameter continuation method over the chemical potential in the GP equations (effectively controlling the number of atoms in a BEC) is employed with step-size adaptivity of the continuation parameter. Finally, the computation of the stability of branches of solutions (i.e. the BdG spectrum), is carried out by accurately solving, at each point in the parameter space, the underlying eigenvalue problem by using the SLEPc2 library. Three-dimensional computations are made affordable in the present toolbox by using the domain decomposition method (DDM). In the course of the computation, the toolbox stores not only the solutions but also the eigenvalues and respective eigenvectors emanating from the solution to the BdG problem. We offer examples for computing stationary configurations and their BdG spectrum in one- and two-component GP equations.Running time: From minutes to hours depending on the mesh resolution and space dimension.

Finite-frequency normal and superfluid drag effects in two-component atomic Bose-Einstein condensates

Finite-frequency normal and superfluid drag effects in two-component atomic Bose-Einstein condensates

Beliaev damping of gapped excitations in a two-component Bose-Einstein condensate

Beliaev damping of gapped excitations in a two-component Bose-Einstein condensate

Superradiant phononic emission from the analog spin ergoregion in a two-component Bose–Einstein condensate

Superradiant phononic emission from the analog spin ergoregion in a two-component Bose–Einstein condensate

Observation of dense collisional soliton complexes in a two-component Bose-Einstein condensate

Solitons are nonlinear solitary waves which maintain their shape over time and through collisions, occurring in a variety of nonlinear media from plasmas to optics. We present an experimental and theoretical study of hydrodynamic phenomena in a two-component atomic Bose-Einstein condensate where a soliton array emerges from the imprinting of a periodic spin pattern by a microwave pulse-based winding technique. We observe the ensuing dynamics which include shape deformations, the emergence of dark-antidark solitons, apparent spatial frequency tripling, and decay and revival of contrast related to soliton collisions. For the densest arrays, we obtain soliton complexes where solitons undergo continued collisions for long evolution times providing an avenue towards the investigation of soliton gases in atomic condensates.

Metastable patterns in one- and two-component dipolar Bose-Einstein condensates

In this paper we study metastable states in single- and two-component dipolar Bose-Einstein condensates. We show that this system supports a rich variety of states that are remarkably stable despite not being ground states. In a parameter region where striped phases are ground states, we find such metastable states that are energetically favorable compared to triangular and honeycomb lattices. Among these metastable states we report a peculiar ring-lattice state, which is led by the competition between triangular and honeycomb symmetries and rarely seen in other systems. In the case of dipolar mixtures we show that via tuning the miscibility these states can be stabilized in a broader domain by utilizing interspecies interactions. Published by the American Physical Society 2024

Stability of vortices in exciton-polariton condensates with spin–orbital-angular-momentum coupling

The existence and dynamics of stable quantized vortices is an important subject of quantum many-body physics. Spin–orbital-angular-momentum coupling (SOAMC), a special type of spin–orbit coupling, has been experimentally achieved to create vortices in atomic Bose–Einstein condensates (BEC). Here, we generalize the concept of SOAMC to a two-component polariton BEC and analyze the emergence and configuration of vortices under a finite-size circular pumping beam. We find that the regular configuration of vortex lattices induced by a finite-size circular pump is significantly distorted by the spatially dependent Raman coupling of SOAMC, even in the presence of a repulsive polariton interaction which can assist the forming of stable vortex configuration. Meanwhile, a pair of vortices induced by SOAMC located at the center of polariton cloud remains stable. When the Raman coupling is sufficiently strong and interaction is weak, the vortices spiraling in from the edge of polariton cloud will disrupt the polariton BEC.

Vortex solutions in a binary immiscible Bose-Einstein condensate

We consider the mean-field vortex solutions and their stability within a two-component Bose-Einstein condensate in the immiscible limit. A variational approach is employed to study a system consisting of a majority component which contains a single quantized vortex and a minority component which fills the vortex core. We show that a super-Gaussian function is a good approximation of the two-component vortex solution for a range of atom numbers of the infilling component by comparing the variational solutions to the full numerical solutions of the coupled Gross-Pitaevskii equations. We subsequently examine the stability of the vortex solutions by perturbing the infilling component away from the center of the vortex core, thereby demonstrating their stability to small perturbations. Finally, we consider the dynamics of infilled vortices. Published by the American Physical Society 2024

Two-dimensional vector solitons in Bose-Einstein-condensate mixtures

We derive two decoupled KP-I equations from the system of two-dimensional (2D) Gross-Pitaevskii equations for a two-component Bose-Einstein condensate (BEC), using the multiple-scale expansion method. We produce asymptotic analytical vector-soliton solutions, viz., dark-dark (DD) and dark-antidark (DAD) one-soliton and two-soliton states, by tuning coupling constants and norms of species, and address their evolution numerically under the action of the harmonic-oscillator (HO) trap, in the local-density approximation. We find that shallow single-line DD and DAD solitons are stable, while single-lump DAD solutions (weakly localized truly-2D states) split and lead to nucleation of two half-vortices. We also find that the BEC mixture placed in the HO trap admits stable asymptotic multi-soliton solutions, e.g., two-line DD and DAD solitons and two-lump DD ones, which were not reported before. In particular, the two-lump solutions describe inelastic collisions between the lumps. The analysis developed in this work may also be applied to systems with spin-orbit coupling and gauge fields, which have been realized in atomic BEC.

Fluctuation-driven self-trapping in Bose-Bose mixtures

We investigate the collective dynamics of two-component Bose-Einstein condensates in a double well potential. By taking into account the Lee-Huang-Yang (LHY) correction from quantum fluctuation, we find that the LHY term, though much smaller than the mean field interactions, can significantly change the coherent oscillating behaviors of the bosonic Josephson junction in the regime of g12≃−g11g22. Besides the quantitative renormalization to the plasma frequencies of the Josephson oscillations, a series of unexpected nonzero fixed points beyond mean field emerges in the stationary state. More remarkably, unique macroscopic self-trapping states, which are usually absent in the mean field dynamics, can be sustained by the LHY nonlinearity. Our results reveal the nontrivial LHY effect on the Josephson dynamics, which can be tested in the current experiment. Published by the American Physical Society 2024

Ground state of Rydberg-dressed Bose gas confined in a toroidal trap

The experimental realization of Rydberg dressing technology in ultracold atomic systems provides another superior platform for studying novel states of matter and macroscopic quantum phenomena. In this work, based on the mean-field theory, we have investigated the ground-state phases of a two-component Bose–Einstein condensate with Rydberg interaction and confined in a toroidal trap. The effects of the Rydberg interaction and external potential, especially the Rydberg blockade radius, on the ground-state structure of such a system have been investigated in full parameter space. Our results show that the Rydberg blockade radius, which can be regarded as another controllable parameter, can be used to obtain a variety of ground-state phases. More interestingly, it is found that for weak Rydberg interactions, the Rydberg blockade radius breaks the spontaneous rotational symmetry of the system, leading to the formation of a discrete unit cell structure. For strongly interacting cases, it can be used to realize different orders of discrete rotational symmetry breaking.

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

Quantum simulation and Anderson localization in vector rogue waves of Bose-Einstein condensate

We report the existence of vector rogue waves in a coupled Bose-Einstein condensate, trapped in a bichromatic optical lattice, which is an appropriate platform for quantum simulation. Such two-component Bose-Einstein condensate plays a vital role to beget hybrid mixtures and structural transition of nonlinear excitations like rogue waves and solitons. An efficient manipulation of rogue waves is embraced, where we identify the slowing down and stopping of dark rogue wave by lattice engineering. This may nurture quantum memory application and transform the rogue wave mixture immiscible. The existence of Anderson localized rogue wave at the central frustrated lattice site is confirmed by showing the exponential nature and localization length of the condensate. A merging of a dual Anderson rogue waves is manifested in their coherent control. Numerical stability analysis is also carried out for a wide range of trap parameters for experimental viability.

Interface of Two-component Bose-Einstein Condensates in Double-parabola Approximation

In this work we proposed a simple method to determine the coordinate of interface of two-component Bose-Einstein condensates (BECs) in double parabola approximation (DPA). Based on this idea, the static properties of BECs have been investigated totally in DPA

Stability analysis of nonlinear localized modes in the coupled Gross-Pitaevskii equations with [Formula: see text] -symmetric Scarf-II potential.

We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability of the nonlinear modes in the focusing and defocusing cases, and get the stable and unstable domains of nonlinear localized modes. Then we validate the results by evolving them with 5% perturbations as an initial condition. Finally, we get stable solitons by considering excitations of the soliton via adiabatical change of system parameters. These findings of nonlinear modes can be potentially applied to physical experiments of matter waves in Bose-Einstein condensates.

Asymmetric solitons induced by transition and beating effects

We investigate the dynamics of beating solitons in a two-component Bose–Einstein condensate with tunable Rabi coupling strength. Our results demonstrate that the balance between transition and beating effects permits the emergence of a novel family of asymmetric solitons in the symmetric physical settings. We derive the exact analytical solutions for them, which primarily consist of one bright soliton and one dark soliton element. The analytical solutions provide us with precise balance conditions required for the formation of asymmetric solitons. We also show that the degree of asymmetry can be effectively manipulated by adjusting the background density flow of dark soliton element, initial relative phase between two soliton elements, and their width. Furthermore, we discuss the oscillation behavior of asymmetric solitons in a harmonic potential, and the interaction between them.

A finite element toolbox for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

We present a finite element toolbox for the computation of Bogoliubov-de Gennes modes used to assess the linear stability of stationary solutions of the Gross-Pitaevskii (GP) equation. Applications concern one (single GP equation) or two-component (a system of coupled GP equations) Bose-Einstein condensates in one, two and three dimensions of space. An implementation using the free software ▪is distributed with this paper. For the computation of the GP stationary (complex or real) solutions we use a Newton algorithm coupled with a continuation method exploring the parameter space (the chemical potential or the interaction constant). Bogoliubov-de Gennes equations are then solved using dedicated libraries for the associated eigenvalue problem. Mesh adaptivity is proved to considerably reduce the computational time for cases implying complex vortex states. Programs are validated through comparisons with known theoretical results for simple cases and numerical results reported in the literature. Program summaryProgram Title: FFEM_BdG_toolbox.zipCPC Library link to program files:https://doi.org/10.17632/dgypyc34gb.1Licensing provisions: Apache 2.0Programming language:▪(v 4.12) free software (www.freefem.org)Nature of problem: The software computes Bogoliubov-de Gennes (BdG) complex modes of Bose-Einstein condensates described by the Gross-Pitaevskii (GP) equation. BdG equations are obtained by linearizing the GP equation (or the system of coupled GP equations) around a stationary solution. Obtained BdG modes are used to assess on the stability of stationary states.Solution method: Stationary states of the GP equation are obtained by a Newton algorithm. Parameter space is explored using a continuation on the chemical potential. Once the stationary (complex or real) state is captured accurately, BdG modes are computed by solving the associated eigenvalue problem with the ARPACK library. Complex eigenvalues and eigenvectors are computed and stored. The wave function is discretized by P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. Mesh adaptation is implemented to reduce the computational time. Examples are given for stationary states in one- and two-component Bose-Einstein condensates.

Construction of infinitely many solutions for two-component Bose-Einstein condensates with nonlocal critical interaction

In this paper, we deal with the coupled Hartree system with axisymmetric potentials,{−Δu+P(|x′|,x″)u=α1(|x|−4⁎u2)u+β(|x|−4⁎v2)uinR6,−Δv+Q(|x′|,x″)v=α2(|x|−4⁎v2)v+β(|x|−4⁎u2)vinR6, where (x′,x″)∈R2×R4, β>max⁡{α1,α2}≥min⁡{α1,α2}>0, P(|x′|,x″) and Q(|x′|,x″) are bounded nonnegative functions in R+×R4. The system is critical in the sense of the Hardy-Littlewood-Sobolev inequality. When the functions r2P(r,x″) and r2Q(r,x″) have a common topologically nontrivial critical point, using a finite dimensional reduction argument and developing new local Pohožaev identities, we construct infinitely many solutions of synchronized type, whose energy can be made arbitrary large. The main difficulty is caused by the non-local terms, since little is known about the nondegeneracy of the positive solutions of the limit system and the error estimates of the nonlocal parts in applying the reduction arguments and establishing the local Pohožaev identities.