Two-component Bose-Einstein Condensates Research Articles

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.

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.

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.

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

Effects of quantum fluctuations on macroscopic quantum tunneling and self-trapping of a BEC in a double-well trap

In this paper, we study the influence of quantum fluctuations (QFs) on the macroscopic quantum tunneling and self-trapping (ST) of a two-component Bose–Einstein condensate in a double-well trap. QFs are described by the Lee–Huang–Yang (LHY) term in the modified Gross–Pitaevskii (GP) equation. Employing the modified GP equation in a scalar approximation, we derive a dimer model using a two-mode approximation. The frequencies of Josephson oscillations and ST conditions under QFs are found analytically and proven by numerical simulations of the modified GP equation. The tunneling and localization phenomena are also investigated for the case of the LHY fluid loaded in a double-well potential.

Systematic solitary waves from their linear limits in two-component Bose–Einstein condensates with unequal dispersion coefficients

We systematically construct vector solitary waves in harmonically trapped one-dimensional two-component Bose–Einstein condensates with unequal dispersion coefficients by a numerical continuation in chemical potentials from the respective analytic low-density linear limits to the high-density nonlinear Thomas-Fermi regime. The main feature of the linear states herein is that the component with the larger quantum number has instead a smaller linear eigenenergy, enabled by suitable unequal dispersion coefficients, leading to new series of solutions compared with the states similarly obtained in the equal dispersion setting. Particularly, the lowest-lying series gives the well-known dark-anti-dark waves, and the second series yields the dark-multi-dark states, and the following series become progressively more complex in their wave structures. The Bogoliubov-de Gennes spectra analysis shows that most of these states bear unstable modes, but they can be long-lived and remarkably all of them can be fully stabilized in suitable parameter regimes.

0D-2D heterostructure for making very large quantum registers using ‘itinerant’ Bose-Einstein condensate of excitons

Presence of coherent resonant tunneling in quantum dot (zero-dimensional) - quantum well (two-dimensional) heterostructure is necessary to explain the collective oscillations of average electrical polarization of excitonic dipoles over a macroscopically large area. This was measured using photo excited capacitance as a function of applied voltage bias. Resonant tunneling in this heterostructure definitely requires momentum space narrowing of charge carriers inside the quantum well and that of associated indirect excitons, which indicates bias dependent itinerant Bose-Einstein condensation of excitons. Observation of periodic variations in negative quantum capacitance points to in-plane coulomb correlations mediated by long range spatial ordering of indirect, dipolar excitons. Enhanced contrast of quantum interference beats of excitonic polarization waves even under white light and observed Rabi oscillations over a macroscopically large area also support the presence of density driven excitonic condensation having long range order. Periodic presence (absence) of splitting of excitonic peaks in photocapacitance spectra even demonstrate collective coupling (decoupling) between energy levels of the quantum well and quantum dots with applied biases, which can potentially be used for quantum gate operations. All these observations point to experimental control of macroscopically large, quantum state of a two-component Bose-Einstein condensate of excitons in this quantum dot - quantum well heterostructure. Therefore, in principle, millions of two-level excitonic qubits can be intertwined to fabricate large quantum registers using such hybrid heterostructure by controlling the local electric fields and also by varying photoexcitation intensities of overlapping light spots.

Oscillating Solitons and ac Josephson Effect in Ferromagnetic Bose-Bose Mixtures.

Close to the demixing transition, the degree of freedom associated with relative density fluctuations of a two-component Bose-Einstein condensate is described by a nondissipative Landau-Lifshitz equation. In the quasi-one-dimensional weakly immiscible case, this mapping surprisingly predicts that a dark-bright soliton should oscillate when subject to a constant force favoring separation of the two components. We propose a realistic experimental implementation of this phenomenon which we interpret as a spin-Josephson effect in the presence of a movable barrier.

Chimera patterns in conservative Hamiltonian systems and Bose–Einstein condensates of ultracold atoms

Experimental realizations of chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been achieved for non-conservative systems with dissipation and exclusively in classical settings. The possibility of observing chimera patterns in quantum systems has rarely been studied and it remains an open question if chimera patterns can exist in closed, or conservative quantum systems. Here, we tackle these challenges by first proposing a conservative Hamiltonian system with nonlocal hopping, where the energy is well-defined and conserved. We show explicitly that such a system can exhibit chimera patterns. Then we propose a physical mechanism for the nonlocal hopping by using an additional mediating channel. This leads us to propose a possible experimentally realizable quantum system based on a two-component Bose–Einstein condensate (BEC) with a spin-dependent optical lattice, where an untrapped component serves as the matter-wave mediating field. In this BEC system, nonlocal spatial hopping over tens of lattice sites can be achieved and simulations suggest that chimera patterns should be observable in certain parameter regimes.

Distributed vorticity model for vortex molecule dynamics

We analyze the effect of a hard wall trapping potential on the dynamics of a vortex molecule in a two-component Bose-Einstein condensate with linear coherent coupling. A vortex molecule consists of a vortex of the same charge in each component condensate connected by a domain wall of the relative phase. In a previous paper [S. Choudhury and J. Brand, Phys. Rev. A 106, 043319 (2022)] we described the interaction of a vortex molecule with the boundary using the method of images by separately treating each component vortex as a point vortex, in addition to a Magnus force effect from the surface tension of the domain wall. Here we extend the model by considering a continuous distribution of image vorticity reflecting the effect of the domain wall on the vortex molecule phase structure. In the case of a precessing centered vortex molecule in an isotropic trap, distributing the image vorticity weakens its contribution to the precession frequency. We test the model predictions against numerical simulations of the coupled Gross-Pitaevskii equations in a two-dimensional circular disk and find support for the improved model.

Making ghost vortices visible in two-component Bose-Einstein condensates

Ghost vortices constitute an elusive class of topological excitations in quantum fluids since the relevant phase singularities fall within regions where the superfluid density is almost zero. Here we present a platform that allows for the controlled generation and observation of such vortices. Upon rotating an imbalanced mixture of two-component Bose-Einstein condensates, one can obtain necklaces of real vortices in the majority component whose cores get filled by particles from the minority one. The wave function describing the state of the latter is shown to harbor a number of ghost vortices which are crucial to support the overall dynamics of the mixture. Their arrangement typically mirrors that of their real counterpart, hence resulting in a ``dual'' ghost-vortex necklace, whose properties are thoroughly investigated in the present paper. We also present a viable experimental protocol for the direct observation of ghost vortices in a $^{23}\mathrm{Na}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}^{39}\mathrm{K}$ ultracold mixture. Quenching the intercomponent scattering length, some atoms are expelled from the vortex cores and, while diffusing, swirl around unpopulated phase singularities, thus turning them directly observable.

Measurement-based quantum computation using two-component BECs

Measurement-based quantum computation (MBQC) using two-component Bose–Einstein condensates (BECs) is proposed in this paper. An arbitrary state for one logical qubit is obtained by three-body measurement. Furthermore, a method is proposed for implementing controlled-Z gates for logical qubits in a graph state using BEC qubits and controlled-Z gates for BEC-type encoding. Results showed that the state after a measurement depends on the number of particles. These results pave the way for a novel quantum computing process based on particle control.

Half-quantum-vortex generation in a two-component Bose-Einstein condensate by an oscillatory magnetic obstacle

We numerically investigate the dynamics of vortex generation in a two-dimensional, twocomponent Bose-Einstein condensate subjected to an oscillatory magnetic obstacle. The obstacle creates both repulsive and attractive Gaussian potentials for the two symmetric spin-$\uparrow$ and $\downarrow$ components, respectively. We demonstrate that, as the oscillating frequency f increases, two distinct critical dynamics arise in the generation of half-quantum vortices (HQVs) with different spin circulations. Spin-$\uparrow$ vortices are nucleated directly from the moving obstacle at low f, while spin-$\downarrow$ vortices are created at high f by breaking a spin wave pulse in front of the obstacle. We find that vortex generation is suppressed for sufficiently weak obstacles, in agreement with recent experimental results by Kim et al. [Phys. Rev. Lett. 127, 095302 (2021)]. This suppression is caused by the finite sweeping distance of the oscillating obstacle and the reduction in friction in a supersonic regime. Finally, we show that the characteristic length scale of the HQV generation dynamics is determined by the spin healing length of the system.