Two-component Bose-Einstein Condensates Research Articles

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.

Spin conductivity spectrum and spin superfluidity in a binary Bose mixture

We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the delta-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum.

Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates.

The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equationson which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.

Universality in nonlinear passage through the miscible-immiscible phase transition in two component Bose-Einstein condensates

In this study, we investigate the formation of domain defects and the universal critical real-time dynamics in a two-component Bose-Einstein condensate with nonlinear quenching across the miscible-immiscible phase transition. By analyzing the Bogoliubov excitations, we obtain the power-law relations among the defect density, the phase transition delay and the quench time near the phase transition. Moreover, by simulating the real-time dynamics across the miscible-immiscible phase transition, we clearly show the formation of domain defects and the delay of the phase transition. Furthermore, we find that the domain defects are suppressed by large nonlinear coefficients and long quench times. To accurately characterize the domain defects, we quantify the defect excitations using the correlation length and the domain number. In addition, by combining the power-law relations between the phase transition delay and the quench time, we extract the critical exponents for different nonlinear coefficients. Our study not only confirms that the critical exponents do not sensitively depend on the nonlinear quenches but also provides a dynamic path toward the suppression of nonadiabatic excitation.

Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns

We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multicomponent nonlinear wave systems of nonlinear Schr\"odinger type. While our computations relate to two-component atomic Bose-Einstein condensates in parabolic traps, our methods can be broadly applied to high-dimensional nonlinear systems of partial differential equations. The combination of the so-called deflation technique with a careful selection of initial guesses enables the computation of an breadth of patterns, including ones combining vortex lines, rings, stars, and vortex labyrinths. Despite their complexity, they may be dynamically robust and amenable to experimental observation, as confirmed by Bogoliubov--de Gennes spectral analysis and numerical evolution simulations.

Kelvin wave in miscible two-component Bose-Einstein condensates

We study the dispersion relation of Kelvin waves propagating along single- and half-quantum vortices in miscible two-component Bose-Einstein condensates based on the analysis of the Bogoliubov--de Gennes equation. With the help of the interpolating formula connecting the dispersion relations in low- and high-wave-number regimes, we reveal the nontrivial dependence of the dispersion relation on the intercomponent interaction through the change in the vortex-core size of the vortical component. We also find the splitting of the Kelvin wave dispersion into gapless and gapped branches when both components have overlapping single-quantized vortices.

Optimal point-wise error estimates of two conservative finite difference schemes for the coupled Gross–Pitaevskii equations with angular momentum rotation terms

This paper is concerned with numerical analysis of two finite difference schemes for solving the coupled Gross–Pitaevskii equations with angular momentum rotation terms which model the dynamics of rotating two-component Bose–Einstein condensates. Both schemes are proved to be uniquely solvable and inherit the conservation laws of mass and energy in the discrete sense. Besides the energy method, the ‘cut-off’ function technique and inductive argument are introduced to establish the optimal error estimates of the numerical methods without any requirement on the grid-ratio or initial values. The convergence order of the numerical solutions to the exact solutions is proved to be of O(τ2+h2) with time-step τ and mesh size h. Several numerical results are reported to validate the error estimates and conservation laws.

High order approximation scheme for a fractional order coupled system describing the dynamics of rotating two-component Bose-Einstein condensates

<abstract><p>A coupled system of fractional order Gross-Pitaevskii equations is under consideration in which the time-fractional derivative is given in Caputo sense and the spatial fractional order derivative is of Riesz type. This kind of model may shed light on some time-evolution properties of the rotating two-component Bose¢ Einstein condensates. An unconditional convergent high-order scheme is proposed based on L2-$ 1_{\sigma} $ finite difference approximation in the time direction and Galerkin Legendre spectral approximation in the space direction. This combined scheme is designed in an easy algorithmic style. Based on ideas of discrete fractional Grönwall inequalities, we can prove the convergence theory of the scheme. Accordingly, a second order of convergence and a spectral convergence order in time and space, respectively, without any constraints on temporal meshes and the specified degree of Legendre polynomials $ N $. Some numerical experiments are proposed to support the theoretical results.</p></abstract>

Dimensional crossover of a Rabi-coupled two-component Bose–Einstein condensate in an optical lattice

Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose–Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Tunable energy-level inversion in spin-orbit-coupled Bose-Einstein condensates

A method to realize controllable inversion of energy levels in a one-dimensional spin-orbit (SO)-coupled two-component Bose-Einstein condensate under the action of a gradient magnetic field and harmonic-oscillator (HO) trapping potential is proposed. The linear version of the system is solved exactly. By adjusting the SO coupling strength and magnetic-field gradient, the energy-level inversion makes it possible to transform any excited state into the ground state. The full nonlinear system is solved numerically, and it is found that the results are consistent with the linear prediction in the case of the repulsive intercomponent interaction. On the other hand, the intercomponent attraction gives rise to states of superposition and edge types. Similar results are also reported for the system with the HO trap replaced by the box potential. These results suggest a possibility to realize any excited state and observe it in the experiment.

Soliton models: Traditional and novel, one- and multidimensional

This article offers an introduction to the vast area of experimental and theoretical studies of solitons. It is composed of two large parts. The first one provides a review of effectively one-dimensional (1D) settings. The body of theoretical and experimental results accumulated for 1D solitons is really large, the most essential among them being overviewed here. The second part of the article provides a transition to the realm of multidimensional solitons. These main parts are split into a number of sections, which clearly define particular settings and problems addressed by them. This article may be used by those who are interested in a reasonably short, but, nevertheless, sufficiently detailed introduction to the modern “soliton science”. It addresses, first, well-known “traditional” topics. In particular, these are the integrable Korteweg–de Vries, sine-Gordon, and nonlinear Schrödinger (NLS) equations in 1D, as well as the Kadomtsev–Petviashvili equations in 2D, and basic physical realizations of these classical equations. Then, several novel topics are addressed. Especially important between them are 2D and 3D solitons of the NLS type, which are stabilized against the collapse (catastrophic self-compression, which is the fundamental problem impeding the realization of multidimensional solitons) by the spin-orbit coupling or effects by quantum fluctuations in two-component Bose–Einstein condensates in ultracold atomic gases. This article introduces a part of the material which is represented in a systematic form in a new book, Multidimensional Solitons (B. A. Malomed, AIPP, 2022).

Observing phase jumps of solitons in Bose-Einstein condensates

The phase difference of the macroscopic wave function is a unique structure of the soliton in an atomic Bose--Einstein condensate (BEC). However, experiments on ultracold atoms so far have observed the valley of the density profile to study the dynamics of solitons. We propose a method to observe the phase difference of a soliton in a BEC by using an interference technique with Raman and rf pulses. We introduce a phase jump factor, which is an indicator to measure the phase difference between two points. It is demonstrated by using the projected Gross--Pitaevskii equation that an interference density ratio, the density ratio of two-component BECs after the Raman and rf pulses, reproduces the phase jump factor well. This technique will become an alternative method to study the decay and breakdown of a phase imprinted soliton in atomic BECs.