Binary Bose-Einstein Condensate Research Articles

Nonequilibrium dynamics of two-component Bose gas with tunable Rydberg interactions: From ring dark soliton to self-structured pattern formation

We explore the nonequilibrium dynamics of ring dark solitons in a two-dimensional binary Bose–Einstein condensate with tunable Rydberg interactions by numerical simulation of the time-dependent Gross–Pitaevskii equation. Our results show that both the vortex dynamics and self-structured pattern formation show strong dependence on the periodic modulation of Rydberg interactions. For the cases without periodic modulation of the interactions, or the periodic modulation part is almost equal to the fixed part, the system exhibits exotic vortex dynamics without self-structured pattern formation. Finally, the effect of periodically varying Rydberg interactions on the lifetime of ring dark soliton is also considered.

Mixed vortex quantum droplets in a radially periodic potential

It is known that nested states composed of ring-shaped hidden vorticity quantum droplets (QDs) with topological charges (S2=−S1, referred to as hidden vorticity) are stable in binary Bose-Einstein condensates (BECs). However, this nested multiring states with hidden vorticity are very extreme cases. Hence, the nested patterns with different topological charges are worth studying. In this paper, we use the imaginary-time-integration method to obtain for the first time the ring-shaped QDs with high topological charge (up to S2=15) in a radially periodic potential. We analyzed in detail the influence of the modulation depth on the stability of the ring-shaped QDs. The trapping capacity of the troughs is studied with fixed modulation depth. Finally, we obtain the nested patterns constructed by ring-shaped QDs with different topological charges, greatly expanding the encoding of topological states. The results provide reference for designing data storage devices using vortex topology charges.

Self-bound droplets with uncorrelated disordered potentials

We investigate the effects of an external random δ-correlated potential on the bulk properties of self-bound droplets in three-dimensional binary Bose–Einstein condensates. The ground-state energy and the quantum fluctuation induced by disorder are computed utilizing the Bogoliubov theory. We provide a comprehensive stability phase-diagram for the resulting dirty droplets. At finite temperature, we calculate the free energy, and the thermal equilibrium density in terms of the disorder parameters. We show that the intriguing interplay of the thermal correction and the disorder may dissolve the droplet.

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate

Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate

Dynamics of localized waves in quasi-one-dimensional imbalanced binary Bose-Einstein condensates

In the framework of coupled Gross-Pitaevskii equations, we explore the dynamics of localized waves in quasi-1D imbalanced binary Bose-Einstein condensates where the intra-component interaction is repulsive, while the inter-component one is attractive. The existence regimes of stable self-trapped localized states in the form of symbiotic solitons have been analyzed. Imbalanced mixtures, where the number of atoms in one component exceeds the number of atoms in the other component, are considered in parabolic potential and box-like trap. A variational approach has been developed which allows us to find the stationary state of the system and frequency of small amplitude oscillations near the equilibrium. It is shown that the strength of inter-component coupling can be retrieved from the frequency of the localized state's vibrations. When all the intra-species and inter-species interactions are repulsive, we numerically find a new type of symbiotic solitons resembling dark-bright solitons. The motion of the minority component in the surrounding gas of the majority component with different velocities reveals its superfluid properties.

Discrete quantum droplets in one-dimensional binary Bose–Einstein condensates

We discuss the propagation and interaction of discrete quantum droplets in one-dimensional binary Bose mixtures by variationally and numerically solving the underlying generalized discrete Gross–Pitaevskii equation. Useful analytical expressions are obtained for the energy, the chemical potential, the density profile, and the droplet separation in the regime of a small droplet. We show that for weak lattice coupling, the stationary state of small droplets remains intact and does not display any special structures. An irregular dynamics is observed in both single and dual droplets with flat-top plateau in the limit of relatively strong coupling. Our results reveal also that two droplets interact weakly and cannot form a bound-state due to the intriguing interplay of the discreteness and quantum fluctuations.

Two-dimensional symbiotic solitons and quantum droplets in a quasi-one-dimensional optical lattice

Symbiotic solitons (SS) and quantum droplets (QD) are self-trapped localized modes emerging in binary Bose-gas mixtures with intra-component repulsion and inter-component attraction. We have shown that two-dimensional (2D) SS can be stabilized against collapse or decay by means of a quasi-one-dimensional optical lattice (OL). Mobility of SSs along the free direction of the potential allows us to explore interactions and collisions of SSs moving in the same channel and neighboring channels of the quasi-1D OL. For the case of equal atom numbers in both components of the binary Bose–Einstein condensate (BEC) we have developed a variational approach that showed the stability of SS. For parameter settings when the SS stays on the verge of collapse/decay instability we take into account the Lee–Huang–Yang quantum fluctuations (QF) term in the coupled Gross–Pitaevskii equations (GPE). The QF term in the 2D GPE has the form of nonlinearity with a logarithmic factor, which is repulsive for large amplitude waves and attractive for opposite situations. This property of the governing equation supports stable QDs immersed in a gaseous phase of the larger component in particle-imbalanced Bose-gas mixtures. We explore the peculiar properties of QD such as incompressibility and surface tension, which are inherent to liquids. The proposed model of binary BEC loaded in a quasi-1D OL allows us to demonstrate the manifestations of the incompressibility and surface tension of 2D QDs.

Polarons in binary Bose–Einstein condensates

Bose polarons are quasiparticles formed through the interaction between impurities and Bose–Einstein condensates. In this paper, we derive an effective Fröhlich Hamiltonian using the generalized Bogoliubov transformation. The effective Fröhlich Hamiltonian encompasses two types of effective interactions: impurity-density (ID) coupling and impurity-spin (IS) coupling. Furthermore, we employ the Lee–Low–Pines variational approach to investigate the relevant properties of Bose polarons induced by the ID and IS coupling. These properties include the ground state energy, effective mass, and average number of virtual phonons. Our findings reveal that the contribution resulting from IS couplings to the ground energy decreases to zero near the miscible–immiscible boundary. Additionally, the increase of the IS coupling induces a greater number of virtual phonons, impeding the movement of impurities and leading to a significant increase in the effective mass of Bose polarons.

Phase transitions in rotating binary Bose–Einstein condensates with Spin–orbit and Rabi couplings

We present the phase transition analysis of binary Bose–Einstein condensates (BECs) with spin–orbit (SO) and Rabi couplings in quasi-two-dimensional system under rotation. In particular, we investigate the superfluid properties induced by rotation and SO coupling within hydrodynamic theory which can explain the emergence of the domain wall. By calculating the evolution of angular momentum with respect to rotation frequency, we discover first-order phase transitions where the domain wall changes into the wall-vortex complex. On the other hand, the angular momentum changes continuously with SO coupling strength accompanying by the elongation of the domain wall along x-direction. When the Rabi coupling strength exceeds a critical value, we observe a transition from the domain wall to vortex lattice resulting from a significant change of angular momentum. A phase diagram demonstrating the boundary regime in the plane of SO and Rabi coupling strengths is obtained. Our result is not only motivated by the search for novel states of matter inaccessible to existing experiments, but also by the need to identify situations where the phase transitions can be benchmarked systematically.

One-dimensional Townes solitons in dual-core systems with localized coupling.

The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons. It is based on a dual-core waveguide with quintic self-focusing and fused (localized) coupling between the cores. The respective system of coupled nonlinear Schrödinger equationsgives rise to exact solutions for full families of symmetric and asymmetric solitons, which are produced by the supercritical SSB bifurcation (i.e., the symmetry-breaking phase transition of the second kind). Stability boundaries of asymmetric solitons are identified by dint of numerical methods. Unstable solitons spontaneously transform into robust moderately asymmetric breathers or strongly asymmetric states with small intrinsic oscillations. The setup can be used in the design of photonic devices operating in coupling and switching regimes.

Matter-wave solitons in an array of spin-orbit-coupled Bose-Einstein condensates.

We investigate matter-wave solitons in a binary Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, loaded in a one-dimensional (1D) deep optical lattice and a three-dimensional anisotropic magnetic trap, which creates an array of elongated sub-BECs with transverse tunneling. We show that the system supports 1D continuous and discrete solitons localized in the longitudinal (along the array) and the transverse (across the array) directions, respectively. In addition, such solitons are always unpolarized in the zero-momentum state but polarized in finite-momentum states. We also show that the system supports stable two-dimensional semidiscrete solitons, including single- and multiple-peaked ones, localized in both the longitudinal and transverse directions. Stability diagrams for single-peaked semidiscrete solitons in different parameter spaces are identified. The results reported here are beneficial not only for understanding the physical property of SO-coupled BECs but also for generating new types of matter-wave solitons.

Exploring the role of beyond mean-field interaction in the structure and dynamics of one-dimensional quantum droplets

We present simulation results of the ground state structure and dynamics of quantum droplets (QDs) in one-dimensional spin–orbit coupled binary Bose–Einstein condensates. We have considered two cases for this analysis, such as (i) the mean-field term has a vanishingly small contribution utilizing the equal and opposite inter- and intraspecies interactions and (ii) unequal inter- and intraspecies interactions. The QD exhibits remarkably different natures in each case. In the former case, it exhibits a bright sech-like droplet nature, while in the latter case, we find the flattened sech-like shape of the droplet. Further, we analyze the effect of velocity perturbation on the dynamics in both cases. For the first case, we find a systematic change from the solitonic droplet nature to the breathing droplet, which finally has a moving droplet feature upon increasing the velocity. However, the second case shows similar dynamics except having more dynamically stable features than the first. Finally, we present various dynamics that ensued in the QD due to the quenching of the interaction parameters, coupling parameters or allowing the droplet to undergo collisions.

Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling

We consider Bose-Einstein condensate (BEC) subject to the action of spin-orbit-coupling (SOC) periodically modulated in the radial direction. In contrast to the commonly known principle that periodic potentials do not create bound states, the binary BEC maintains multiple localized modes in the linear limit, with their chemical potential falling into spectral gaps of the (numerically found) radial band structure induced by the spatial modulation of the SOC. In the presence of the repulsive nonlinearity, the SOC modulation supports fundamental gap solitons of the semi-vortex types, as well as higher-order vortex gap solitons. The localization degree and stability of the gap solitons strongly depend on the location of their chemical potential in the gap. Stability intervals for vortex gap solitons in a broad range of the intrinsic vorticity, from −2 to 3, are identified. Thus, the analysis reveals the previously unexplored mechanism of linear and nonlinear localization provided by the spatially periodic modulation of SOC, which may be extended to other settings, such as those for optical beams and polaritons. Unlike the commonly known quartets of eigenvalues for small perturbations, in the present system the instability is accounted for by shifted complex eigenvalue pairs.

Structure and dynamics of binary Bose–Einstein condensates with vortex phase imprinting

Structure and dynamics of binary Bose–Einstein condensates with vortex phase imprinting

Modulational instability in two-dimensional dissipative open Bose-Einstein condensates with mixed helicoidal and Rashba-Dresselhaus spin-orbit couplings

The letter proposes a modified set of coupled two-dimensional (2D) cubic complex Ginzburg-Landau (CGL) equations that include Rashba and Dresselhaus as well as helicoidal spin-orbit couplings (SOCs) and further study matter-wave formation using modulational instability (MI) in 2D Bose-Einstein condensates (BECs). Analytically, the linear stability analysis proposes an expression for the MI gain. The subsequent parametric study explores the effects of the included SO coupling, principally the competition involving the Rashba-Dresselhaus (RD) SOCs and the helicoidal SOC. Numerically, analytical predictions are confirmed through the emergence of dissipative nonlinear patterns under a suitable balance of the competing SOC terms, manifested by the disintegration of the continuous waves in a broad range of structures under effective energy exchange between the two BEC components. Combining dissipative effects and SOC in a 2D context extends the class of physical models that can investigate various suitable wave patterns in binary BECs.

Analogous Hawking radiation from gapped excitations in a transonic flow of binary Bose-Einstein condensates

Analogous Hawking radiation from gapped excitations in a transonic flow of binary Bose-Einstein condensates

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.

Two-Dimensional Quantum Droplets in Binary Dipolar Bose-Bose Mixture

We study two-dimensional (2D) isotropic quantum droplets (QDs) in dipolar binary Bose–Einstein condensates (BECs). The QDs are supported by the competition between the 2D form of the Lee-Huang-Yang (LHY) term and the isotropic dipole-dipole interactions (DDIs). Moreover, the DDIs in the 2D plane can be tuned to be either repulsive or attractive. Before that, QDs in dipolar BECs were often explored in three-dimensional (3D) systems, with competition between the attractive DDIs and the repulsive LHY term. Unlike the 3D system, the LHY term of the 2D binary system behaves in a logarithmic form, which can feature both attraction and repulsion. In this case, the QDs can be produced regardless of the interactions (attraction, repulsion, or zero) that the mean-field effect represents. In this paper, we model the aforementioned QDs via the 2D binary dipolar BECs with the competition between isotropic DDIs and the logarithmic LHY term. Their characteristic parameters (the peak density, IP, chemical potential, μ, and effective area, Aeff) using both numerical and theoretical methods are discussed. The centripetal collision and oblique collision between moving QDs are also studied.

On stability of rotational 2D binary Bose–Einstein condensates

We consider a two-dimensional nonlinear Schrödinger equation proposed in Physics to model rotational binary Bose–Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both the external confining potential and rotating frame makes it difficult to apply standard techniques to directly construct ground states, as we explain in an appendix. The goal of the present paper is to analyze the orbital stability of the set of energy minimizers under mass constraint, according to the relative strength of the confining potential compared to the angular frequency. The main novelty concerns the critical case where these two effects compensate exactly (lowest Landau Level): orbital stability is established by using techniques related to magnetic Schrödinger operators.