Binary Mixture Of Bose-Einstein Condensates Research Articles

Dynamical self-trapping of two-dimensional binary solitons in cross-combined linear and nonlinear optical lattices.

Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates in cross-combined lattices, consisting of a one-dimensional (1D) linear optical lattice (LOL) in the x direction for the first component and a 1D nonlinear optical lattice (NOL) in the y direction for the second component, are analytically and numerically investigated. The existence and stability of 2D binary matter wave solitons in these settings are demonstrated both by variational analysis and by direct numerical integration of the coupled Gross-Pitaevskii equations. We find that in the absence of the NOL, binary solitons, stabilized by the action of the 1D LOL and by the attractive intercomponent interaction, can freely move in the y direction. In the presence of the NOL, we find, quite remarkably, the existence of threshold curves in the parameter space separating regions where solitons can move from regions where the solitons become dynamically self-trapped. The mechanism underlying the dynamical self-trapping phenomenon (DSTP) is qualitatively understood in terms of a dynamical barrier induced by the NOL, similar to the Peirls-Nabarro barrier of solitons in discrete lattices. DSTP is numerically demonstrated for binary solitons that are put in motion both by phase imprinting and by the action of external potentials applied in the y direction. In the latter case, we show that the trapping action of the NOL allows one to maintain a 2D binary soliton at rest in a nonequilibrium position of a parabolic trap or to prevent it from falling under the action of gravity. Possible applications of the results are also briefly discussed.

Compacton existence and spin-orbit density dependence in Bose-Einstein condensates.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates

We study the massive point-vortex model introduced in Ref. [Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.

Thermodynamics of dilute Bose gases: Beyond mean-field theory for binary mixtures of Bose-Einstein condensates

We study the thermodynamic properties of binary Bose mixtures, by developing a beyond mean-field Popov theory which properly includes the effects of quantum and thermal fluctuations in both the density and spin channels. Results for key thermodynamic quantities, such as the isothermal compressibility and the magnetic susceptibility, are derived from a perturbative calculation of the grand-canonical potential. We find that thermal fluctuations can play a crucial role on the miscibility condition of a binary mixture, favoring phase separation at finite temperature even if the mixture is soluble at zero temperature, as already anticipated in a previous work [Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intra-species interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.

Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

A binary mixtures of Bose-Einstein condensate structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter- and intra-atomic interactions, the transition from mixed to separated phase, which is also known as the miscibility-immiscibility transition, has been reported in different setups and by different groups. Here, we describe such type of quantum phase transition in an effective Hamiltonian approach, by applying Holstein-Primakoff transformation in the limit of large number of particles. We demonstrate that non-trivial geometric phase near the critical coupling is present, which confirms the connection between Berry phase and quantum phase transition. We also show that, by using the spin form of Hillery & Zubairy criterion, a two mode entanglement accompanies this transition in the limit of large, but not infinite number of particles.

Vortices with massive cores in a binary mixture of Bose-Einstein condensates

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying them their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.

Impact of higher-order nonlinearity on modulational instability in two-component Bose-Einstein condensates.

We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.

Flat bands and dynamical localization of spin-orbit-coupled Bose-Einstein condensates

Flat bands and dynamical localization of binary mixtures of Bose-Einstein condensates, with spin-orbit coupling subjected to a deep optical lattice which is shaking in time and to a periodic time modulation of the Zeeman field, are investigated. In contrast with usual dynamical localization in the absence of spin-orbit coupling, we find that to fully suppress the tunneling in the system the optical lattice shaking is not enough, and a proper tuning of the spin-orbit term, achievable via the Zeeman field modulation, is also required. This leads to a sequence of Zeeman parameter values where energy bands become flat, the tunneling in the system is suppressed, and the dynamical localization phenomenon occurs. Exact wave functions at the dynamical localization points show that the binary mixture localizes on a dimer with the two components occupying different sites. This type of localization occurs in exact form also for the ground state of the system at the dynamical localization points in the presence of nonlinearity and remains valid, although in approximate form, for a wide range of the Zeeman parameter around these points. The possibility of observing the above phenomena in real experiments is also briefly discussed.

Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a double-parabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength $K\,(>1)$ of the phase segregation. The dispersion relation $\omega \propto k^{3/2}$ is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength $2\pi/k$ is much larger than the healing length $\xi $. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $\omega (k)$ of order $k^{5/2}$ is calculated analytically, entailing a finite-wavelength correction factor $(1+\frac{\sqrt{K-1} \,k\xi}{4\sqrt{2}\,(\sqrt{2}+\sqrt{K-1})})$. This prediction may be tested experimentally using (quasi-)uniform optical-box traps. Explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity $\omega/k$ to the sound velocity $c$. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface.

A Dynamical Phase Transition of Binary Species BECs Mixtures in a Double Well Potential

We investigate the critical behavior in tunneling dynamics of a binary mixture of Bose-Einstein condensates (BECs) trapped in a symmetric double well potential. By gradually increasing the interspecies interaction, we characterize a continuous dynamical phase transition behavior which involves power law scaling. This dynamical phase transition is a consequence of separatrix crossing as we revealed by poincare section analysis.

Tunable spin-orbit-coupled Bose-Einstein condensates in deep optical lattices

Binary mixtures of Bose-Einstein condensates trapped in deep optical lattices and subjected to equal contributions of Rashba and Dresselhaus spin-orbit coupling (SOC), are investigated in the presence of a periodic time modulation of the Zeeman field. SOC tunability is explicitly demonstrated by adopting a mean-field tight-binding model for the BEC mixture and by performing an averaging approach in the strong modulation limit. In this case, the system can be reduced to an unmodulated vector discrete nonlinear Schr\"odinger equation with a rescaled SOC tunning parameter $\alpha$, which depends only on the ratio between amplitude and frequency of the applied Zeeman field. The dependence of the spectrum of the linear system on $\alpha$ has been analytically characterized. In particular, we show that extremal curves (ground and highest excited states) of the linear spectrum are continuous piecewise functions (together with their derivatives) of $\alpha$, which consist of a finite number of decreasing band lobes joined by constant lines. This structure also remains in presence of not too large nonlinearities. Most important, the interactions introduce a number of localized states in the band-gaps that undergo change of properties as they collide with band lobes. The stability of ground states in the presence of the modulating field has been demonstrated by real time evolutions of the original (un-averaged) system. Localization properties of the ground state induced by the SOC tuning, and a parameter design for possible experimental observation have also been discussed.

Quantum properties of a binary bosonic mixture in a double well

This work contains a detailed analysis of the properties of the ground state of a two-component two-sites Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters while the hopping terms are kept fixed. To characterize the ground state we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g. Schr\"odinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.

Split and overlapped binary solitons in optical lattices

We analyze the energetic and dynamical properties of bright-bright (BB) soliton pairs in a binary mixture of Bose-Einstein condensates subjected to the action of a combined optical lattice, acting as an external potential for the first species, while modulating the intraspecies coupling constant of the second. In particular, we use a variational approach and direct numerical integrations to investigate the existence and stability of BB solitons in which the two species are either spatially separated (split soliton) or located at the same optical lattice site (overlapped soliton). The dependence of these solitons on the interspecies interaction parameter is explicitly investigated. For repulsive interspecies interaction we show the existence of a series of critical values at which transitions from an initially overlapped soliton to split solitons occur. For attractive interspecies interaction only single direct transitions from split to overlapped BB solitons are found. The possibility to use split solitons for indirect measurements of scattering lengths is also suggested.

Static interfacial properties of Bose-Einstein-condensate mixtures

The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\ensuremath{\xi}}_{1}$ and ${\ensuremath{\xi}}_{2}$ and by the interspecies repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=1/2$ and $K=3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\ensuremath{\xi}}_{1},\phantom{\rule{0.28em}{0ex}}{\ensuremath{\xi}}_{2}$, and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

Critical wetting, first-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries.

The nature of superfluidity and Bose-Einstein condensation: From liquid4He to dilute ultracold atomic gases (Review Article)

We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.

Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived.

Domain wall suppression in trapped mixtures of Bose-Einstein condensates

The ground state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of $^{87}$Rb atoms in two different hyperfine states in a double well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the inter-species interaction vary.

Stable bright solitons in two-component Bose-Einstein condensates

Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of different type are considered. The general properties of the stationary states are investigated variationally and numerically, and the stability regions of the soliton-soliton pairs are determined.

Quantum dynamics of a binary mixture of BECs in a double-well potential: a Holstein–Primakoff approach

We study the quantum dynamics of a binary mixture of Bose–Einstein condensates (BECs) in a double-well potential starting from a two-mode Bose–Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto an SU(2) spin problem together with a Holstein–Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunnelling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.