Multicomponent Bose-Einstein Condensates Research Articles

An efficient spectral method for computing dynamics of rotating two-component Bose–Einstein condensates via coordinate transformation

In this paper, we propose an efficient and accurate numerical method for computing the dynamics of rotating two-component Bose–Einstein condensates (BECs) which is described by the coupled Gross–Pitaevskii equations (CGPEs) with an angular momentum rotation term and an external driving field. By introducing rotating Lagrangian coordinates, we eliminate the angular momentum rotation term from the CGPEs, which allows us to develop an efficient numerical method. Our method has spectral accuracy in all spatial dimensions and moreover it can be easily implemented in practice. To examine its performance, we compare our method with those reported in the literature. Numerical results show that to achieve the same accuracy, our method takes much shorter computing time. We also apply our method to study issues such as dynamics of vortex lattices and giant vortices in rotating two-component BECs. Furthermore, we generalize our method to solve the vector Gross–Pitaevskii equations (VGPEs) which is used to study rotating multi-component BECs.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices

We theoretically study the role of the mode structure of a multicomponent Bose–Einstein condensate (BEC) in the potential created by a nonlinear optical lattice. We describe a multisoliton complex (MSC) as a superposition of different fundamental soliton modes in the matter-wave system. Using a similarity transformation, we solve the nonlinear evolution equation of the multimode coupled matter-wave field and construct a set of analytical bright soliton solutions. A perturbation method is used to examine the linear stability of the constructed solitons. Based on these particular solutions, we numerically analyze the mode structure of a MSC. The results show that the periodicity causes a Bloch modulation in the envelopes of the density distribution. When different fundamental modes collide with each other in the nonlinear lattice, the collision-induced shifts, and the space-dependent modulation of external potentials change the density profile of the multimode soliton complex. Therefore, the mode structure, which is absent in a one-mode BEC, provides the possible multiscale modeling of the matter-wave field with extra degrees of freedom.

Dynamics of inertial vortices in multicomponent Bose-Einstein condensates

With use of the nonlinear Schr{\"o}dinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multi-component Bose-Einstein condensates (BECs) with a harmonic trap in 2 dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The inter-particle (vortex-vortex) interaction is singularly-repulsive and short-ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. "Chaos in the three-body problem" in the three vortices system can be seen, which is not expected in the corresponding point vortices without inertia in 2 dimensions.

Rotating multicomponent Bose–Einstein condensates

In the understanding of the spatial behavior of interacting components of multicomponent Bose–Einstein condensates (BECs), a central problem is to establish whether coexistence of all the components occurs, or the interspecies interaction leads to extinction, that is, configurations where one or more densities are null. In this paper, for the rotating k-mixture BEC, we prove that the interspecies interaction leads to extinction in the Thomas–Fermi approximation.

Stability properties of vector solitons in two-component Bose—Einstein condensates with tunable interactions

By using a unified theory of the formation of various types of vector-solitons in two-component Bose—Einstein condensates with tunable interactions, we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schrödinger equations. Moreover, the Bogoliubov equation shows that there exists stable dark soliton in specific situations. Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose—Einstein condensates.

Emergent gravitational dynamics from multi-Bose-Einstein-condensate hydrodynamics?

In this paper, we examine the possibility to implement some form of emergent Newtonian gravity in a generic multicomponent Bose-Einstein condensate. Parallel to what happens for the emergence of low-energy Lorentz invariance, strong requirements have to be imposed on the underlying condensed matter model. We will show, within a simplified model, that the presence of a global symmetry alleviates the problems associated with Lorentz violation, allowing the presence of a long range potential, to which the analog matter fields (the quasiparticles) are coupled following a weaker form of equivalence principle.

Topological Excitations in Spinor Bose-Einstein Condensates

A rich variety of order parameter manifolds of multicomponent Bose-Einstein condensates (BECs) admit various kinds of topological excitations, such as fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss two topological excitations in spinor BECs: non-Abelian vortices and knots. Unlike conventional vortices, non-Abelian vortices neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. We discuss the collision dynamics of non-Abelian vortices in the cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is a unique topological object characterized by a linking number or a Hopf invariant [$\pi_3 (S^2)=Z$], can be created using a conventional quadrupole magnetic field in a cold atomic system.

Creating versatile atom traps by applying near-resonant laser light in magnetic traps

We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over conventional trapping potentials. One can easily convert the type of the trap, for example, from a single-well to a double-well trap. Atoms in different internal states can be trapped in different trap types, thereby enabling the realization of experiments with multicomponent Bose-Einstein condensates. Moreover, one can achieve variations of the trapping potential on small length scales without the need of microstructures. We present the potential surfaces for different setups, demonstrate their tunability, give a semianalytical expression for the potential, and propose experiments which can be realized within such a trap.

Some features in multi-component Bose-Einstein condensates

We give a brief description of theoretical studies on multi-component systems and detailed discussions on systems with atom-to-molecule conversion. The conversion of two species of atoms into stable molecules through the Feshbach resonance assisted by stimulated Raman adiabatic passage in photoassociation is studied with the help of mean-field Langrange density. The conversion efficiency is large for the fully bosonic system as well as the boson-fermion mixture as long as the general two-photon resonance condition is satisfied.

Vector azimuthons in two-component Bose-Einstein condensates

We introduce matter-wave vector azimuthons, i.e., spatially localized vortex states with azimuthal modulations of density, in multicomponent Bose-Einstein condensates. These localized states generalize spatially modulated vortex solitons introduced earlier in nonlinear optics [A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005)] and Bose-Einstein condensates [V. M. Lashkin, Phys. Rev. A 77, 025602 (2008)]. We find, numerically, nonrotating and rotating two-component azimuthons in a Bose-Einstein condensate with a negative scattering length confined by a quasi-two-dimensional parabolic trap.

STIRAP transport of Bose-Einstein condensate in triple-well trap

The irreversible transport of multi-component Bose-Einstein condensate (BEC) is investigated within the Stimulated Adiabatic Raman Passage (STIRAP) scheme. A general formalism for a single BEC in M-well trap is derived and analogy between multi-photon and tunneling processes is demonstrated. STIRAP transport of BEC in a cyclic triple-well trap is explored for various values of detuning and interaction between BEC atoms. It is shown that STIRAP provides a complete population transfer at zero detuning and interaction and persists at their modest values. The detuning is found not to be obligatory. The possibility of non-adiabatic transport with intuitive order of couplings is demonstrated. Evolution of the condensate phases and generation of dynamical and geometric phases are inspected. It is shown that STIRAP allows to generate the unconventional geometrical phase which is now of a keen interest in quantum computing.

Blow-up profile to the solutions of two-coupled Schrödinger equations

The model of the following two-coupled Schrödinger equations, it+12Δu=(g11|u|2p+g|u|p−1|v|p+1)uu, (t,x)∊R+×RN, and ivt+12Δv=(g|u|p+1|v|p−1+g22|v|2p)v, (t,x)∊R+×RN, is proposed in the study of the Bose–Einstein condensates [Mitchell, et al., “Self-traping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490 (1996)]. We prove that for suitable initial data and p the solution blows up exactly like δ function. As a by-product, we prove that similar phenomenon occurs for the critical two-coupled Schrödinger equations with harmonic potential [Perez-Garcia, V. M. and Beitia, T. B., “Sybiotic solitons in heteronuclear multicomponent Bose-Einstein condensates,” Phys. Rev. A 72, 033620 (2005)], iut+12Δu=Ω2|x|2u+(g11|u|2p+g|u|p−1|v|p+1)u, x∊RN, and ivt+12Δv=Ω2|x|2v+(g|u|p+1|v|p−1+g22|v|2p)v, x∊RN.

Topological objects in two-gap superconductor

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology π2(S 2) and π1(S 1), in addition to the well-known Abelian topology π1(S 1). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology π3(S 2) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB2, Sr2RuO4, 3He, and liquid metallic hydrogen.

Rabi switch of condensate wave functions in a multicomponent Bose gas

Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wave function of one component to the other. This ``Rabi switch'' can be generated in a binary BEC mixture by an electromagnetic field between the two components, typically two hyperfine states. When the wave function to be transferred is, at a given time, a stationary state of the multicomponent Hamiltonian, then, after a time delay (depending on the Rabi frequency), it is possible to have the same wave function on the other condensate. The Rabi switch can be used to transfer also moving bright matter-wave solitons, as well as vortices and vortex lattices in two-dimensional (2D) condensates. The efficiency of the proposed switch is shown to be 100% when interspecies and intraspecies interaction strengths are equal. The deviations from equal interaction strengths are analyzed within a two-mode model, and the dependence of the efficiency on the interaction strengths and on the presence of external potentials is examined in both 1D and 2D settings.

Collective spin tunneling in spinor Bose-Einstein condensates

We investigate a novel aspect of rotational tunneling of the macroscopic spin for multicomponent spinor Bose-Einstein condensate (BEC). The Lagrangian is deduced from the multi-component BEC system formalism, and is written in terms of spin coherent states. From the effective Hamiltonian for the collective spin, the tunneling rate is obtained through a functional integral of the spin variable. It is pointed out that the cooperative effect between the Zeeman energy and the anisotropic nature of the spin-dependent inter-atomic interaction plays a key role for occurrence of collective spin tunneling.

Phase separation of multi-component Bose–Einstein condensates in optical lattices

In this paper, we analyze phase separation of multi-component Bose–Einstein condensates (BECs) in the presence of strong optical lattices. This paper is in threefold. We first prove that when the inter-component scattering lengths go to infinity, phase separation of a multi-component BEC occurs. Furthermore, particles repel each other and form segregated nodal domains. Secondly, we show that the union of these segregated nodal domains equal to the entire domain. Thirdly, we show that if the intra-component scattering lengths are bounded by some finite number, each nodal domain is connected. For large intra-component scattering lengths, however, the third result is not true and a counter example of non-connected nodal domains is given.

Exact dynamics of multicomponent Bose-Einstein condensates in optical lattices in one, two, and three dimensions

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one-, two-, and three-dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-antivortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.

Dynamical and energetic instabilities in multicomponent Bose-Einstein condensates in optical lattices

We study dynamical and energetic instabilities in the transport properties of Bloch waves for atomic multicomponent Bose-Einstein condensates in optical lattices in the tight-binding limit. We obtain stability criteria analytically, as a function of superfluid velocities and interaction parameters, in several cases, for two-component and spinor condensates. In the two-species case we find that the presence of the other condensate component can stabilize the superfluid flow of an otherwise unstable condensate and that the free space dynamical miscibility condition of the two species can be reversed by tuning the superfluid flow velocities. In spin-1 condensates, we find the steady-state Bloch wave solutions and characterize their stability criteria. We find that generally more regions of dynamical instability arise for the polar than for the ferromagnetic solutions. In the presence of magnetic Zeeman shifts, we find a richer variety of condensate solutions and find that the linear Zeeman shift can stabilize the superfluid flow in several cases of interest.

Static and Dynamic Properties of Multicomponent Bose–Einstein Condensates of Ytterbium Atoms

We consider theoretically static and dynamic properties of multicomponent Bose–Einstein condensates (BECs) composed of a mixture of 174Yb and 176Yb atoms. The condensate of 176Yb atoms has an attractive interaction, collapsing above a certain critical particle number. This criterion is modified by the presence of another repulsive condensate of 174Yb atoms. We discuss the stability condition of this condensate mixture and collapsing dynamics due to the instability.