Inhomogeneous Bose-Einstein Condensates Research Articles

Projection hypothesis from the von Neumann-type interaction with a Bose-Einstein condensate

We derive the projection hypothesis in projective quantum measurement by restricting the set of observables. This projection hypothesis accompanies a bipartite system with the von Neumann-type interaction, which consists of a quantum mechanical system, with a meter variable to be measured, and a quantum field theoretically macroscopic extended object, that is, a spatiotemporally inhomogeneous Bose-Einstein condensate in quantum field theory with the quantum coordinate, that is, the zero-energy Goldstone mode(s) of the spontaneously broken global spatial translational symmetry. The key steps in the derivation are the return of the symmetry translation of this quantum coordinate to the inverse translation of the c-number spatial coordinate in quantum field theory and the reduction of quantum fluctuations to classical fluctuations with respect to the Goldstone mode(s) due to a superselection rule.

Time parametrizations in long-range interacting Bose-Einstein condensates

Time-reparametrization invariance in general relativistic space-time does not allow us to single out a time in quantum mechanics in a mechanical way of measurement. Motivated by this problem, we examine this gauge invariance in the ground state of the quasi-stationary coarse-grained state of a long-range interacting closed system of identical or identified, macroscopic, and spatiotemporally inhomogeneous Bose–Einstein condensates in the thermodynamic and Newtonian limits. As a result, we find that it is a theoretical counterexample of this gauge invariance, except for proper-time translational invariance, at a coarse-grained level.

Dissipative motion of vortices in spatially inhomogeneous Bose-Einstein condensates

A dissipative model of vortex motion within a two-dimensional Gross-Pitaevskii equation is studied. With the asymptotic coordination method of solutions, a system of ordinary first-order differential equations describing vortex motion in rotating Bose-Einstein condensate was derived. The model takes into account the effect of various external factors: magnetic trap frequencies, number of particles in the condensate, angular rotational velocity of the condensate, dissipation parameter, etc. In special cases of dissipation-free motion, the results are coordinated with the known results of other authors. The addition of dissipation generalizes the known equations and makes it possible to see the vortex motion to the equilibrium points and to define the equilibrium configurations of any number of vortices. The model is illustrated by a large number of examples.

Variational Wave Function for Inhomogeneous Bose–Einstein Condensate with 3/2-Body Correlations

We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.

Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate

We investigate some aspects of the Bose-Einstein condensation (BEC) of quantum gases in the presence of inhomogeneous conditions. We consider three-dimensional (3D) quantum gases trapped by an external potential when the temperature is sufficiently low to show a BEC phase region around the center of the trap. If the trap is sufficiently large, different phases may coexist in different space regions, when moving from the center of the trap. We show that the quantum gas develops a peculiar critical behavior at the boundary of the BEC region, whose scaling behavior is controlled by the universality class of the homogenous BEC transition. We provide numerical evidence of this phenomenon, for lattice atomic gases modeled by the 3D Bose-Hubbard Hamiltonian.

Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose–Einstein condensates

We examine the spectral properties of single and multiple matter-wave dark solitons in Bose–Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.

Dynamics of quantum vortices in a quasi-two-dimensional Bose–Einstein condensate with two “holes”

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

Realization of negative mass regime and bound state of solitons in inhomogeneous Bose-Einstein condensates

We study the dispersion mechanism of Lieb mode excitations of both single and multi component ultra-cold atomic Bose gas, subject to a harmonic confinement through chirp management. It is shown that in some parameter domain, the hole-like excitations lead to the soliton's negative mass regime, arising due to the coupling between chirp momentum and Kohn mode. In low momenta region the trap considerably affects the dispersion of the grey soliton, which opens a new window to observe Lieb-mode excitations. Further, we extend our analysis to binary condensate, which yields usual shape compatible grey-bright soliton pairs. The inter-species interaction induces a shift in the Lieb-mode excitations, where the pair can form a bound state. We emphasize that the present model provides an opportunity to study such excitations in the low momenta regime, as well as the formation of bound state in binary condensate.

The off-diagonal long-range order and inhomogeneous Bose-Einstein condensate

It is shown that the hypothesis on anomalous averages is not a necessary condition for the occurrence of the off-diagonal long-range order in an inhomogeneous system with the Bose-Einstein condensate.

Publisher's Note: Faraday waves in collisionally inhomogeneous Bose-Einstein condensates [Phys. Rev. A 89, 023609 (2014)

Publisher's Note: Faraday waves in collisionally inhomogeneous Bose-Einstein condensates [Phys. Rev. A 89, 023609 (2014)

Modulated amplitude waves with non-trivial phase in quasi-1D inhomogeneous Bose–Einstein condensates

Abstract We consider a 1D nonlinear Schrodinger equation (NLSE) which describes the mean field dynamics of an elongated Bose–Einstein condensate and prove the existence of modulated amplitude waves with non-trivial phase and minimal spatial period tending to infinite. The proof combines the theory of local continuation of non-degenerate periodic solutions with a property of the Ermakov–Pinney equation.

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar-shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.

Spatial structure of a collisionally inhomogeneous Bose-Einstein condensate

The spatial structure of a collisionally inhomogeneous Bose-Einstein condensate (BEC) in an optical lattice is studied. A spatially dependent current with an explicit analytic expression is found in the case with a spatially dependent BEC phase. The oscillating amplitude of the current can be adjusted by a Feshbach resonance, and the intensity of the current depends heavily on the initial and boundary conditions. Increasing the oscillating amplitude of the current can force the system to pass from a single-periodic spatial structure into a very complex state. But in the case with a constant phase, the spatially dependent current disappears and the Melnikov chaotic criterion is obtained via a perturbative analysis in the presence of a weak optical lattice potential. Numerical simulations show that a strong optical lattice potential can lead BEC atoms to a state with a chaotic spatial distribution via a quasiperiodic route.

Discrete localized modes supported by an inhomogeneous defocusing nonlinearity

We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF) onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete bright solitons, which do not exist in lattices with the spatially uniform SDF nonlinearity. The UnST solitons coexist with stable staggered (ST) localized modes, which are always possible under the defocusing onsite nonlinearity. The results are obtained in a numerical form and also by means of variational approximation (VA). In the semi-infinite (truncated) system, some solutions for the UnST surface solitons are produced in an exact form. On the contrary to surface discrete solitons in uniform truncated lattices, the threshold value of the norm vanishes for the UnST solitons in the present system. Stability regions for the novel UnST solitons are identified. The same results imply the existence of ST discrete solitons in lattices with the spatially growing self-focusing nonlinearity, where such solitons cannot exist either if the nonlinearity is homogeneous. In addition, a lattice with the uniform onsite SDF nonlinearity and exponentially decaying intersite coupling is introduced and briefly considered. Via a similar mechanism, it may also support UnST discrete solitons. The results may be realized in arrayed optical waveguides and collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical lattices. A generalization for a two-dimensional system is briefly considered.

Collisionally inhomogeneous Bose–Einstein condensates with binary and three-body interactions in a bichromatic optical lattice

We study the impact of collisionally inhomogeneous binary and three-body interaction on Bose–Einstein condensates (BECs) of a dilute gas in a bichromatic optical lattice. We observe that the localized matter wave density which decreases after the introduction of repulsive spatially inhomogeneous binary interaction can be sustained by the addition of constant attractive binary strength in equal amounts. If the balance between repulsive spatially inhomogeneous binary interaction and constant attractive interaction is disturbed, the condensates collapse. Reversal of interaction sign ensures the longevity of BECs. Any imbalance between attractive spatially inhomogeneous interaction and constant repulsive interaction either results in the collapse of BECs or in the occupation of the condensates at multiple sites on either side. The introduction of a weak three-body interaction in phase with the binary interaction increases the extent of the instability of BECs. Reversing the sign of spatially inhomogeneous and constant interaction enhances the stability of BECs.

Dark solitary waves in a class of collisionally inhomogeneous Bose-Einstein condensates

We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional inhomogeneity yields a nonlinear lattice, which we tune from a small-amplitude, approximately sinusoidal structure to a periodic sequence of densely spaced spikes. We start by investigating time-independent inhomogeneities, and we subsequently examine the dynamical response when one starts with a collisionally homogeneous BEC and then switches on an inhomogeneity either adiabatically or nonadiabatically. Using Bogoliubov-de Gennes linearization as well as direct numerical simulations of the Gross-Pitaevskii equation, we observe dark solitary waves, which can become unstable through oscillatory or exponential instabilities. We find a critical wavelength of the nonlinear lattice that is comparable to the healing length. Near this value, the fundamental eigenmode responsible for the stability of the dark solitary wave changes its direction of movement as a function of the strength of the nonlinearity. When it increases, it collides with other eigenmodes, leading to oscillatory instabilities; when it decreases, it collides with the origin and becomes imaginary, illustrating that the instability mechanism is fundamentally different in wide-well versus narrow-well lattices. When starting from a collisionally homogeneous setup and switching on inhomogeneities, we find that dark solitary waves are preserved generically for aligned lattices. We briefly examine the time scales for the onset of solitary-wave oscillations in this scenario.

Dynamical properties of a condensate in a moving random potential

We study the dynamics of an inhomogeneous Bose-Einstein condensate subject to a one-dimensional harmonic trap and a moving random potential of finite extent. Above the critical velocity, a part of a condensate glues to the moving random potential with a consequent displacement of the condensate center-of-mass along the harmonic trap. We show that the center-of-mass turning point provides a direct measure of the average drag force acting on the condensate.

Localization of an inhomogeneous Bose-Einstein condensate in a moving random potential

We study the dynamics of a harmonically trapped quasi-one-dimensional Bose-Einstein condensate subjected to a moving disorder potential of finite extent. We show that, due to the inhomogeneity of the sample, only a percentage of the atoms is localized at supersonic velocities of a random potential. We find that this percentage can be sensitively increased by introducing suitable correlations in the disorder potential such as those provided by random dimers.

Propagation and annihilation of vortex pairs in a smoothly inhomogeneous Bose-Einstein condensate

An asymptotic theory has been developed to describe the propagation and annihilation of vortex pairs in a smoothly inhomogeneous Bose-Einstein condensate with the repulsive interaction between atoms. It has been shown that the trajectories of vortex pairs coincide with geometric-optical rays in an equivalent isotropic medium with the refractive index depending both on the density of the unperturbed inhomogeneous condensate and on the energy of structures under study. The transformation of vortex pairs to vortex-free quasisolitons and back has been described.

Dynamics of two-dimensional dark quasisolitons in a smoothly inhomogeneous Bose-Einstein condensate

Dynamics of two-dimensional dark quasisolitons in a smoothly inhomogeneous Bose-Einstein condensate