Photo-induced dynamics of Bose-Einstein condensates in optical superlattice

The photo-induced dynamics of cold atoms in a one-dimensional optical superlattice is observed. Steady state distribution of the probability amplitudes and the site population in a one-dimensional optical superlattice is found. It is shown that this solution of the equations, which describes the temporal behavior of a Bose-Einstein condensate in a superlattice, is unstable at the sufficiently high level of boson density. The expression for the increment of modulational instability is obtained on the basis of the linear stability analysis. The numerical examples of non-stationary solutions for boson density in a superlattice for the general model are discussed as applied to both the attraction and repulsion potentials of boson interaction.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

The nonlinear Dirac equation in Bose-Einstein condensates: Foundation and symmetries

We show that Bose-Einstein condensates in a honeycomb optical lattice can be described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.     

Oscillatory motion in confined potential systems with dissipation in the context of the Schrödinger-Langevin-Kostin equation

The quantum dissipative motion of wave packets in confined systems with polynomial potentials is numerically investigated in the context of the Schrödinger-Langevin-Kostin equation. Oscillatory patterns are studied in detail and they confirm the validity of the correspondence principle. The transition to the stationary state is also discussed.     

The dynamics and stabilities of Bose-Einstein condensates in deep optical lattices

The dynamics and stabilities of Bose-Einstein condensate (BEC) trapped in a deep one-dimensional periodic optical lattices with three-body interactions are investigated. By using the tight-binding approximation, the Bloch and the Bogoliubov excitation stabilities and the dynamics of the BEC wavepacket with the effects of the three-body interactions are studied. The critical conditions for occurrence of the dynamical/Landau instabilities, self-trapping/diffusion/breather of wavepacket, and localized soliton are obtained analytically. The results show that the boundaries of the dynamical instability and Landau instability are modified significantly due to the presence of the three-body interactions. It is also revealed that, the initial wavepacket width, the initial momentum, especially, the strength of the three-body force have strong effect on the critical conditions which are used to describe the dynamics of the wavepacket. It is shown that the regions of self-trapping, diffusion, and breather for BEC wavepacket in the parameter space are modified dramatically by the three-body interactions. The analytical results are confirmed by the direct numerical solutions of the discrete GPE.     

Geometry,commutation relations and the quantum fictitious force

We express the commutation relation between the operators of the momentum and the radial unit vectors in D dimensions in differential and integral form. We connect this commutator with the quantum fictitious potential emerging in the radial Schr?dinger equation of an s-wave. Received: 6 August 2002 / Revised version: 30 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-731/502-3086, E-mail: markus.cirone@physik.uni-ulm.de     

Particle trapping induced by the interplay between coherence and decoherence

We propose a novel scheme to trap a particle based on a delicate interplay between coherence and decoherence. If the decoherence occurs as a particle is located in the scattering region and subsequently the appropriate destructive interference takes place, the particle can be trapped in the scattering area. We consider two possible experimental realizations of such trapping: a ring attached to a single lead and a ring attached to two leads. Our scheme has nothing to do with a quasi-bound state of the system, but has a close analogy with the weak localization phenomena in disordered conductors.     

Quantum wave equations and non-radiating electromagnetic sources

A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined and which are non-radiating electromagnetic sources. It is also proven that and the advanced and retarded fields are exactly equal for these sources. Implications of these results are discussed.     

Bright solitary waves of trapped atomic Bose-Einstein condensates

Motivated by recent experimental observations, we study theoretically multiple bright solitary waves of trapped Bose-Einstein condensates. Through variational and numerical analyses, we determine the threshold for collapse of these states. Under π-phase differences between adjacent waves, we show that the experimental states lie consistently at the threshold for collapse, where the corresponding in-phase states are highly unstable. Following the observation of two long-lived solitary waves in a trap, we perform detailed three-dimensional simulations which confirm that in-phase waves undergo collapse while a π-phase difference preserves the long-lived dynamics and gives excellent quantitative agreement with experiment. Furthermore, intermediate phase differences lead to the growth of population asymmetries between the waves, which ultimately triggers collapse.     

Collapse of triaxial bright solitons in atomic Bose-Einstein condensates

We study triaxial bright solitons made of attractive Bose-condensed atoms characterized by the absence of confinement in the longitudinal axial direction but trapped by an anisotropic harmonic potential in the transverse plane. By numerically solving the three-dimensional Gross-Pitaevskii equation we investigate the effect of the transverse trap anisotropy on the critical interaction strength above which there is the collapse of the condensate. The comparison with previous predictions [A. Gammal, L. Tomio, T. Frederico, Phys. Rev. A 66 (2002) 043619] shows significant differences for large anisotropies.     

Experimental studies of Bose-Einstein condensates in disorder

We review recent studies of the effects of disorder on an atomic Bose-Einstein condensate (BEC). We focus particularly on our own experiments with ⁷Li BECs in laser speckle. Both the interaction, which gives rise to the nonlinearity in a BEC, and the disorder can be tuned experimentally. This opens many opportunities to study the interplay of interaction and disorder in both condensed matter physics and nonlinear science.     

Generation of generalized coherent states with two coupled Bose-Einstein condensates

We present a scheme to prepare generalized coherent states in a system with two species of Bose-Einstein condensates. First, within the two-mode approximation, we demonstrate that a Schrödinger cat-like state can be dynamically generated and, by controlling the Josephson-like coupling strength, the number of coherent states in the superposition can be varied. Later, we analyze numerically the dynamics of the whole system when interspecies collisions are inhibited. Variables such as fractional population, Mandel parameter and variances of annihilation and number operators are used to show that the evolved state is entangled and exhibits sub-Poisson statistics.     

Periodic spin domains of spinor Bose-Einstein condensates in an optical lattice

The periodic spin domains of spinor Bose-Einstein condensates confined in a one-dimensional optical lattice are studied in terms of the equation of motion of the spinor which is reduced to the nonlinear Schrödinger equation with the help of Holstein-Primakoff transformation. It is shown that the spin domains obtained analytically can be easily controlled by adjusting the light-induced dipole-dipole interaction, which is realizable in optical lattice created by red-detuned laser beams with modulating intensity. The dynamical stability of the spin domains is also demonstrated.     

Matter-wave interference in Bose-Einstein condensates: A dispersive hydrodynamic perspective

The interference pattern generated by the merging interaction of two Bose-Einstein condensates reveals the coherent, quantum wave nature of matter. An asymptotic analysis of the nonlinear Schrödinger equation in the small dispersion (semiclassical) limit, experimental results, and three-dimensional numerical simulations show that this interference pattern can be interpreted as a modulated soliton train generated by the interaction of two rarefaction waves propagating through the vacuum. The soliton train is shown to emerge from a linear, trigonometric interference pattern and is found by use of the Whitham modulation theory for nonlinear waves. This dispersive hydrodynamic perspective offers a new viewpoint on the mechanism driving matter-wave interference.     

Ratchet-induced matter-wave transport and soliton collisions in Bose-Einstein condensates

We study the dynamics of bright matter-wave solitons in a Bose-Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter-wave excitation as an effective classical particle.     

Stabilities of one-dimensional stationary states of Bose-Einstein condensates

We explore the dynamical stabilities of a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed N atoms with time-independent external potential. For the stationary states with zero flow density the general solution of the perturbed time evolution equation is constructed, and the stability criterions concerning the initial conditions and system parameters are established. Taking the lattice potential case as an example, the stability and instability regions on the parameter space are found. The results suggest a method for selecting experimental parameters and adjusting initial conditions to suppress the instabilities.     

Dynamical stabilization of self-trapping of two weakly coupled Bose-Einstein condensates

We investigate the effect of an external periodic driving field on the self-trapping of two weakly coupled Bose-Einstein condensates with dissipation. It is shown that the macroscopic self-trapping can be stabilized against dissipation by a high frequency periodic driving field. The parameter ranges for stabilizing self-trapping are found analytically and confirmed numerically.     

Effective one-dimensional dynamics of elongated Bose-Einstein condensates

By using a variational approach in combination with the adiabatic approximation we derive a new effective 1D equation of motion for the axial dynamics of elongated condensates. For condensates with vorticity ∣q∣ = 0 or 1, this equation coincides with our previous proposal [A. Muñoz Mateo, V. Delgado, Phys. Rev. A 77 (2008) 013617]. We also rederive the nonpolynomial Schrödinger equation (NPSE) in terms of the adiabatic approximation. This provides a unified treatment for obtaining the different effective equations and allows appreciating clearly the differences and similarities between the various proposals. We also obtain an expression for the axial healing length of cigar-shaped condensates and show that, in the local density approximation and in units of the axial oscillator length, it coincides with the inverse of the condensate axial half-length. From this result it immediately follows the necessary condition for the validity of the local density approximation. Finally, we obtain analytical formulas that give the frequency of the axial breathing mode with accuracy better than 1%. These formulas can be relevant from an experimental point of view since they can be expressed in terms only of the axial half-length and remain valid in the crossover between the Thomas-Fermi and the quasi-1D mean-field regimes. We have corroborated the validity of our results by numerically solving the full 3D Gross-Pitaevskii equation.     

Tomographic approach to the violation of Bell's inequalities for quantum states of two qutrits

The tomographic method is employed to investigate the presence of quantum correlations in two classes of parameter-dependent states of two qutrits. The violation of some Bell's inequalities in a wide domain of the parameter space is shown. A comparison between the tomographic approach and a recent method elaborated by Wu, Poulsen, and Mølmer shows the better adequacy of the former method with respect to the latter one.