Dipole oscillations of a Bose-Einstein condensate in the presence of defects and disorder

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.     

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti et al. on atomic Josephson oscillation [Science 293, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti et al. [New J. Phys. 5, 71 (2003)].Received: 20 March 2003, Published online: 30 July 2003PACS: 03.75.-b Matter waves - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow     

Spatial chaos of trapped Bose-Einstein condensate in one-dimensional weak optical lattice potential

The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system.     

Nonlinear dynamics of a Bose-Einstein condensate in a magnetic waveguide

We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.     

Anderson localization of elementary excitations in a one-dimensional Bose-Einstein condensate

We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the “one-dimensional mean field regime”, in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.     

Consequence of superfluidity on the expansion of a rotating Bose-Einstein condensate

We propose an easily detectable signature of superfluidity in rotating, vortex-free gaseous Bose-Einstein condensates. We have studied the time evolution of the expansion of such a condensate after it is released from the confining trap. We find that if such a condensate is not initially rotating, then at some moment it will instantaneously achieve a circular cross section. If the condensate is initially rotating its irrotational flow and the conservation of angular momentum prevent the released condensate from attaining a circular cross section, since the instantaneous moment of inertia is then proportional to the asymmetry of this cross section.     

The one-dimensional soliton state of Bose-Einstein condensate

Under certain conditions, the Bose-Einstein condensate confined in a two-dimensional harmonic trap is associated with a one-dimensional nonlinear Schrödinger equation and a soliton solution. The influence of the initial condition on the solution is discussed. The critical initial number of condensed atoms to maintain a soliton is evaluated. In the Li case, this number is of the order of thousand. The energy per particle of the solitons is also calculated.     

Expansion of a Bose-Einstein condensate in the presence of disorder

Expansion of a Bose-Einstein condensate (BEC) is studied in the presence of a random potential. The expansion is controlled by a single parameter, (microtau(eff)/variant Planck's over 2pi), where micro is the chemical potential, prior to the release of the BEC from the trap, and tau(eff) is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location.     

Manipulating a Bose-Einstein condensate with a single photon

We propose a method to create macroscopic superpositions, so-called Schr?dinger cat states, of different motional states of an ideal Bose-Einstein condensate. The scheme is based on the scattering of a freely expanding condensate by the light field of a high-finesse optical cavity in a quantum superposition state of different photon numbers. The atom-photon interaction creates an entangled state of the motional state of the condensate and the photon number, which can be converted into a pure atomic Schr?dinger cat state by operations only acting on the cavity field. We discuss in detail the fully quantised theory and propose an experimental procedure to implement the scheme using short coherent light pulses. Received 26 June 2000 and Received in final form 2nd October 2000     

Effect of quasiparticle renormalization on the localization of the excitations of a one-dimensional Bose-Einstein condensate in a random potential

We investigate the effects of renormalization on the localization of the quasiparticle excitations of one-dimensional Bose-Einstein condensate in a random potential. Starting with a set of linearized equations of motion for the phases of superfluid grains coupled by Josephson interactions, we use mode-counting techniques to calculate the inverse localization length for large (10⁸) arrays. Employing distributions for the interaction parameters that are the same as the initial (pre-renormalization) distributions used by Gurarie et al. (Phys. Rev. Lett. 101 (2008) 170407), we compare the initial-interaction results for the localization length with those obtained using renormalization group techniques.     

Nonlinear interaction of optical beams in a Bose-Einstein condensate

The results of simulation of the interaction of optical beams with different frequencies in an inhomogeneous Bose-Einstein condensate are given. The potential well has a parabolic profile, and the nonlinearity belongs to a defocusing class. The total reflection of a signal wave induced by a pump beam at a negative inhomogeneity during the wave capture in the potential well is considered.     

Self-organization of a Bose-Einstein condensate in an optical cavity

The spatial self-organization of a Bose-Einstein condensate (BEC) in a high-finesse linear optical cavity is discussed. The condensate atoms are laser-driven from the side and scatter photons into the cavity. Above a critical pump intensity the homogeneous condensate evolves into a stable pattern bound by the cavity field. The transition point is determined analytically from a mean-field theory. We calculate the lowest lying Bogoliubov excitations of the coupled BEC-cavity system and the quantum depletion due to the atom-field coupling.     

Band structures of a slowly rotating dipolar Bose-Einstein condensate with a quantized vortex along a one-dimensional optical lattice

We derive the effective Gross-Pitaevskii equation for a slowly rotating dipolar Bose-Einstein condensate (BEC) with a quantized vortex along a one-dimensional optical lattice and calculate its band structures. The band structure of a slowly rotating BEC in a lattice becomes interesting when dipole-dipole interaction (DDI) is involved. Under rotation, a dipolar rotating term emerges from the DDI potential. The dipolar rotating term makes a BEC with an attractive DDI more stable than one with a repulsive DDI. The dipolar rotating term changes and generalizes the definition for the type of BEC, which cannot be simply determined by an s-wave scattering length or an effective contact interaction term. The dipolar rotating term also makes the band structure fascinating and tunable. A so-called swallowtail band structure, i.e., a multi-valued solution due to nonlinear interaction, can either elongate or shrink as the band index increases, in contrast to a non-rotating dipolar BEC system with a monotonic dependence. With the dipolar rotating term, various band structures as well as an attractive BEC without collapse can be easily achieved. We demonstrate that a rotating dipolar BEC system subject to an optical lattice combines features of a crystal and a superfluid and promises wide applications.     

Stability of a single vortex in a trapped Bose-Einstein condensate

We investigate the lowest state of a Bose-Einstein condensate with an off-center vortex state that is confined in a rotating harmonic potential. Our results are consistent with the fact that any single off-center vortex is unstable. Furthermore, a vortex state located at the center of the cloud first becomes locally stable as the rotational frequency increases. Finally our study implies the existence of hysteresis effects.     

Dynamics of a single vortex line in a Bose-Einstein condensate

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 sec. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.     

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.     

Scattering effect of atoms through a Bose-Einstein condensate in an optical Lattice with a single defect

We study the transport of atoms across a localized Bose-Einstein condensate in an onedimensional optical lattice with a single defect. Our analytical and numerical results show that the defect as well as the nonlinear parameter can control the transmission of the atoms beam and the position of total reflection caused by Fano resonance. These interesting features may be a very useful basis for devising tunable atom filters or a button.     

Remote entanglement between a single atom and a Bose-Einstein condensate

Entanglement between stationary systems at remote locations is a key resource for quantum networks. We report on the experimental generation of remote entanglement between a single atom inside an optical cavity and a Bose-Einstein condensate (BEC). To produce this, a single photon is created in the atom-cavity system, thereby generating atom-photon entanglement. The photon is transported to the BEC and converted into a collective excitation in the BEC, thus establishing matter-matter entanglement. After a variable delay, this entanglement is converted into photon-photon entanglement. The matter-matter entanglement lifetime of 100 μs exceeds the photon duration by 2 orders of magnitude. The total fidelity of all concatenated operations is 95%. This hybrid system opens up promising perspectives in the field of quantum information.     

Coherence properties of a Bose-Einstein condensate in an optical superlattice

We study the effect of a one dimensional optical superlattice on the superfluid properties (superfluid fraction, number squeezing, dynamic structure factor) and the quasi-momentum distribution of the Mott-insulator. We show that due to the secondary lattice, there is a decrease in the superfluid fraction and the number fluctuation. The dynamic structure factor which can be measured by Bragg spectroscopy is also suppressed due to the addition of the secondary lattice. The visibility of the interference pattern (the quasi-momentum distribution) of the Mott-insulator is found to decrease due to the presence of the secondary lattice. Our results have important implications in atom interferometry and quantum computation in optical lattices.     

Pulsating instability of a Bose-Einstein condensate in an optical lattice

We find numerically that in the limit of weak atom-atom interactions a Bose-Einstein condensate in an optical lattice may develop a pulsating dynamical instability in which the atoms nearly periodically form a peak in the occupation numbers of the lattice sites, and then return to the unstable initial state. Multiple peaks behaving similarly are also found. Simple arguments show that the pulsating instability is a remnant of integrability, and give a handle on the relevant physical scales.