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.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Finite number of vortices and bending of finite vortex lines in a confined rotating Bose-Einstein condensate

The minimal energy configurations of finite N_v-body vortices in a rotating trapped Bose-Einstein condensate is studied analytically by extending the previous work [Y. Castin, R. Dum, Eur. Phys. J. D 7, 399 (1999)], and taking into account the finite size effects on z-direction and the bending of finite vortex lines. The calculation of the energy of the vortices as a function of the rotation frequency of the trap gives number, curvature, configuration of vortices and width of vortex cores self-consistently. The numerical results show that (1) the simplest regular polynomial of the several vortex configurations is energetically favored; while the hexagonal vortex lattice is more stable than square lattice; (2) bending is more stable then straight vortex line along the z-axis for λ<1; (3) the boundary effect is obvious: compared with the estimation made under infinite boundary, the finite size effect leads to a lower vortex density, while the adding vortex bending results in a less higher density because of the expansion. The results are in well agreement with the other authors' ones.     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices

Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices have been studied. For a weak lattice potential, the perturbed correction to the heteroclinic orbit in a repulsive system is constructed. We find the boundedness conditions of the perturbed correction contain the Melnikov chaotic criterion predicting the onset of Smale-horseshoe chaos. The effect of the chemical potential on the spatiotemporal dynamics is numerically investigated. It is revealed that the variance of the chemical potential can lead the systems into chaos. Regulating the intensity of the lattice potential can efficiently suppress the chaos resulting from the variance of the chemical potential. And then the effect of the phenomenological dissipation is considered. Numerical calculation reveals that the chaos in the dissipative system can be suppressed by adjusting the chemical potential and the intensity of the lattice potential.     

Internal structure of a quantum soliton and classical excitations due to trap opening

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: from the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: it deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.     

Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model

We investigate the quantum dynamics of repulsively bound atom pairs in an optical lattice described by the periodic Bose-Hubbard model both analytically and numerically. In the strongly repulsive limit, we analytically study the dynamical problem by the perturbation method with the hopping terms treated as a perturbation. For a finite-size system, we numerically solve the dynamic problem in the whole regime of interaction by the exact diagonalization method. Our results show that the initially prepared atom pairs are dynamically stable and the dissociation of atom pairs is greatly suppressed when the strength of the on-site interaction is much greater than the tunneling amplitude, i.e., the strongly repulsive interaction induces a self-localization phenomenon of the atom pairs.     

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.     

Mott transition in anharmonic confinement

Two effects are identified that affect the visibility of the Mott transition in an atomic gas in an optical lattice confined in a power-law potential. The transition can be made more pronounced by increasing the power law, but at the same time, experimental uncertainty in the number of particles will induce corresponding fluctuations in the measured condensate fraction. Calculations in two dimensions indicate that a potential slightly more flat-bottomed than a quadratic one is to be preferred for a wide range of particle number fluctuation size.     

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.     

Stability of two-dimensional,controlled, Bose-Einstein coherent states

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schr?dinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold. Electronic supplementary material  Supplementary Online Material     

Matter-wave bright solitons: Internal atomic recombination and external feeding

We consider matter-wave bright solitons in the presence of three-body atomic recombination, an axial periodic modulation and a feeding term, and use a variational method to derive conditions to have dynamically stabilized solitons due to compensation between the dissipation and alimentation of atoms from external sources. We critically examine how the BEC soliton is affected by the imbalance between the internal atom loss and external feeding. We pay special attention to study the influence of these terms on the soliton dynamics in optical lattice potentials that cause periodic modulation.     

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.     

Momentum interferences of a freely expanding Bose-Einstein condensate due to interatomic interaction change

A Bose-Einstein condensate may be prepared in a harmonic trap with negligible interatomic interactions using a Feshbach resonance. If a strong repulsive interatomic interaction is switched on and the trap is removed to let the condensate evolve freely, a time dependent quantum interference pattern takes place in the short time (Thomas-Fermi) regime, in which the number of peaks of the momentum distribution increases one by one, whereas the spatial density barely changes. The effect is stable for initial states with interactions and realistic time-dependence of the scattering length.     

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.     

On the critical point of an interacting two-dimensional trapped Bose gas

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.     

Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence

We provide a simple physical picture of the loss of coherence between two coherently split one-dimensional Bose-Einstein condensates. The source of the dephasing is identified with nonlinear corrections to the elementary excitation energies in either of the two independent condensates. We retrieve the result by Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on the subexponential decay of the coherence ∝exp [-(t/t₀)^2/3] for the large time t, however, the scaling of t₀ differs.     

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.     

Emergence of superfluid transport in a dynamical system of ultra-cold atoms

The dynamics of a Bose-Einstein condensate is studied theoretically in a combined periodic plus harmonic external potential. Different dynamical regimes of stable and unstable collective dipole and Bloch oscillations are analysed in terms of a quantum mechanical pendulum model. Nonlinear interactions are shown to counteract quantum-mechanical dephasing and lead to phase-coherent, superfluid transport.     

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of Bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.