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.     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.     

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.     

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.     

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.     

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.     

Lattice bosons in quartic confinement

We present a theoretical study of bose condensation of non-interacting bosons in finite lattices in quartic potentials in one, two, and three dimensions. We investigate dimensionality effects and quartic potential effects on single boson density of energy states, condensation temperature, condensate fraction, and specific heat. The results obtained are compared with corresponding results for lattice bosons in harmonic traps.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

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.     

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.     

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.     

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

Quantum phase transition of two-component Bose–Einstein condensates in optical lattices

In this Letter we study the superfluid–Mott-insulator (SMI) phase transition of two-component Bose–Einstein condensates (BECs) in an optical lattice. The analytic exciation energy spectrum is obtained by means of Bogoliubov transformation and hence the SMI phase transition condition is determined explicitly. Moreover, the characteristics of superfluid phase are explained from the energy spectrum.     

Ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic quantum gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive (U < 0) asymmetric (t_↑≠t_↓) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. We present the phase diagram of the homogeneous system and numerical results for unbalanced Fermi-mixtures obtained within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.     

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.     

Time-reversal symmetry breaking of p-orbital bosons in a one-dimensional optical lattice

We study bosons loaded in a one-dimensional optical lattice of twofold p-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p(x)+ip(y), a homogeneous p(x) Mott-insulator phase, and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and paraorbital). The anti-ferro-orbital order breaks time-reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time-reversal symmetry breaking in the first Mott phase.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.     

Modulational instability of matter waves under strong nonlinearity management

We study modulational instability of matter-waves in Bose-Einstein condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an optical lattice and homogeneous BEC are considered in the framework of the Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in an optical lattice, it is shown that the loop formed on a dispersion curve undergoes transformation due to the nonlinearity-management. A critical strength for the nonlinearity-management strength is obtained that changes the character of instability of an attractive condensate. MI is shown to occur below (above) the threshold for the positive (negative) effective mass. The enhancement of number of atoms in the nonlinearity-managed gap soliton is revealed.     

Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates

We investigate the relaxation effects on the dynamics of two-component dilute gas Bose-Einstein condensates (BEC) with relatively different two-body interactions and Josephson couplings between the two components. Three types of relaxation effects, i.e., one- and three-body losses and a pure phase relaxation caused by elastic two-body collision between condensed and noncondensed atoms, are examined on the dynamical behavior of a macroscopic superposition, i.e., Schr?dinger cat state, of two states with atom-number differences between the two components, which is known to be created by the time evolution in certain parameter regimes. Although three-body losses show a relatively large suppression of the revival behavior of Schr?dinger cat state and the Pegg-Barnett phase-difference distribution between the two components for a small-size Schr?dinger cat state, one- and three-body loss effects are not shown to directly depend on the size of Schr?dinger cat state. In contrast, the pure-phase relaxation effects, causing a reduction of phase-difference distribution and then decaying the Schr?dinger cat state, significantly increase with the increase of the size of Schr?dinger cat state. These features suggest that a detection of damped collapse-revival behavior is highly possible for medium-size Schr?dinger cat states in small-size two-component BECs.