We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.
In this paper we derive the dispersion relation of the surface waves at the interfaces between Mott insulating and Superfluid phases for confined Bose-Einstein Condensates. We then calculate their contribution to the heat capacity of the system and show how its low temperature scaling allows an experimental test of the existence and properties of Mott Insulator-Superfluid domains.
We study single-particle excitations in the Mott insulator phase of a Bose gas in an optical lattice. The characteristic feature of the single-particle spectrum in the Mott insulator phase is the existence of an energy gap between the particle and hole excitations. We show that this energy gap can be directly probed by an output coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott insulator phase using the Bose-Hubbard model. We find that the …
We present a theoretical study of vortices within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. We find that proximity to the Mott insulating state dramatically effects the vortex structures. To illustrate we give examples in which the vortices: (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. We model time-of-flight expansion to demonstrate the experimental observability of our predictions.
We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in optical lattices across the superfluid to Mott-insulator phase transition. Elementary excitations are created with a non-zero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated atomic phases in optical lattices.
The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultra cold atomic gases placed in optical lattices. We…
We analyze the Mott-insulator phases of dipolar bosonic gases placed in neighboring but unconnected 1D traps. Whereas for short-range interactions the 1D systems are independent, the non-local dipole-dipole interaction induces a direct Mott-insulator to pair-superfluid transition which significantly modifies the boundaries of the lowest Mott-insulator phases. The lowest boundary of the lowest Mott regions becomes progressively constant as a function of the hopping rate, eventually inverting its slope, leading to a re-entrant configuration which is retained in 2D. We discuss the consequences of…
We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how applying a periodic driving field can induce coherent destruction of tunneling. In the low-frequency regime, we obtain the novel result that the destruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with the depth of the trapping potential (``multi-photon resonances''), which allows the quantum phase transition between the Mott insulator and the superfluid state to be controlled with high precision. W…
We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator transition. We focus on the computation of the one - body density matrix and its Fourier transform, the momentum distribution which is directly obtainable from `time of flight'' measurements. The expected number of particles with zero momentum may be identified with the condensate population, if it is close to the total number of particles. Our main result is an …
We have studied the superfluid - Mott insulator transition in a BEC confined in an optical lattice and driven by an additional external electromagnetic field, which excites another internal state. It is shown that due to resonant strong driving the critical values of the transition parameter depend on external field parameters (the Rabi frequency and the detuning from resonance) and can be tuned to a given value. It is also shown that for driven system there are two optical potential depths at a phase transition which are always more than without driving.
We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling $ν\le1.$ While at $ν=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $ν<1$ it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at {\it all} energy and momentum scales within the $t-J$ approximation. This allows us to derive the propagator of transverse spin waves and the shape of t…
We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the inversely linear dependence on the bare on-site interaction U_0 is explained both in smaller and larger U_0. For a smaller U_0, it comes from a second order correction. For a larger U_0, except the breakdown of adiabaticity as analyzed by Gerbier et al, there might be another source to cause this…
We present a statistical description of Bose-Einstein condensates with general higher order nonlinearities. In particular, we investigate the case of cubic-quintic nonlinearities, of particular interest for dilute condensates. The implication of decoherence for the stability properties of the condensate is discussed.
We study an ultracold Bose gas in the presence of 1D disorder for repulsive inter-atomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.
We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensate, the popular Gross-Pitaevskii theory and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensate, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like…
We compare the collective modes for Bose-condensed systems with two degenerate components with and without spontaneous intercomponent coherence at finite temperature using the time-dependent Hartree-Fock approximation. We show that the interaction between the condensate and non-condensate in these two cases results in qualitatively different collective excitation spectra. We show that at zero temperature the single-particle excitations of the incoherent Bose condensate can be probed by intercomponent excitations.
We study the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0$. Our investigations were based on the field-theoretical Green's functions. On the basis of the use of empirical data about the speeds of the first and second sounds is described superfluid state at $T \neq 0$. It is studied the structure of superfluid state taking into account appearance with the different from zero temperatures of normal component and taking into account the branch of the second sound, wh…
We observe the formation of momentum distributions indicative of spatial period-doubling of superfluid Bose-Einstein condensates in periodically translated optical lattices. The effect is attributed to dynamic instability of the condensate wavefunction caused by modulation-induced coupling of ground and excited bands.
We show that it is possible to observe matter wave interference patterns in the collision of bright solitons (Bose Einstein condensates) without free ballistic expansion for suitable choices of scattering length and time dependent trap.
I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.
How does a rapidly rotating condensed Bose gas carry extreme amounts of angular momentum? The energetically favored state of a not-too-rapidly rotating Bose condensed gas is, as observed, a triangular lattice of singly quantized vortices. This paper describes the fates of the vortex lattice in both harmonic and anharmonic traps when condensates are rotated extremely rapidly.
The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.
We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for…
An ultracold gas of coupled two-component atoms in an optical field is studied. Due to the internal two-level structure of the atoms, three competing energy terms exist; atomic kinetic, atomic internal, and atom-atom interaction energies. A novel outcome of this interplay, not present in the regular Bose-Hubbard model, is that in the single band and tight binding approximations four different phases appear: two superfluid and two Mott phases. When passing through the critical point between the two superfluid or the two Mott phases, a swapping of the internal atomic populations takes place. By …
We derive an effective Bose-Hubbard model that predicts a phase transition from Bose-Einstein condensate to Mott insulator in two different systems subject to applied periodic potentials: microcavity exciton-polaritons and indirect excitons. Starting from a microscopic Hamiltonian of electrons and holes, we derive an effective Bose-Hubbard model for both systems and evaluate the on-site Coulomb interaction U and hopping transition amplitudes t. Experimental parameters required for observing a phase transition between a Bose-Einstein condensate and a Mott insulator are discussed. Our results su…
We study the dynamics of phase transitions in the one dimensional Bose-Hubbard model. To drive the system from Mott insulator to superfluid phase, we change the tunneling frequency at a finite rate. We investigate the build up of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.
To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various prop…
We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be consistent with the phase diagrams of two- and three-component condensates that are derived from energetic arguments.
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram …
We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different ex…
We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.
