Dimensional Bose Gas Research Articles

Thermal Melting of a Vortex Lattice in a Quasi-Two-Dimensional Bose Gas.

We report the observation of the melting of a vortex lattice in a fast rotating quasi-two dimensional Bose gas, under the influence of thermal fluctuations. We image the vortex lattice after a time-of-flight expansion, for increasing rotation frequency at constant atom number and temperature. We detect the vortex positions and study the order of the lattice using the pair correlation function and the orientational correlation function. We evidence the melting transition by a change in the decay of orientational correlations, associated with a proliferation of dislocations. Our findings are consistent with the hexatic to liquid transition in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario for two-dimensional melting.

Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems.

We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form F(t)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second-order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two-dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many-body systems.

Collisionless Sound in a Uniform Two-Dimensional Bose Gas.

Using linear response theory within the random phase approximation, we investigate the propagation of sound in a uniform two dimensional (2D) Bose gas in the collisionless regime. We show that the sudden removal of a static density perturbation produces a damped oscillatory behavior revealing that sound can propagate also in the absence of collisions, due to mean-field interaction effects. We provide explicit results for the sound velocity and damping as a function of temperature, pointing out the crucial role played by Landau damping. We support our predictions by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii equation. The results are consistent with the recent experimental observation of sound in a weakly interacting 2D Bose gas both below and above the superfluid Berezinskii-Kosterlitz-Thouless transition.

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

We study the unitary dynamics of a 1D gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency . Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

Full counting statistics of time-of-flight images

Inspired by recent advances in cold atomic systems and non-equilibrium physics, we introduce a novel characterization scheme, the time of flight full counting statistics. We benchmark this method on an interacting one dimensional Bose gas, and show that there the time of flight image displays several universal regimes. Finite momentum fluctuations are observed at larger distances, where a crossover from exponential to Gamma distribution occurs upon decreasing momentum resolution. Zero momentum particles, on the other hand, obey a Gumbel distribution in the weakly interacting limit, characterizing the quantum fluctuations of the former quasi-condensate. Time of flight full counting statistics is demonstrated to capture thermalization processes after a quantum quench, and can be useful for characterizing exotic quantum states such as many-body localized systems or models of holography.

Metastability of Bose and Fermi gases on the upper branch

We study three dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the S-matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length.

Lattice bosons with infinite-range checkerboard interactions

Motivated by experiments performed by Landig et al. [Nature 532, 476-479], we consider a two dimensional Bose gas in an optical lattice, trapped inside a single mode superradiant Fabry Perot cavity. The cavity mediates infinite range checkerboard interactions between the atoms, which produces competition between Mott insulator, charge density wave, superfluid and supersolid phases. We calculate the phase diagram of this Bose gas in a homogeneous system and in the presence of a harmonic trap.

Semiclassical and quantum description of an ideal Bose gas in a uniform gravitational field

We consider an ideal Bose gas contained in a cylinder in three spatial dimensions, subjected to a uniform gravitational field. It has been claimed by some authors that there is discrepancy between the semiclassical and quantum calculations in the thermal properties of such a system. To check this claim, we calculate the heat capacity and isothermal compressibility of this system semiclassically as well as from the quantum spectrum of the density of states. The quantum calculation is done for a finite number of particles. We find good agreement between the two calculations when the number of particles are taken to be large. We also find that this system has the same thermal properties as an ideal five dimensional Bose gas.

Spreading of correlations and Loschmidt echo after quantum quenches of a Bose gas in the Aubry-André potential

We study the spreading of density-density correlations and the Loschmidt echo, after different sudden quenches in an interacting one dimensional Bose gas on a lattice, also in the presence of a superimposed aperiodic potential. We use a time dependent Bogoliubov approach to calculate the evolution of the correlation functions and employ the linked cluster expansion to derive the Loschmidt echo.

Variational Monte Carlo study of soliton excitations in hard-sphere Bose gases

By using a full many-body approach, we calculate the excitation energy, the effective mass and the density profile of soliton states in a three dimensional Bose gas of hard spheres at zero temperature. The many-body wave function used to describe the soliton contains a one-body term, derived from the solution of the Gross-Pitaevskii equation, and a two-body Jastrow term which accounts for the repulsive correlations between atoms. We optimize the parameters in the many-body wave function via a Variational Monte Carlo procedure, calculating the grand-canonical energy and the canonical momentum of the system in a moving reference frame where the soliton is stationary. As the density of the gas is increased, significant deviations from the mean-field predictions are found for the excitation energy and the density profile of both dark and grey solitons. In particular, the soliton effective mass $m^\ast$ and the mass $m\Delta N$ of missing particles in the region of the density depression are smaller than the result from the Gross-Pitaevskii equation, their ratio being however well reproduced by this theory up to large values of the gas parameter. We also calculate the profile of the condensate density around the soliton notch finding good agreement with the prediction of the local density approximation.

Equation of state and contact of a strongly interacting Bose gas in the normal state

We theoretically investigate the equation of state and Tan's contact of a non-degenerate three dimensional Bose gas near a broad Feshbach resonance, within the framework of large-$N$ expansion. Our results agree with the path-integral Monte Carlo simulations in the weak-coupling limit and recover the second-order virial expansion predictions at strong interactions and high temperatures. At resonance, we find that the chemical potential and energy are significantly enhanced by the strong repulsion, while the entropy does not change significantly. With increasing temperature, the two-body contact initially increases and then decreases like $T^{-1}$ at large temperature, and therefore exhibits a peak structure at about $4T_{c0}$, where $T_{c0}$ is the Bose-Einstein condensation temperature of an ideal, non-interacting Bose gas. These results may be experimentally examined with a non-degenerate unitary Bose gas, where the three-body recombination rate is substantially reduced. In particular, the non-monotonic temperature dependence of the two-body contact could be inferred from the momentum distribution measurement.

Bose-Einstein condensation of photons with nonlocal nonlinearity in a dye-doped graded-index microcavity

We consider a microcavity made by a graded-index (GRIN) glass, doped by dye molecules, placed within two planar mirrors and study Bose-Einstein condensation (BEC) of photons. The presence of the mirrors leads to an effective photon mass, and the index grading provides an effective trapping frequency; the photon gas becomes formally equivalent to a two dimensional Bose gas trapped in an isotropic harmonic potential. The inclusion of nonlinear effects provides an effective interaction between photons. We discuss, in particular, thermal lensing effects and nonlocal nonlinearity, and quantitatively compare our results with the reported experimental data.

Renormalization Theory of a Two Dimensional Bose Gas: Quantum Critical Point and Quasi-Condensed State

We present a renormalization group construction of a weakly interacting Bose gas at zero temperature in the two-dimensional continuum, both in the quantum critical regime and in the presence of a condensate fraction. The construction is performed within a rigorous renormalization group scheme, borrowed from the methods of constructive field theory, which allows us to derive explicit bounds on all the orders of renormalized perturbation theory. Our scheme allows us to construct the theory of the quantum critical point completely, both in the ultraviolet and in the infrared regimes, thus extending previous heuristic approaches to this phase. For the condensate phase, we solve completely the ultraviolet problem and we investigate in detail the infrared region, up to length scales of the order $(\lambda^3 \rho_0)^{-1/2}$ (here $\lambda$ is the interaction strength and $\rho_0$ the condensate density), which is the largest length scale at which the problem is perturbative in nature. We exhibit violations to the formal Ward Identities, due to the momentum cutoff used to regularize the theory, which suggest that previous proposals about the existence of a non-perturbative non-trivial fixed point for the infrared flow should be reconsidered.

Behavior of the anomalous correlation function in a uniform two-dimensional Bose gas

We investigate the behavior of the anomalous correlation function in two dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify in particular the chemical potential, the ground sate energy, the depletion and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the non-condensed one at zero temperature. The single-particle anomalous correlation function is expressed in two dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature while it does not exist at finite temperature.

Nonadiabatic creation of macroscopic superpositions with strongly correlated one-dimensional bosons in a ring trap

We consider a strongly interacting quasi-one dimensional Bose gas on a tight ring trap subjected to a localized barrier potential. We explore the possibility to form a macroscopic superposition of a rotating and a nonrotating state under nonequilibrium conditions, achieved by a sudden quench of the barrier velocity. Using an exact solution for the dynamical evolution in the impenetrable-boson (Tonks-Girardeau) limit, we find an expression for the many-body wavefunction corresponding to a superposition state. The superposition is formed when the barrier velocity is tuned close to multiples of integer or half-integer number of Coriolis flux quanta. As a consequence of the strong interactions, we find that (i) the state of the system can be mapped onto a macroscopic superposition of two Fermi spheres, rather than two macroscopically occupied single-particle states as in a weakly interacting gas, and (ii) the barrier velocity should be larger than the sound velocity to better discriminate the two components of the superposition.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b 2 and b 3 for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b 2, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301–1306. < arXiv:physics/0405150>] that Dodd and Gibbs’ result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expression for b 3 - b 3 0 (where b 3 0 is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.

Weakly interacting Bose gas in a random environment

Zero temperature properties of a dilute weakly interacting $d$-dimensional Bose gas in a random potential are studied. We calculate geometrical and energetic characteristics of the localized state of a gas confined in a large box or in a harmonic trap. Different regimes of the localized state are found depending on the ratio of two characteristic length scales of the disorder, the Larkin length and the disorder correlation length. Repulsing bosons confined in a large box with average density $n$ well below a critical value $n_c$ are trapped in deep potential wells of extension much smaller than distance between them. Tunneling between these wells is exponentially small. The ground state of such a gas is a random singlet with no long-range phase correlation For $n>n_c$ repulsion between particles overcomes the disorder and the gas transits from the localized to a coherent superfluid state. The critical density $n_c$ is calculated in terms of the disorder parameters and the interaction strength. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.

Functional renormalization group approach to the two dimensional Bose gas

We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.

Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

We introduce a new class of sine-Gordon models, for which the interaction term is present in a region different from the domain over which the quadratic part is defined. We develop a nonperturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for one-dimensional and two-dimensional gases with nonzero temperatures.

Metallic Glass in Two Dimensional Disordered Bose Systems; A Renormalization Group Approach

We consider the quantum critical properties of a disordered two dimensional Bose gas based on the renormalization group approach. To account for disorder, we consider that the Bose gas interacts with an external random field. The system’s behavior in the critical region of the quantum phase transition is obtained in the universality class z=2 and includes contributions beyond the Gaussian approximation by considering interactions between bosonic degrees of freedom. The evaluation of the system’s conductivity close to the transition point proves the occurrence of a nonzero conductivity (metallic-like) state in the system in the ω=0 and T→0 K limit.