Effects of the anomalous density in two-dimensional homogeneous Bose gases (original) (raw)

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

Physical Review A, 2012

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 singleparticle 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.

Correlation effects in ultracold two-dimensional Bose gases

Physical Review A, 2008

We study various properties of an ultracold two-dimensional (2D) Bose gas that are beyond a mean-field description. We first derive the effective interaction for such a system as realized in current experiments, which requires the use of an energy dependent T-matrix. Using this result, we then solve the mean-field equation of state of the modified Popov theory, and compare it with the usual Hartree-Fock theory. We show that even though the former theory does not suffer from infrared divergences in both the normal and superfluid phases, there is an unphysical density discontinuity close to the Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field description by using a renormalization group approach and show how the density discontinuity is resolved. The flow equations in two dimensions, in particular, of the symmetry-broken phase, already contain some unique features pertinent to the 2D XY model, even though vortices have not been included explicitly. We also compute various many-body correlators, and show that correlation effects beyond the Hartree-Fock theory are important already in the normal phase as criticality is approached. We finally extend our results to the inhomogeneous case of a trapped Bose gas using the local-density approximation and show that close to criticality, the renormalization group approach is required for the accurate determination of the density profile.

Correlation properties of a one-dimensional repulsive Bose gas at finite temperature

New Journal of Physics

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms.

Anomalous Fluctuations of the Condensate in Interacting Bose Gases

Physical Review Letters, 1998

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume V follow the law δN 2 0 ∼ V 4/3 . This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.

Correlations in a one-dimensional Bose gas

1999

We study the correlation effects in a one-dimensional Bose gas with repulsive delta-function interaction. The correlation effects are described by a local-field correction which takes into account the short-range correlations. We find that the ground state energy is in good agreement with the exact result up to intermediate coupling strengths, showing an improvement over the Bogoliubov and other related approximations. The velocity of sound, the static structure factor, and pair-correlation function are also calculated within the present approximation. ͓S0163-1829͑99͒00314-8͔

Bose condensed gas in strong disorder potential with arbitrary correlation length

Applied Physics B, 2007

We study the properties of a dilute Bose condensed gas at zero temperature in the presence of a strong random potential with arbitrary correlation length. Starting from the underlying Gross-Pitaevskii equation, we use the random phase approximation in order to get a closed integral equation for the averaged density distribution which allows the determination of the condensate and the superfluid density. The obtained results generalize those of Huang and Meng (HM) to strong disorder. In particular, we find the critical value of the disorder strength, where the superfluid phase disappears by a first-order phase transition. We show how this critical value changes as a function of the correlation length.

Momentum-Space Correlations of a One-Dimensional Bose Gas

Physical Review Letters, 2016

Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations δnpδn p , which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is however characterized by the presence of negative correlations between different momenta, in contrast to Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab-initio calculations.

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

Physical Review A, 2004

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.

Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature

Physical Review A, 2009

The behavior of the spatial two-particle correlation function is surveyed in detail for a uniform onedimensional Bose gas with repulsive contact interactions at finite temperatures. Long-, medium-, and shortrange effects are investigated. The results span the entire range of physical regimes from ideal gas to strongly interacting and from zero temperature to high temperature ͑Gross-Pitaevskii͒ and strongly interacting ͑Tonks-Girardeau͒ gases. We present perturbative analytic methods, available at strong and weak couplings, and first-principles numerical results using imaginary time simulations with the gauge-P representation in regimes where perturbative methods are invalid. Nontrivial effects are observed from the interplay of thermally induced bunching behavior versus interaction induced antibunching.

Superfluidity versus Bose-Einstein condensation in a Bose gas with disorder

Physical Review A, 2002

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the Diffusion Monte-Carlo method we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.