Browsing by Subject "Bose gases"

Now showing 1 - 6 of 6

Open Access
Density profile of a Bose-Einstein condensate inside a pancake-shaped trap: Observational consequences of the dimensional cross-over in the scattering properties
(Elsevier Science B.V., 2002) Tanatar, Bilal; Minguzzi, A.; Vignolo, P.; Tosi, M. P.
It is theoretically well known that two-dimensionality of the scattering events in a Bose-Einstein condensate introduces a logarithmic dependence on density in the coupling constant entering a mean-field theory of the equilibrium density profile, which becomes dominant as the s-wave scattering length gets larger than the condensate thickness. We trace the regions of experimentally accessible system parameters for which the cross-over between different dimensionality behaviors in the scattering properties may become observable through in situ imaging of the condensed cloud with varying trap anisotropy and scattering length.
Open Access
Real-space condensation in a dilute Bose gas at low temperature
(Natsional'na Akademiya Nauk Ukrainy, 2001) Kulik, I. O.
We show with a direct numerical analysis that a dilute Bose gas in an external potential - which is choosen for simplicity as a radial parabolic well - undergoes at certain temperature Tc a phase transition to a state supporting macroscopic fraction of particles at the origin of the phase space (r = 0, p = 0). Quantization of particle motion in a well wipes out sharp transition but supports a distribution of radial particle density p(r) peacked at r = 0 (a real-space condensate) as well as the phase-space Wigner distribution density W(r, p) peaked at r = 0 and p = 0 below the crossover temperature Tc* of order of Tc. Fixed-particle-number canonical ensemble which is a combination of the fixed-N condensate part and the fixed-μ excitation part is suggested to resolve the difficulty of large fluctuation of the particle number (δN ∼ N) in the Bose-Einstein condensation problem treated within the orthodox grand canonical ensemble formalism.
Open Access
Rotons and Bose condensation in Rydberg-dressed Bose gases
(American Physical Society, 2020) Seydi, I.; Abedinpour, S. H.; Zillich, R. E.; Asgari, R.; Tanatar, Bilal
We investigate the ground-state properties and excitations of Rydberg-dressed bosons in both three and two dimensions, using the hypernetted-chain Euler-Lagrange approximation, which accounts for correlations and thus goes beyond the mean-field approximation. The short-range behavior of the pair distribution function signals the instability of the homogeneous system with respect to the formation of droplet crystals at strong couplings and large soft-core radius. This tendency to spatial density modulation coexists with off-diagonal long-range order. The contribution of the correlation energy to the ground-state energy is significant at large coupling strengths and intermediate values of the soft-core radius while for a larger soft-core radius the ground-state energy is dominated by the mean-field (Hartree) energy. We have also performed path integral Monte Carlo simulations at selected system parameters to verify the performance of our hypernetted-chain Euler-Lagrange results in three dimensions. In the homogeneous phase, the two approaches are in very good agreement. Moreover, Monte Carlo simulations predict a first-order quantum phase transition from a homogeneous superfluid phase to the quantum droplet phase with face-centered cubic symmetry for Rydberg-dressed bosons in three dimensions.
Open Access
Temperature dependence of the density and excitations of dipolar droplets
(American Physical Society, 2020) Öztürk, S. F.; Enes, Aybar; Oktel, M. Özgür
Droplet states of ultracold gases which are stabilized by fluctuations have recently been observed in dipolar and two-component Bose gases. These systems present an alternate form of equilibrium where an instability at the mean-field level is arrested by higher-order correlations, making the droplet states sensitive probes of fluctuations. In a recent paper, we argued that thermal fluctuations can play an important role for droplets even at low temperatures where the noncondensed density is much smaller than the condensate density. We used the Hartree-Fock-Bogoliubov theory together with the local density approximation for fluctuations to obtain a generalized Gross-Pitaevskii (GP) equation and solved it with a Gaussian variational ansatz to show that the transition between the low density and droplet states can be significantly modified by the temperature. In this paper, we first solve the same GP equation numerically with a time-splitting spectral method to check the validity of the Gaussian variational ansatz. Our numerical results are in good agreement with the Gaussian ansatz for a large parameter regime and show that the density of the gas is most strongly modified by temperature near the abrupt transition between a pancake-shaped cloud and the droplet. For cigar-shaped condensates, as in the recent Er experiments, the dependence of the density on temperature remains quite small throughout the smooth transition. We then consider the effect of temperature on the collective oscillation frequencies of the droplet using both a time-dependent Gaussian variational ansatz and real-time numerical evolution. We find that the oscillation frequencies depend significantly on the temperature close to the transition for the experimentally relevant temperature regime (≃100nK).
Open Access
Temperature dependence of the energy of a vortex in a two-dimensional Bose gas
(Elsevier, 2004) Rajagopal, K. K.; Tanatar, Bilal; Vignolo, P.; Tosi, M. P.
We evaluate the thermodynamic critical angular velocity Ωc(T) for creation of a vortex of lowest quantized angular momentum in a strictly two-dimensional Bose gas at temperature T, using a mean-field two-fluid model for the condensate and the thermal cloud. Our results show that (i) a Thomas-Fermi description of the condensate badly fails in predicting the particle density profiles and the energy of the vortex as functions of T; and (ii) an extrapolation of a simple Thomas-Fermi formula for Ωc(0) is nevertheless approximately useful up to T≃0.5Tc.
Open Access
Thermodynamic properties of harmonically trapped D-dimensional ideal gases within generalized exclusion statistics
(Elsevier B.V., 2007) Sevinçli, S.; Tanatar, Bilal
We consider an ideal gas trapped with harmonic potential and obeying the generalized exclusion statistics. We analytically calculate the density of states from which the thermodynamic properties of the gas are calculated for a general energy spectrum ε (p) = a ps in D-dimensional space. Internal energy and the specific heat as a function of temperature are evaluated numerically for different dimensions and energy-momentum dispersion relations. In particular, we show that the specific heat is independent of the statistical parameter g for the constant density of states regime which corresponds D = 1 and s = 2 for this system.