Exact crossover function for the Casimir force in a non-interacting Bose gas

An exact calculation of the Casimir force for a non-interacting Bose gas confined between two parallel plates is presented. The gas can be free or trapped, parallel to the plates. Depending on the finite size parameter λ/L (λ is the de Bröglie wavelength and L is the separation of the plates) and the density parameter nλ³ (n, the number density), the Casimir force crosses over from a power law to an exponential fall off is clearly seen. Since the Casimir force measurement requires very small values of L, one needs to take into account of the condensation in a finite system.     

Atomic density of a harmonically trapped ideal gas near Bose-Einstein transition temperature

We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-state contribution to be accurate.     

Transition temperatures of the trapped ideal spinor Bose gas

The thermodynamic properties of the trapped ideal spinor Bose gas are studied in details with the constraints of fixed total number of atoms N, and magnetization M. The double transition temperatures, their corresponding corrections due to finite particle number, and the population of each component are investigated. The generalization to the ideal spinor Bose gas of hyperfine quantum number F is also discussed. We propose that the order and disorder parameters to describe the symmetry broken of condensation.     

Probing the thermal atoms of a Bose gas through Raman transition

We explore the many body physics of a Bose condensed atom gas at finite temperature through the Raman transition between two hyperfine levels. Unlike the Bragg scattering where the phonon-like nature of the collective excitations has been observed, a different branch of thermal atom excitation is found theoretically in the Raman scattering. This excitation is predicted in the generalized random phase approximation (GRPA) and has a gapped and parabolic dispersion relation. The gap energy results from the exchange interaction and is released during the Raman transition. The scattering rate is determined versus the transition frequency ω and the transferred momentum q and shows the corresponding resonance around this gap. Nevertheless, the Raman scattering process is attenuated by the superfluid part of the gas. The macroscopic wave function of the condensate deforms its shape in order to screen locally the external potential displayed by the Raman light beams. This screening is total for a condensed atom transition in order to prevent the condensate from incoherent scattering. The experimental observation of this result would explain some of the reasons why asuperfluid condensate moves coherentlywithout any friction with its surrounding.     

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.     

Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap

We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra- and inter-atomic interactions. For the case with equal intra- and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra- and inter-atomic interactions and show the rich configurations of the density profiles.     

The q-deformed Bose gas: integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.     

Correlation functions in the Non Perturbative Renormalization Group and field expansion

The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain n-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method recently introduced which includes simultaneously all vertices although approximating their momentum dependence. The study is performed using the self-energy of the tridimensional scalar model at criticality. At least in this example, low order truncations miss quantities as the critical exponent η by as much as 60%. However, if one goes to high order truncations the procedure seems to converge rapidly.     

Delay times for symmetrized and antisymmetrized quantum tunneling configurations

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature T_c of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on T_c and find that ΔT_c/T_c is larger in quartic potential as compared to quadratic potential for number of particles <10⁵. Interestingly, the situation is reversed if the number of particles is 10⁵.     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

On the critical point of an interacting two-dimensional trapped Bose gas

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.     

Bose-Einstein transition in a dilute interacting gas

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates. Received 15 July 2001     

Collective excitations of harmonically trapped ideal gases

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.     

Density and stability in ultracold dilute boson-fermion mixtures

We analyze in detail recent experiments on ultracold dilute ⁸⁷Rb–⁴⁰K mixtures in Hamburg and in Florence within a mean-field theory. To this end we determine how the stationary bosonic and fermionic density profiles in this mixture depend in the Thomas-Fermi limit on the respective particle numbers. Furthermore, we investigate how the observed stability of the Bose-Fermi mixture with respect to collapse is crucially related to the value of the interspecies s-wave scattering length.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.     

Collective spin tunneling in spinor Bose-Einstein condensates

We investigate a novel aspect of rotational tunneling of the macroscopic spin for multicomponent spinor Bose-Einstein condensate (BEC). The Lagrangian is deduced from the multi-component BEC system formalism, and is written in terms of spin coherent states. From the effective Hamiltonian for the collective spin, the tunneling rate is obtained through a functional integral of the spin variable. It is pointed out that the cooperative effect between the Zeeman energy and the anisotropic nature of the spin-dependent inter-atomic interaction plays a key role for occurrence of collective spin tunneling.     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

Matter-wave amplification and collective internal excitations in a trapped Bose gas

Received: 23 May 1997/Revised version: 29 July 1997     

Stability of two-dimensional,controlled, Bose-Einstein coherent states

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schr?dinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold. Electronic supplementary material  Supplementary Online Material     

Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence

We provide a simple physical picture of the loss of coherence between two coherently split one-dimensional Bose-Einstein condensates. The source of the dephasing is identified with nonlinear corrections to the elementary excitation energies in either of the two independent condensates. We retrieve the result by Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on the subexponential decay of the coherence ∝exp [-(t/t₀)^2/3] for the large time t, however, the scaling of t₀ differs.