Pathway from condensation via fragmentation to fermionization of cold bosonic systems

For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density {\it gradually} acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes {\it fermionized}. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and {\it coexistence} of condensed and fermionized parts that are separated in space.Comment: 12 pages, 2 figure

Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice

By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasi-periodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. {Finally, we consider the localization of a BEC in a random 1D potential in the form of several identical repulsive spikes arbitrarily distributed in space

Approximating Steady States in Equilibrium and Nonequilibrium Condensates

We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly valid approximation for the condensate density of an ultracold Bose gas confined in a harmonic trap that extends into the classically forbidden region. This provides an accurate approximation of the condensate density that includes healing effects at leading order that are missing in the widely adopted Thomas-Fermi approximation. The results presented herein allow us to formulate useful approximations to a range of experimental systems including the equilibrium properties of a finite temperature Bose gas and the steady-state properties of a 2D nonequilibrium condensate. Comparisons between our asymptotic and numerical results for the conservative and forced-dissipative forms of the GP equations as applied to these systems show excellent agreement between the two sets of solutions thereby illustrating the accuracy of these approximations.Comment: 5 pages, 1 figur

Condensate fraction of cold gases in non-uniform external potential

Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows to calculate the condensate fraction as well as the corresponding eigenfunction of the one-body density matrix. We successfully validate this procedure in diffusion Monte Carlo simulations of a Bose gas in an optical lattice at zero temperature. We also discuss relation between different criteria used for testing coherence in cold Bose systems, such as fraction of particles that are superfluid, condensed or are in the zero-momentum state.Comment: 4 pages, 2 figure

Quantitative test of thermal field theory for Bose-Einstein condensates II

We have recently derived a gapless theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature and used it to explain quantitatively the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et.al., Phys. Rev. Lett. 78, 764 (1997)]. The theory describes the dynamic coupling between the condensate and non-condensate via a full quasiparticle description of the time-dependent normal and anomalous averages and includes all Beliaev and Landau processes. In this paper we provide a full discussion of the numerical calculations and a detailed analysis of the theoretical results in the context of the JILA experiment. We provide unambiguous proof that the dipole modes are obtained accurately within our calculations and present quantitative results for the relative phase of the oscillations of the condensed and uncondensed atom clouds. One of the main difficulties in the implementation of the theory is obtaining results which are not sensitive to basis cutoff effects and we have therefore developed a novel asymmetric summation method which solves this problem and dramatically improves the numerical convergence. This new technique should make the implementation of the theory and its possible future extensions feasible for a wide range of condensate populations and trap geometries.Comment: 23 pages, 11 figures, revtex 4. Submitted to PRA. Sequel to: S. A. Morgan et al, PRL, 91, 250403 (2003

Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates

By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A \textbf{75}, 063610 (2007)] we derive an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.Comment: 11 pages, 7 figures; Final version published in Phys. Rev. A; Manuscript put in the archive and submitted to Phys. Rev. A on 17 July 200