Momentum-space correlations of a one-dimensional Bose gas

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 $langle delta n_p delta n_{p}rangle$, 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 {it ab-initio} calculations.

Quench-induced breathing mode of one-dimensional Bose gases

We measure the position- and momentum- space breathing dynamics of trapped one-dimensional Bose gases. The profile in real space reveals sinusoidal width oscillations whose frequency varies continuously through the quasicondensate to ideal Bose gas crossover. A comparison with theoretical models taking into account the effect of finite temperature is provided. In momentum space, we report the first observation of a frequency doubling in the quasicondensate regime, corresponding to a self-reflection mechanism. The disappearance of this mechanism through the quasicondensation crossover is mapped out.

Momentum distribution of 1D Bose gases at the quasi-condensation crossover: theoretical and experimental investigation

We investigate the momentum distribution of weakly interacting 1D Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of single 1D Bose gases is measured using a focusing technique, whose resolution we improve via a guiding scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on in situ density fluctuation measurements. The quasi-condensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasi-condensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations.

Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations.

Density Functional of a Two-Dimensional Gas of Dipolar Atoms: Thomas-Fermi-Dirac Treatment

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.