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arXiv:1502.05991 · Physical Review A

Temporal and spatiotemporal correlation functions for trapped Bose gases

M. Kohnen, Robert A. Nyman

Published Mar 10, 2015• 6 citations
arXivHTMLPDF

Abstract

Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into account the effects of finite-size and -duration measurements made by light beams passing through the atom cloud. We specialize to the case of Bose gases in harmonic traps above critical temperature, for weakly perturbative measurements. For overlapping measurement regions, shot-noise correlations revive after a trap oscillation period. For nonoverlapping regions, bosonic correlations dominate at long times, and propagate at finite speeds. Finally, we give a realistic measurement protocol for performing such experiments.

DOI
10.1103/physreva.91.033612

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We investigate the position- and momentum-space two-body correlations in a weakly interacting, harmonically trapped atomic Bose-Einstein condensed gas at low temperatures. The two-body correlations are computed within the Bogoliubov approximation and the consequences of the finite system size are highlighted in contrast to the spatially homogeneous case. In the position space, we recover the antibunching induced by the repulsive interatomic interaction in the condensed fraction localized around the trap center and the bunching in the outer thermal cloud. In the momentum space, bunching signatures appear for either equal or opposite values of the momentum and display peculiar features as a function of the momentum and the temperature. In analogy to the optical Hanbury-Brown and Twiss effect, the amplitude of the bunching signal at closeby momenta is fixed by the chaotic nature of the matter field state and its linewidth is shown to be set by the (inverse of the) finite spatial size of the associated in-trap momentum components. In contrast, the linewidth of the bunching signal at opposite momenta is only determined by the condensate size.
This thesis presents two experiments on ultracold gases of metastable Helium that constitute the extension, to matter waves, of experiments that have been fundamental for the development of quantum optics. Both experiments have been realized by using a single atom detector, that allows one to reconstruct the position of the atoms in three dimensions. In the first experiment we directly compared the two-body correlation function for a cold cloud of identical fermions and for a cold cloud of identical bosons at the same temperature issued from the same experimental apparatus. Since bosons and fermions obey different quantum statistics, the two-body correlation functions are different: identical bosons tend to be detected bunched in pairs, while identical fermions tend to antibunch because of the Pauli exclusion principle. In the second experiment we studied the correlation between pairs of bosonic atoms generated in the collision of two Bose-Einstein condensates. The measurement of the correlation function allows us to demonstrate that atoms flying back to back in the centre of mass frame are correlated in pairs. Furthermore the observation of a Hanbury Brown Twiss correlation between atoms with collinear velocity demonstrates that our system cannot be interpreted in terms of classical mechanics, but that the bosonic statistics plays a crucial role. A new version of the experiment will allow us to measure the angular dependence of the population of the scattering modes and the number difference squeezing between two correlated modes.
We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.
We measure the temporal pair correlation function g(2)(τ) of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed in situ by using a local, time-resolved single-atom sensitive probing technique. Third- and fourth-order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement. We discuss, finally, the role of interactions. Our results promote temporal correlations as new observables to study the dynamical evolution of ultracold quantum gases.
The use of temporal correlations in scattered photons to probe the microscopic dynamics of ultracold quantum gases has emerged as a powerful, minimally destructive approach for in situ analysis. Here, we demonstrate that temporal coherence spectroscopy can quantitatively characterize atomic motion in a magnetic trap, despite the perturbative effects of the probing light. By measuring the first-order correlation function g (1) (τττ ) of light scattered by a 87 Rb cloud confined in a quadrupole trap, we identify radiation-pressure-induced acceleration and heating as the origin of the apparent discrepancy between coherence spectra and temperatures inferred from time-of-flight measurements. A simple dynamical model incorporating these effects restores agreement between theory and experiment, establishing coherence spectroscopy as a reliable in situ probe of velocity distributions in trapped atomic ensembles. Our results pave the way for time-resolved studies of nonequilibrium dynamics and thermalization processes in confined cold gases, complementing conventional destructive imaging techniques.