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arXiv:1103.3028 · Physical Review Letters

Sub-Poissonian Fluctuations in a 1D Bose Gas: From the Quantum Quasicondensate to the Strongly Interacting Regime

T. Jacqmin, Julien Armijo, Tarik Berrada, Karen V. Kheruntsyan, Isabelle Bouchoule

Published Jun 10, 2011• 197 citations
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Abstract

We report on local, in situ measurements of atom number fluctuations in slices of a one-dimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super- to sub-Poissonian as the density is increased, which is a signature of the transition between the subregimes where the two-body correlation function is dominated, respectively, by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to sub-Poissonian, as expected for a "fermionized" gas.

DOI
10.1103/physrevlett.106.230405

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We report on local, in situ measurements of atom number fluctuations in slices of a one-dimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super- to sub-Poissonian as the density is increased, which is a signature of the transition between the subregimes where the two-body correlation function is dominated, respectively, by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to sub-Poissonian, as expected for a "fermionized" 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 ⟨δn_{p}δn_{p^{'}}⟩, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from 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 the Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab initio calculations.
We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small subvolumes of a weakly interacting, ultracold atomic 1D cloud are studied using in situ absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the quantum quasicondensate regime, the ratio of chemical potential to thermal energy is μ/k(B)T≃4, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a nonlocal analysis at variable observation length, we observe a clear deviation from a classical field prediction, which reveals the emergence of dominant quantum fluctuations at short length scales, as the thermodynamic limit breaks down.
We investigate the momentum distribution of weakly interacting one-dimensional (1D) Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of 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 quasicondensation 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 quasicondensation 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.
In this manuscript, we present spatial one and two-body correlation measurements performed on a one-dimensional gas of ultra-cold bosons trapped at the surface of a microstructure. Two body correlations are highlighted by measurements of in situ density fluctuations and one-body correlations are probed through measurements of momentum distributions.We observed sub-Poissonian density fluctuations in the regime of weak interactions, thus demonstrating for the first time the regime of quasi-condensate in which the two-body correlation function is dominated by quantum fluctuations. We also observed sub-Poissonian fluctuations regardless of the density in the regime of strong interactions. Our measurement is the first observation of a single one-dimensional gas of bosons in this regime.The magnetic trap that we used is a modulated trap that has the remarkable property of decoupling between transverse and longitudinal confinements. This specificity has enabled us to engineer at will the shape of the longitudinal confinement. In particular, we were able to obtain harmonic and quartic traps.