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arXiv:1112.4199 · Physical Review Letters

Direct Observation of Quantum Phonon Fluctuations in a One-Dimensional Bose Gas

Julien Armijo

Published Jun 1, 2012• 36 citations
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Abstract

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.

DOI
10.1103/physrevlett.108.225306

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We report the first direct in situ observation of density fluctuations on the scale of the thermal de Broglie wavelength in an ultracold gas of bosons. Bunching of ^{87}Rb atoms in a quasi-two-dimensional system is observed by single-atom imaging using a quantum gas microscope. Compared to a classical ensemble, we observe a 30% enhancement of the second-order correlation function. We show the spatial and thermal dependence of these correlations. The reported method of detecting in situ correlations can be applied to interacting many-body systems and to the study of critical phenomena near phase transitions.
We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.
Collective excitations in one-dimensional (1D) quantum fluids are expected to propagate almost without dissipation. Here we directly excite phonon modes in a weakly interacting 1D Bose gas and study their time evolution. In the linear response regime, damping is surprisingly fast and quantitatively follows the non-analytic scaling predicted by Andreev's hydrodynamic description. For stronger excitations, we observe a crossover to a highly nonlinear regime characterized by wave breaking, captured by the finite-temperature nonlinear Schrödinger evolution. Our results resolve a long-standing question on the fate of phonons in 1D Bose gases, and open new pathways to study non-linear relaxation in quantum many-body systems.
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.