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

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.

Many-body processes in black and gray matter-wave solitons

“…Despite of the g 2 -correlation function being one of the simplest observables sensitive to beyond mean-field properties, such correlations have not been studied in the context of dark solitons -except for the perturbative treatment with a different focus in [58]. Besides its conceptual simplicity, the experimental accessibility via in situ densitydensity fluctuation measurements [59][60][61][62][63][64][65] makes the g 2 -correlation function attractive such that experimental interest in the correlation properties of dark solitons has already been triggered [65]. Due to the involved averaging process, probing beyond mean-field physics on the level of density fluctuations can turn out to be more robust than inspecting signatures becoming manifest only in singleshot n-body (n 2) absorption image measurements as considered in e.g.…”

Two-body correlations and natural-orbital tomography in ultracold bosonic systems of definite parity

“…The latter have theoretically been proven to give valuable physical insights in particular for low-dimensional systems [31][32][33][34][35][36] and are measurable both after ToF and in situ nowadays [37][38][39][40][41][42][43][44][45][46][47][48]. For this purpose, we derive the two-body density…”

Correlation lengths of the repulsive one-dimensional Bose gas

“…An important role in the analysis performed in Sec. V is played by the dressed charge Z(λ) defined by the following integral equation: (23) and the resolvent of the operator I + 1 2π K which satisfies…”

“…Comparison with the integral equation for the dressed phase (25) and dressed charge (23) shows that v 1 (λ) = iπZ(λ) − 2iπF (λ|q). Using the first identity in (26) the solution to this equation can be rewritten as v 1 …”

“…The paradigmatic example is the Bose gas with contact interaction [2], also known as the Lieb-Liniger model, whose experimental realization [3][4][5][6][7][8] has spurred renewed interest in computing physical properties which are experimentally accessible. In particular, the correlation functions, which can be measured using interference [9][10][11][12], analysis of particle losses [6,13], photoassociation [14], Bragg and photoemission spectroscopy [15][16][17][18][19], density fluctuation statistics [20][21][22][23], time-of-flight correlation statistics [24], and scanning electron microscopy [25] are extremely important.…”