Finite-resolution fluctuation measurements of a trapped Bose-Einstein condensate

We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study susceptibility scaling in a trapped two-component Bose-Einstein condensate. This system supports a second-order phase transition between miscible (co-spatial) and immiscible (symmetry-broken) states that is driven by a diverging susceptibility to magnetic fluctuations. As the transition is approached from the miscible side the magnetic susceptibility is found to depend strongly on the geometry and orientation of the observation cell. However, a scaling exponent consistent with that for the homogenous gas (γ = 1) can be recovered, for all cells considered, as long as the fit excludes the region in the immediate vicinity of the critical point. As the transition is approached from the immiscible side, the magnetic fluctuations exhibit a non-trivial scaling exponent γ 1.30. Interestingly, on both sides of the transition, we find it best to extract the exponents using an observation cell that encompasses half of the trapped system. This implies that relatively low-resolution in situ imaging will be sufficient for the investigation of these exponents. We also investigate the gap energy and find exponents νz = 0.505 on the miscible side and, unexpectedly, νz = 0.60(3) for the immiscible phase.

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“…5(a) of Ref. [49]). For cells positioned off-center, the magnetic fluctuations tend to diverge on approach to the critical point.…”

Section: Resultsmentioning

confidence: 95%

Scaling of fluctuations in a trapped binary condensate

2015

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“…The total number of atoms N at can be computed according to the definition of the column density and to Eq. (7), and related to R ph using Eq. ( 8):…”

Section: Beer-lambert Law For Objects Below Imaging Resolutionmentioning

confidence: 99%

“…the equation of state of quantum fluids [1][2][3][4] or 1D gases [5], these objects are extremely small and sometimes even below the resolution limit of the imaging system. More generally, quantum gases reveal interesting phenomena in small, local features: vortices [6] whose size is set by condensates' healing length and typically cannot be resolved in situ, density fluctuations [7], Wannier functions in optical lattices, etc. Resolving such structures is a difficult but rewarding problem that prompted important technical developments, using for example high-resolution objectives in the quantum gas microscope approach [8] (which are nevertheless still limited to the diffraction limit), the newly demonstrated quantum gas magnifier [9], super-resolution imaging [10,11], scanning probes using electrons [12] or ions [13].…”

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confidence: 99%

Measuring densities of cold atomic clouds smaller than the resolution limit

Litvinov,

Bataille,

Maréchal

et al. 2021

Preprint

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We propose and demonstrate an experimental method to measure by absorption imaging the size and local column density of a cloud of atoms, even when its smallest dimension is smaller than the resolution of the imaging system. To do this, we take advantage of the fact that, for a given total number of atoms, a smaller and denser cloud scatters less photons when the gas is optically thick. The method relies on making an ansatz on the cloud shape along the unresolved dimension(s), and on providing an additional information such as the total number of atoms. We demonstrate the method on in-situ absorption images of quasi-1D 87 Sr Fermi gases. We find significant non-linear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an un-distorted longitudinal density profile, and to measure transverse sizes as small as one fourth of our imaging resolution. The ultimate limit of our method is the wavelength that is used for imaging.

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“…One approach that is already in use is to examine the distributions and moments of the occupations of small imaging bins of length Δ, as discussed in section 3.1 or [42]. This approach amounts to looking at statistics of small bins in the gas that correspond closely to the density grains.…”

Section: Analysis Of Imaging Binsmentioning

confidence: 99%

Mesoscopic density grains in a 1D interacting Bose gas from the exact Yang–Yang solution

Pietraszewicz

Deuar

2017

New J. Phys.

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Number fluctuations in a one-dimensional Bose gas consist of contributions from grainy fluctuations of localized domains (the density grains). We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature that exactly determine all higher-order moments of number fluctuations. These moments are closely related to the statistics of the localized (but not zerorange) density grains. We directly calculate the mean occupation of these fluctuations, and the variance, skewness, and kurtosis of their distribution across the whole parameter space of the gas. Findings include: large mesoscopic density grains with a fat-tailed distribution in the thermal quasicondensate of the dilute gas and in the nonperturbative quantum turbulent regime; regions of negative skewness and below-Gaussian kurtosis in a part of the fermionized gas, and an unexplained crossover region along T T ; d g the existence of a peak in the density-density correlation function at finite interparticle spacing. We relate these density grain statistics to measurable behavior such as the statistics of coarse imaging bins, and finite-size scaling of number fluctuations. We propose how to experimentally test the relationship between thermodynamically independent density grains and density concentrations visible in single-shot images.

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Finite-resolution fluctuation measurements of a trapped Bose-Einstein condensate

Cited by 6 publications

References 57 publications

Scaling of fluctuations in a trapped binary condensate

Scaling of fluctuations in a trapped binary condensate

Measuring densities of cold atomic clouds smaller than the resolution limit

Mesoscopic density grains in a 1D interacting Bose gas from the exact Yang–Yang solution

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