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arXiv:2105.10296 · Physical Review A

Measuring densities of cold atomic clouds smaller than the resolution limit

A. N. Litvinov, P. Bataille, É. Maréchal, P. Pedri, O. Gorceix, Martin Robert-De-Saint-Vincent, B. Laburthe-Tolra

Published Sep 8, 2021• 2 citations
arXivHTMLPDF

Abstract

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 elongated $^{87}\mathrm{Sr}$ Fermi gases. We find significant nonlinear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an undistorted 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.

DOI
10.1103/physreva.104.033309

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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 elongated 87Sr^{87}\mathrm{Sr}87Sr Fermi gases. We find significant nonlinear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an undistorted 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.
We describe an experimental method to calibrate an absorption imaging system for ultracold atom clouds. Optical density profiles of an atom cloud are obtained for various probe beam intensities and are analyzed to determine the correction factor for the effective probe beam intensity directly from saturation effects. We find that the temporal shape of the probe-beam pulse needs to be taken into account for a quantitative analysis of the optical density measured in saturation absorption imaging. We show that this pulse-shape effect can lead to distortion of the density profile due to its nonlinear dependence on the optical depth.
Cold atoms are a quantum system well-isolated from the environment. Since the 80s, they have been used to make high-sensitivity atomic sensors and to deepen the understanding of quantum physics phenomena. At low temperatures, degenerate atomic gas regimes can be reached. They are characterized by a macroscopic quantum state that can be manipulated and controlled by lasers. Placing such atomic wave function in optical lattices provide a way to study the dynamics of complex many-body systems. In this context, diffraction-limited quantum gas microscopes have emerged as standard tools to probe such complex systems and to measure atomic density correlations between lattice sites. By further reducing the optical lattices dimensions, the energy scales are strongly enhanced and favor novel quantum phases. Such reduction of optical lattice dimensions requires novel trapping and imaging techniques to manipulate cold-atoms with subwavelength spatial resolutions.In this PhD thesis, we experimentally perform subwavelength imaging of ultra-cold atoms of Rubidium 87 using a dressed excited state method, initially proposed for generating subwavelength trapping potentials. The measurement are performed using in situ absorption imaging. A quantitative comparison of data and theory lead us to reinterprete and modify a method for atom number calibrations that is commonly used in the community. This reinterpretation requires a fine understanding of the interaction of a single quantum multi-level system and a coherent saturating field. The measurement of the in situ transmission of a coherent probe shows a linear reduction of the single-atom scattering cross-section with the optical density for which we propose a physical interpretation and a model. Once calibrated, we use our subwavelength imaging method that reaches down to 20 nm resolution in a few microseconds to super-resolve a tiny quantum object : the longitudinal wave function of a BEC in a very tight lattice.
Quantum gas microscopes have become a major element for quantum simulations using ultra-cold atoms in optical lattices. They are for example used to observe long-range order such as anti-ferromagnetic correlations in far field optical lattices using density and spin resolved microscopy. Decreasing the period of such lattice offer interesting perspective to increase atom-atom interaction energies and engineer atom-light coupling that our group tackles via the hybridization of cold atoms and nano-structured surfaces.In this poster, we will present how such type of sub-wavelength lattice potentials can be generated by trapping atoms in proximity (tens to hundreds of nanometers) of a nano-structured surface. At such atom to surface distance, the attractive Casimir-Polder force can be compensated by a doubly dressed state trapping method that I will discuss. Such method additionally offers solutions to overcome the diffraction limit of conventional imaging that become critical for sub-wavelength lattices. In this work, I will present the experimental characterization of a sub-wavelength resolution absorption imaging applicable to quantum gas detection. This method requires a quantitative determination of the atom number of dense clouds which has been characterized in this work and demonstrate that the scattering cross section reduces linearly with the optical density. Modelling the propagation of light in dense cloud we show that this reduction can be attributed to re-scattering of the incoherent part of the resonant fluorescence spectrum.The poster will additionally present an update on our recent work on the spectroscopy of Acetylene in sealed hollow core fibers.
In recent years, Rydberg excitations in atomic quantum gases have become a successful platform to explore quantum impurity problems. A single impurity immersed in a Fermi gas leads to the formation of a polaron, a quasiparticle consisting of the impurity being dressed by the surrounding medium. With a radius of about the Fermi wavelength, the density profile of a polaron cannot be explored using in situ optical imaging techniques. In this Letter, we propose a new experimental measurement technique that enables the in situ imaging of the polaron cloud in ultracold quantum gases. The impurity atom induces the formation of a polaron cloud and is then excited to a Rydberg state. Because of the mesoscopic interaction range of Rydberg excitations, which can be tuned by the principal numbers of the Rydberg state, atoms extracted from the polaron cloud form dimers with the impurity. By performing first principle calculations of the absorption spectrum based on a functional determinant approach, we show how the occupation of the dimer state can be directly observed in spectroscopy experiments and can be mapped onto the density profile of the gas particles, hence providing a direct, real-time, and in situ measure of the polaron cloud.
Abstract Cold atom experiments often use images of the atom clouds as their exclusive source of experimental information. The most commonly used technique is absorption imaging, which provides accurate information about the shapes of the atom clouds, but requires care when seeking the absolute atom number for small atom samples. In this paper, we present an independent, absolute calibration of the atom numbers. We directly compare the atom number detected using dark-ground imaging to the one observed by fluorescence imaging of the same atoms in a magneto-optical trap. We normalise the signal using single-atom resolved fluorescence imaging. In order to be able to image the absorption of the very low atom numbers involved, we use diffractive dark-ground imaging as a novel, ultra-sensitive method of in situ imaging for untrapped atom clouds down to only 100 atoms. We demonstrate that the Doppler shift due to the acceleration of the atoms by the probe beam has to be taken into account when measuring the atom-number.
We consider the inverse problem of in-line holography, applied to minimally destructive imaging of cold atom clouds. Absorption imaging near resonance provides a simple, but destructive measurement of atom column density. Imaging off resonance greatly reduces heating, and sequential images may be taken. Under the conditions required for off-resonant imaging, the generally intractable inverse problem may be linearized. A minimally destructive, quantitative and high-resolution image of the atom cloud column density is then retrieved from a single diffraction pattern.