Abstract
High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements, each of which contributes to loss and light scattering, making them unsuitable for quantum backaction limited "weak" measurements. We employ a low-cost high NA aspheric lens as an objective for a practical and economical-although aberrated-high-resolution microscope to image 87Rb Bose-Einstein condensates. Here, we present a methodology for digitally eliminating the resulting aberrations that is applicable to a wide range of imaging strategies and requires no additional hardware. We recover nearly the full NA of our objective, thereby demonstrating a simple and powerful digital aberration correction method for achieving optimal microscopy of quantum objects. This reconstruction relies on a high-quality measure of our imaging system's even-order aberrations from density-density correlations measured with differing degrees of defocus. We demonstrate our aberration compensation technique using phase-contrast imaging, a dispersive imaging technique directly applicable to quantum backaction limited measurements. Furthermore, we show that our digital correction technique reduces the contribution of photon shot noise to density-density correlation measurements which would otherwise contaminate the desired quantum projection noise signal in weak measurements.
Highlights
In many fields of study—from biophysics [1] and medicine to astrophysics [2,3] and atomic physics [4]—images are a key source of data, making high-quality imaging systems essential
Our power spectral density (PSD) measurements exhibit additional structures, and we focus on the pair at positive ky giving additional limits to the effective vertical numerical aperture (NA)
We presented a versatile high-resolution ultracold atom microscope composed of two main components: (i) an economical and practical imaging system based on high NA off-the-shelf optics, and (ii) a high-fidelity digital aberration removal technique that is compatible with a wide range of imaging techniques
Summary
The majority of ultracold atom measurements rely on images of light that has interacted with an atomic ensemble. We summarize the theoretical description of laser light propagating along ez through a dilute atomic cloud: a nonpermeable dielectric medium. We relate the absorption and phase shift of the incident laser to a fundamental quantity in ultracold atom experiments: the 2D column density ρ2D(r⊥) = ρ(r)dz, where ρ(r) is the 3D atomic density with spatial coordinates r = xex + yey + zez and transverse coordinates r⊥ = xex + yey
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