RESUMEN
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.
RESUMEN
Coherent fluorescence imaging with two objective lenses (4Pi detection) enables single-molecule localization microscopy with sub-10 nm spatial resolution in three dimensions. Despite its outstanding sensitivity, wider application of this technique has been hindered by complex instrumentation and the challenging nature of the data analysis. Here we report the development of a 4Pi-STORM microscope, which obtains optimal resolution and accuracy by modeling the 4Pi point spread function (PSF) dynamically while also using a simpler optical design. Dynamic spline PSF models incorporate fluctuations in the modulation phase of the experimentally determined PSF, capturing the temporal evolution of the optical system. Our method reaches the theoretical limits for precision and minimizes phase-wrapping artifacts by making full use of the information content of the data. 4Pi-STORM achieves a near-isotropic three-dimensional localization precision of 2-3 nm, and we demonstrate its capabilities by investigating protein and nucleic acid organization in primary neurons and mammalian mitochondria.