We have designed, built, and characterized a high-resolution objective lens that is compatible with an ultrahigh vacuum environment. The lens system exploits the principle of the Weierstrass sphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 μm. Our two-lens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning near-field optical microscopy, to measure the point spread function (PSF) of a high NA optical system. From the PSF, we infer the wavefront aberration for the entire field of view of about 75 μm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technologies such as quantum control of atoms in optical microtraps with an unprecedented spatial resolution and photon collection efficiency.

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We present a scheme to directly probe the Wigner function of the motional state of a neutral atom confined in an optical trap. The proposed scheme relies on the well-established fact that the Wigner function at a given point $(x,p)$ in phase space is proportional to the expectation value of the parity operator relative to that point. In this work, we show that the expectation value of the parity operator can be directly measured using two auxiliary internal states of the atom: parity-even and parity-odd motional states are mapped to the two internal states of the atom through a Ramsey interferometry scheme. The Wigner function can thus be measured point-by-point in phase space with a single, direct measurement of the internal state population. Numerical simulations show that the scheme is robust in that it applies not only to deep, harmonic potentials but also to shallower, anharmonic traps.