Direct measurement of the Wigner function of atoms in an optical trap

TL;DR

This paper introduces a Ramsey interferometry-based method to directly measure the Wigner function of a neutral atom in an optical trap, enabling phase space characterization through internal state measurements.

Contribution

It proposes a novel scheme that maps motional parity states to internal states for direct Wigner function measurement in various trap potentials.

Findings

Scheme is robust for harmonic and anharmonic traps

Allows point-by-point phase space measurement

Uses internal state populations for Wigner function retrieval

Abstract

We present a scheme that uses Ramsey interferometry to directly probe the Wigner function 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 parity-even and parity-odd motional states can be mapped to two distinct internal states of the atom by using state-dependent trapping potentials. 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.