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

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