Fresnel Representation of the Wigner Function: An Operational Approach

P. Lougovski, E. Solano, Z. M. Zhang, H. Walther, H. Mack, W. P. Schleich

Published 2002-06-13, updated 2003-04-16Version 3

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] and in cavity QED [B. Varcoe et al., Nature 403, 743 (2000)]. The values of the Wigner functions of the underlying states at the origin of phase space are W(0)=+1.75 for the vibrational ground state and W(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.