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Springer eBooks

Measurement of the Wigner Function via Atomic Beam Deflection

Ashfaq H. Khosa, Shi‐Yao Zhu, Muhammad Suhail Zubairy

Published Jan 1, 2000• 0 citations
Publisher
DOI
10.1007/978-3-662-07313-1_52

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Journal of Physics B Atomic Molecular and Optical Physics•Feb 1, 2011•7 citations
A method for the reconstruction of photon statistics and even the Wigner function of a quantized cavity field state is proposed. The method is based on the measurement of momentum distribution of two-level atoms in the Raman–Nath regime. Both the cases of resonant and off-resonant atom–field interaction are considered. The Wigner function is reconstructed by displacing the photon statistics of the cavity field. This reconstruction method is straightforward and does not need much mathematical manipulation of experimental data.
We investigate deflection of atomic beams on two co-propagating standing waves excited in a bimodal cavity. The novelty is that the standing waves are in an entangled, photon-number correlated state and interactions with three-level atoms of V-type and Λ-type configurations are considered. The splitting of atomic states, quantum interference effects and spatial atomic localization due to phase measurements is investigated on the framework of both the conditional position distributions of atomic wave packets as well as the Wigner functions for atomic translation variables. It is demonstrated that these quantities for V-type atoms passing the cavity are essentially modified when entangled states of standing waves are used instead of statistically independent waves. The deflection patterns and the Wigner functions are also modified if atoms are initially prepared in a superposition of low-level states. It is best demonstrated for the Λ-type configuration, where transition through the Raman resonance is realized, and proposed for testing superposition states in a new non-spectroscopic manner.