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Abstract:

Various schemes for the determination of a single-mode cavity state from the photon statistics of the field both before and after an interaction with one or two level atoms is presented. The state vector from the measured statistics is calculated and its simplicity is shown. The number states and coherent states fall within the class that may be measured with one atom interaction while squeezed states and Schrodinger cats are within those states that may be measured with two atom interaction. The complexity of the data inversion or measured statistics increases as the number of interacting atom increases.

Abstract:

We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and 'Schrödinger cats' are among those that may be measured with a two-atom interaction.