Measuring statistical characteristics of a quantized mode in various photodetection regimes

Abstract

We develop a theory of the discrete photodetection model where individual unexcited atoms from the atomic beam passing through a cavity are used as pointers. Atomic energy state selective detectors (ionization chambers) measure the escape statistics of ground-or excited-state atoms. Mandelstam’s method of successive indirect quantum measurements underlies the theory being developed. In contrast to the available works, the suggested approach takes into account the atomic beam statistics, the operation nonideality (quantum efficiencies) of ionization chambers, the detector recovery time, the back action of the probe on the quantized mode, and the relaxation process in the time interval when the cavity is empty (without atoms). We derive formulas that relate the a posteriori probabilities of photodetector clicks to the elements of the main diagonal of the initial density matrix for the cavity mode. Our numerical simulations confirm that the inverse problem of reconstructing the initial photon number distribution in a cavity can be solved using the statistics of detector clicks measured during the transient process.