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Journal of Experimental and Theoretical Physics

Measuring statistical characteristics of a quantized mode in various photodetection regimes

George P. Miroshnichenko

Published May 1, 2007• 2 citations
Publisher

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.

DOI
10.1134/s1063776107050068

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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.
A theory of the discrete photodetection of quantum jumps on the V configuration of atomic levels has been developed. A three-level source atom is placed in a cavity excited by a resonance fluorescence field. The cavity is tuned to exact resonance with an atomic transition. The cavity mode state is tested by a flux of unexcited (at the entrance) probe atoms passing through the cavity. The energy states of the outgoing probe atoms are detected by ionization chambers, which are assumed ideal. This a posteriori statistical information is indirectly related to the numerical characteristics of a measured quantum system consisting of the source atom and cavity mode. The “tuning” conditions for a discrete photodetector, i.e., the rules for choosing the parameters and durations of the interactions of the cavity mode with the probe and source atoms, intensities of the pump and probe fields that are necessary for observing quantum jumps from the “bright” state to the “dark” one and vice versa, have been determined. A two-state model that describes the dynamics of a quantum jump has been analyzed. The formulas have been obtained for the observable characteristics of quantum jumps: the mean residence time of the quantum system in quasistationary states (durations of the bright and dark periods), probabilities of quantum jumps, mean excitation levels of the quantized cavity mode, etc.
We describe and theoretically study a process of photon distribution statistics measurement for intra-cavity mode of EM field monitored by indirect photo-detection scheme.In particular, we investigate photon number distribution and Mandel's parameter (normalized dispersion) of the mode using statistics of atomic state detector clicks.In our model, a two-level atom-pointer which passes through the cavity interacts with the mode and environment, distorting the measured statistical properties of the mode.To account for this, phase distortion (decoherece) and population relaxation are introduced in the model.In this paper, we use the super-operators approach to intra-cavity mode evolution conditioned by atomic state detector clicks.
Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and helps with various relevant applications. Nevertheless, no detector that can reliably discriminate the number of incident photons is available. On the other hand, the alternative of reconstructing the density matrix by quantum tomography leads to various technical difficulties that are particularly severe in the pulsed regime (where mode matching between a signal and local oscillator is very challenging). Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photo-counters, it was recently shown how reconstruction of photon statistics is possible by considering a variable quantum efficiency. Here we present experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams in a scheme based on on/off avalanche photodetection assisted by maximum-likelihood estimation. Reconstructions of the distribution for both semiclassical and quantum states of light (as single photon, coherent, pseudothermal, and multithermal states) are reported for single-mode and multimode beams. The stability and good accuracy obtained in the reconstruction of these states clearly demonstrate the interesting potentialities of this simple technique.
A method is proposed for generating conditional single-photon states with a high degree of purity in a single-mode cavity by successive discrete photodetection. The cavity is pumped by resonance fluorescence emission from a source atom driven by a classical field. The cavity is tuned to a Mollow sideband. A relation between detector parameters is found that makes it possible to interpret the detection of a probe atom in the excited state as unambiguous evidence that a pure single-photon state has been prepared in the cavity. An expression is derived for the prior probability of such an event, and dependence of the one-photon state population of the cavity field on detuning, relaxation rate, and time is examined.
An indirect quantum state measurement process is under investigation. Common evolution of detector's microscopic part (pointer) and measured system (target) is considered to be nonunitary due to the interaction between pointer and environment. System of differential equations for superoperators, which map initial target state to it's conditional final state is obtained. Developed formalism is applied to the problem of cavity quantum mode photodetection to investigate basic information characteristics of this measurement process.