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Journal of Physics A Mathematical and General

Open-system theory of photodetection: dynamics of field and atomic moments

Annabella Selloni, P. Schwendimann, A. Quattropani, H. Baltes

Published Jul 1, 1978• 18 citations
Publisher

Abstract

A theory of photodetection is presented which takes fully into account the relaxation of the photosensitive atoms representing the detector. Atoms, electromagnetic field, and atom-field interaction are described in terms of the Dicke Hamiltonian with additional coupling of the atoms to a reservoir. The time evolution of the joint detector and field states is derived using master equation techniques. Simple relations between the dynamics of field and atomic moments are obtained in the case of zero detector temperature. The attenuation of the field moments as well as the photocounting probability for any initial field state are found to involve not only the atom-field, but also the atom-reservoir coupling parameters.

DOI
10.1088/0305-4470/11/7/029

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Temperature effects in photodetection

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We present a theoretical study of photodetection with coupling of the photosensitive atoms to a reservoir. We investigate the effects of nonzero detector temperature, where the initial thermal-equilibrium occupation of the atomic levels and the thermalization of the radiation field interfere with the measurement of the photon statistics. We derive formulas exhibiting the temperature dependence of the field dynamics, the relationship between field and atomic moments, and the photocounting probability. We present examples illustrating how the coherence properties of the incoming field are affected by the detection process in the presence of thermal noise.

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arXiv:quant-ph/0612067•Journal of Physics Conference Series•Oct 1, 2007•0 citations
A theory of photodetection is presented which takes fully into account the relaxation of the photosensitive atoms representing the detector. Atoms, electromagnetic field, and atom-field interaction are described in terms of the Dicke Hamiltonian with additional coupling of the atoms to a reservoir. The time evolution of the joint detector and field states is derived using master equation techniques. Simple relations between the dynamics of field and atomic moments are obtained in the case of zero detector temperature. The attenuation of the field moments as well as the photocounting probability for any initial field state are found to involve not only the atom-field, but also the atom-reservoir coupling parameters.
We present a theoretical study of photodetection with coupling of the photosensitive atoms to a reservoir. We investigate the effects of nonzero detector temperature, where the initial thermal-equilibrium occupation of the atomic levels and the thermalization of the radiation field interfere with the measurement of the photon statistics. We derive formulas exhibiting the temperature dependence of the field dynamics, the relationship between field and atomic moments, and the photocounting probability. We present examples illustrating how the coherence properties of the incoming field are affected by the detection process in the presence of thermal noise.
A nonequilibrium open-system theory for continuous photodetection processes is developed using a probability-density functional combined with the path-integral technique. Nonunitary time evolution of the system-environment density operator due to measurement back action and continuous measurement is exactly described for three familiar photodetection processes. New exact photocounting formulas are obtained for these three processes; in particular, Mollow's photocounting formula is generalized for a nonequilibrium open system. Distinctive features between a closed system and an open system are presented; for example, the probability distribution for the number of counts is shown to contain complete information about photoelectron statistics for a closed system, whereas it does not for an open system. The obtained formulas are applied to photodetection of a single-mode photon field that interacts linearly with a pump source consisting of a single harmonic oscillator and a reservoir consisting of an infinite number of harmonic oscillators. In the former case, increasing the ratio of the source-field coupling constant to the field-detector coupling constant causes the photon field to cross over from a closed attenuating field to an open stationary field. In the latter case, a quantum-mechanical fluctuation-dissipation theorem in the continuous photodetection context is discussed.
A quantum-mechanical theory of photon detection is presented which takes fully into account the attenuation of the field due to the detection process. The time evolution of the joint quantum state of the detector and the field is found, to all orders in perturbation theory. Formulas are derived for the probabilities of absorbing specified numbers of photons within a given time interval, and for the correlations in the positions and times at which absorptions take place. The results are free from the inconsistencies which arise in the conventional theory of photon detection, and remain valid even when the field becomes appreciably attenuated during the experiment. It is found that an initially coherent field state remains coherent during its interaction with a given detector, and that its amplitude becomes attenuated by an amount which is completely independent of the number of counts which the detector records. This independence is shown to be a simple consequence of the Poisson quantum-number distribution of coherent fields. The counting statistics for arbitrary fields are expressed in a way which shows explicitly the relationship between the attenuation of the field and the absorption of quanta by the detector. The analysis is performed by first treating the case in which the field is confined within a homogeneous detecting medium throughout the experiment, and then generalizing to the case in which the field spends a limited amount of time in a spatially localized detecting region. The detector is assumed to consist of harmonic oscillators, which are shown to represent a suitable formal model for the absorption of radiation by large numbers of conventional detecting atoms.
One can attempt to derive some information of the field from the measured random properties of the photoelectron process: this is the object of photodetection theory developed first for classical fields. This chapter presents a review of photodetection theory, quantum theory and population monitoring model. It discusses two interesting applications to photostatistics. The photodetection equation is used to classify quantum and classical fields. The chapter presents an example of collective antibunching of photons. The double random character of the photodetection process prevents a simple correspondence between the statistical properties of the intensity and the statistics of the photocounts. However it is more instructive to connect the photoelectron process with the quantum nature of the electromagnetic field. Although the problem of photodetection appears to be satisfactorily solved for free fields interacting only with the detector, a heuristic model permits evolution of the detected field during the detection process.
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.
We examine some aspects of the continuous photodetection model for photocounting processes in cavities. First, we work out a microscopic model that describes the field-detector interaction and deduce a general expression for the Quantum Jump Superoperator (QJS), that shapes the detector's post-action on the field upon a detection. We show that in particular cases our model recovers the QJSs previously proposed ad hoc in the literature and point out that by adjusting the detector parameters one can engineer QJSs. Then we set up schemes for experimental verification of the model. By taking into account the ubiquitous non-idealities, we show that by measuring the lower photocounts moments and the mean waiting time one can check which QJS better describes the photocounting phenomenon.