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Physical Review A

Temperature effects in photodetection

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

Published Nov 1, 1978• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.18.2234

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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.
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.
A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.
The photon counting statistics of the fluorescence of a single atom driven by a resonant coherent field has been calculated and the results checked experimentally. The authors examine the effect of detuning the coherent field and/or the effect of an additional thermal field on the photon counting statistics. They work with a master equation that they have used previously and derive exact results for the probability distribution function P(n, tau ) for the emitted photons and for the normalised second factorial moment Q. The subPoissonian character of the photon statistics, for which Q<0, is most pronounced for weak thermal fields or weak detuned coherent fields. For short counting times tau the statistic is dominated by any spontaneous emission that occurs, as expected. Increasing numbers of black-body photons tend to increase the Q values, as might be expected-especially in the case of an initially excited atom-but no simple rule emerges. The recent experiments in the microwave region on Rydberg atoms interacting with thermal radiation in (low-Q) cavities offers the possibility of observing thermal-field effects on the photon counting statistics.
We reconsider various approaches to the quantum theory of photodetection from the point of view of the quantum theory of measurement, and show that important differences between them depend upon the manner in which they take into account the modification of the field distribution produced by the presence of the detector. We show that the Mandel photon counting formula may lead to unphysical results, such as negative probabilities, in some situations just because this modification is not incorporated into the model. We also show that the recently developed quantum theory of continuous measurements provides a completely satisfactory framework for discussing photon counting experiments. As an illustration, an exact derivation of the photon statistics of a single-mode free field is presented, and some of the results are shown to be identical to those derived earlier by Mollow and others. We also indicate how our approach can be extended to discuss the photon statistics of fields in interaction with sources and reservoirs.
A simple model is introduced to simulate the detection of cavity radiation with the detector placed outside the cavity. Explicit expressions, in terms of initial photon-number distribution, for the time-dependent distributions of photoelectron number and conditional as well as unconditional waiting times are derived. The effect of photodetection on the quantum state of the radiation in the present arrangement is found to be unchanged from that with the detector placed inside the cavity. The well-known Q parameter introduced by Mondel [Opt. Lett. 4, 205 (1979)] is found to be exactly equal to the change in the expectation value of photon number due to the detection of a photon. Photon bunching or antibunching, reflecting classical or nonclassical radiation, is determined by whether conditional waiting time is less or greater than unconditional waiting time. When this criterion is applied to three specific examples, namely, coherent, thermal, and number states, the results are as expected.
We study in this paper the possible influence of vacuum fluctuations on photo detection and its background noise in Bell tests. We analyze its consequences on the standard statistical analysis of data showing that it is not fulfilled anymore the conventional hypothesis of a Poisson like probability density distribution of single photodetection events. We assume that vacuum fluctuations are due to real and measurable fluctuating fields, as recently confirmed experimentally, and that their non null correlations outside the light cone contribute to photon coincidence rates making them time dependent. We introduce a generalized Bell like correlation function which contains a new term due to supposed vacuum induced photon counting events. We deduce then a generalization of CH-inequality which takes in account the effect of these vacuum electric fields on detector efficiency. We predict an apparatus temperature fluctuations during photon detection which we suggest could be observed by looking for colored noise thermal emission of the photodetectors, generalizing the standard white noise prediction of C.S.L. models on wave function collapse postulate. We discuss an experimental test of this prediction, based on the idea of inducing a thermal wave on the whole quantum detectors, aimed to observe time dependent deviations from standard stationary statistical predictions of Quantum Mechanics.