Correlations between the outputs of two photodetectors illuminated by arbitrary radiation fields are discussed in terms of quantum field theory. Emphasis is placed on evaluating contributions to the mean correlation which originate in the nonzero commutators of the photon field and are within the frequency response of common detectors. The model for a photodetector, which is applicable to detectors with semiconductors or metals as sensitive elements, is described in terms of the one-electron approximation of the band theory of solids. Time-dependent perturbation theory utilizing methods of scattering theory is used to obtain the lowest-order contribution to the mean detector current and mean cross correlation. In contrast to previous discussions, contributions to the mean correlation which are fourth-order in the field-detector coupling and originate in the quantum nature of the photon field are shown to be exactly zero under reasonable assumptions about the physical properties of the detectors.
Correlations between the outputs of two photodetectors illuminated by arbitrary radiation fields are discussed in terms of quantum field theory. Emphasis is placed on evaluating contributions to the mean correlation which originate in the nonzero commutators of the photon field and are within the frequency response of common detectors. The model for a photodetector, which is applicable to detectors with semiconductors or metals as sensitive elements, is described in terms of the one-electron approximation of the band theory of solids. Time-dependent perturbation theory utilizing methods of scattering theory is used to obtain the lowest-order contribution to the mean detector current and mean cross correlation. In contrast to previous discussions, contributions to the mean correlation which are fourth-order in the field-detector coupling and originate in the quantum nature of the photon field are shown to be exactly zero under reasonable assumptions about the physical properties of the detectors.
A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]
Quantum detection processes in quantum field theory (QFT) must play a key role in the description of quantum-field correlations, such as the appearance of entanglement, and of causal effects. We consider the detection in the case of a simple QFT model with a suitable interaction to exact treatment, consisting of a quantum scalar field coupled linearly to a classical scalar source. We then evaluate the response function to the field quanta of two-level pointlike quantum model detectors, and analyze the effects of the approximation adopted in standard detection theory. We show that the use of the RWA, which characterizes the Glauber detection model, leads in the detector response to nonlocal terms corresponding to an instantaneously spreading of source effects over the whole space. Other detector models, obtained with nonstandard or no application of RWA, give instead local responses to field quanta, apart from source-independent vacuum contribution linked to preexisting correlations of zero-point field.
In the Maxwell continuum wave theory of light, a photodetector measures the intensity of the Electro Magnetic wave. The output current of the photodetector is proportional to the intensity of input light. Since the introduction of the concept of photon, or the concept of field quantization, physicists started to premeditate single-photon detection, theoretically and experimentally. Due to slight differences in their optical paths, at certain locations, the radiations superposed constructively, at other locations the field superposed destructively. A sinusoidal modulation is thus observable. However, people found this interpretation may not be appropriate when the experimental physicists improved the sensitivity of their photodetector to the single-photon level. Almost everyone was surprised that the interference was still observable in the observation plane, and the sinusoidal modulation observed from single-photon was exactly the same as before. A single-photon counting detector is able to count photons one by one.
It is shown how certain classes of problems dealing with the interaction of radiation with atoms can be formulated in terms of four-operator perturbation series. The case of an isolated atom coupled to a single-mode field is discussed in detail within the resolvent formalism. The process where no photon is effectively absorbed by the atom is described, to all orders, in terms of a series involving four operators which simultaneously increase and/or decrease the photon number and the orbital quantum number. This series is exactly summed and the summation technique is generalized to single-atom, two-field and to two-atom, single-field systems exhibiting zero, one, and two net photon absorptions or emissions. The theory is applied to induced emission of a single photon from a pair of two-level atoms coupled to a monomode radiation field. The energy diagrams, the time dependence of the probability, and the resonance curves are discussed for systems where (i) both atoms are in the upper state and (ii) atom 1 is in the upper state and atom 2 is in the lower state at t=0. In comparing these results to the ones obtained with a single atom, we find that the important intensity-dependent correlations give rise to trapping effects even when the atoms are initially in the upper state.
Correlation effects in parametric photon-pair production are studied within the framework of a physically realistic model. The analysis, which is fully quantum mechanical, takes into account the finite sizes of the target and the beam cross section, and allows for dispersion and anisotropy in the linear susceptibility. The correlations in position and time at which the two members of a parametrically generated pair may be detected are carefully evaluated. These correlations, which have been measured experimentally, are intrinsically quantum mechanical; i.e., they can be explained by no theory in which the subharmonic fields are described purely by c-number functions. A complete solution, from which field correlation functions of arbitrarily high order may be evaluated, is obtained by a method which at the same time allows for an arbitrary degree of parametric gain. The solution is expressed entirely in terms of a particular two-point field-correlation-function, as evaluated in lowest order in the incident field strength, at points distant from the target. The function in question is found by directly examining the fluctuating currents in the material medium, rather than by eliminating the matter variables at the outset through the introduction of a nonlinear electomagnetic susceptibility.
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.