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arXiv:quant-ph/0307089 · Journal of Optics B Quantum and Semiclassical Optics

A consistent quantum model for continuous photodetection processes

M. C. de Oliveira, Salomon Sylvain Mizrahi, V. V. Dodonov

Published Jun 1, 2003• 23 citations
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Abstract

We modify some aspects of the continuous photodetection theory proposed by Srinivas and Davies (SD) (1981 Opt. Acta 28 981), which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the ‘annihilation’ and ‘creation’ operators that enter in the photocount super-operators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to SD precepts, but also avoids some weird result appearing when previous definitions are used.

DOI
10.1088/1464-4266/5/3/358

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We modify some aspects of the continuous photodetection theory proposed by Srinivas and Davies (SD) (1981 Opt. Acta 28 981), which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the ‘annihilation’ and ‘creation’ operators that enter in the photocount super-operators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to SD precepts, but also avoids some weird result appearing when previous definitions are used.
In this manuscript, we explore the effects of continuous measurements upon the quantized electromagnetic field through a series of simple examples. For this purpose, we consider the Srinivas-Davies model to describe the optical field dynamics probed continuously by a photodetector. Through the application of this continuous photodetection model to some specific situations, it is possible to cover some basic concepts of quantum mechanics such as the principle of superposition, the collapse of the wave function, the probabilistic character of the possible outcomes associated with projective measurements, as well as some advanced topics such as the description of open quantum systems, irreversible processes in quantum mechanics, decoherence and dissipation associated with non-unitary evolution of quantum systems. Besides, we also consider the important concept of entanglement between two electromagnetic fields and how it is affected by the photodetection process. This work aims to provide complementary material for undergraduate and graduate students interested in the effects of measuring devices acting on quantum systems.
This paper proposes a microscopic model for the continuous measurement of photon numbers where the continuous measurement is simulated by a sequence of infinitesimal processes. Each process is composed of a unitary evolution for the coupled system, which consists of the field and the measuring apparatus, followed by a projection according to the readout of the measuring apparatus. The proposed model consists of two-level atoms that are coupled one by one with an optical cavity field via the electric-dipole interaction. Each atomic level is then read out after the interaction, causing a nonunitary state reduction of the field. In particular, it is shown that this microscopic model leads to the Srinivas-Davies model that has been postulated for the photodetection process.
The concept of photodetection as a continuous quantum measurement introduced by Srinivas and Davies is extended to the detection of resonance fluorescence. This is a new approach to an old subject. This is also a new development in continuous photodetection in the sense that a fermion rather than the traditional boson field is the subject of monitoring. The superoperators for the no-count and the one-count processes are postulated, following the examples of Srinivas and Davies. The probability for the m-count process is then derived on the basis of these postulates. The first two factorial moments of the photon-number distribution are calculated, which are then used to evaluate the non-classical effects in resonance fluorescence. A parameter slightly different from Mandel's is found to be more suitable indicator of photon antibunching in the transient state.
We develop a quantum theory for continuous photodetection processes that describes nonunitary time development of the field under continuous measurement of photon number. Exact expressions are obtained for time evolutions of the photon-field density operator, average and variance of the photon number, and the Fano factor. These are applied to typical quantum states, i.e., number, coherent, thermal, and squeezed states. The continuous photodetection process is made up of two elementary processes in terms of the referring measurement process, that is, one-count and no-count processes. Just after the one-count process in which a photodetector registers one photoelectron, the average photon number 〈n(t)〉 of the remaining field is shown to increase for super-Poissonian states (e.g., thermal state) and decrease for sub-Poissonian states (e.g., number state); for the Poissonian state (e.g., coherent light), 〈n(t)〉 does not change. During the no-count process in which the photodetector registers no photoelectrons, on the other hand, 〈n(t)〉 decreases in time for all states except the number state. The physical origins for these results are clarified from the viewpoint of nonunitary state reduction by continuous measurement of photon number. Furthermore, we introduce a nonreferring measurement process in which the detector registers photocounts, but we discard all readout information. We discuss the difference in the way the photon field evolves in this process compared to the referring measurement process.
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.
We examine some aspects of the continuous photodetection model for photocounting processes in cavities. 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.