Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0808.1660

Cavity photon counting: ab-initio derivation of the quantum jump superoperators and comparison of the existing models

Teppo Häyrynen, Jani Oksanen, Jukka Tulkki

Published Aug 12, 2008• 0 citations
arXivHTMLPDF

Abstract

Time development of electromagnetic fields in closed cavities under continuous detection of photons continues to be a subject of confusing controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued that their model of quantum superoperators (E model) invalidates some of the predictions of the previously introduced photon counting model of Srinivas and Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models are based on two postulated quantum jump superoperators: (1) the one-count operator corresponding to the absorption of a single photon and (2) the no-count operator. In this work we develop a stochastic difference equation that describes the dissipative coupling of the cavity field and the detector. The difference equation is based on non-perturbative treatment of the cavity-detector coupling. In spite of being non-integrable due to the coupling of the detector with an external reservoir it can be used to derive the exact forms of the quantum jump superoperators. When applied to a particular photon counting measurement our theory gives predictions identical with those of the SD model which should be considered a non-perturbative and ab-initio result. It is pointed out that available experimental results coincide with the results given by the ab-initio SD model. We summarize some of the key characteristics of cavity fields and photon counting processes to demonstrate that the results given by the SD model are consistent with the principles of quantum mechanics while those given by the E model are not.

DOI
10.48550/arxiv.0808.1660

Related papers

On the origin of divergences in the coincidence probabilities in cavity photodetection experiments

Teppo Häyrynen, Jani Oksanen, Jukka Tulkki

The theory of photon correlation is an established part of quantum electronics. However, recently reported divergences in the theory of time correlated detection of photons show that important details of cavity photon statistics are still incompletely understood. The quantum jump superoperators of the SD photon counting model given by Srinivas and Davies (1981 J. Mod. Opt. 28 981–96 ) do not fulfil the assumption of the bounded interaction rate. This has raised doubts about the consistency of the SD photon counting model and especially about the existence of coincidence probability density (CPD) functions (Dodonov et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 99–108). In this work, we start from the first principles of the quantum trajectory theory and show how the different coincidence probability densities and coincidence probabilities (CPs) have to be calculated. CPDs derived by us are well defined, and CPs are finite and correctly normalized for all fields with finite photon number expectation value. Furthermore, we show that the SD model reproduces photon bunching and antibunching phenomena when consistent derivation for the second-order coherence degree is used.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 17, 2009•8 citations

Superoperators and their implications in the hybrid model for photodetection

Ching Tsung Lee

The external photodetection of cavity radiation is considered as a continuous quantum measurement in the sense of Srinivas and Davies [Opt. Acta 28, 981 (1981)]. It is analyzed in terms of three elementary processes: the no-leak process, the one-leak-undetected process, and the one-leak-detected process. The first two form a no-count process and the last one, a one-count process. Superoperators for these elementary processes are postulated, following the examples of Srinivas and Davies. The superoperators for the one-count process, the no-count process, the m-count process, and the nonreferring process are then derived based on the postulates. The following implications of these superoperators are found: (1) the change of average photon number due to the one-count process is identical to the well-known Q parameter introduced by Mandel [Opt. Lett. 4, 205 (1979)]; (2) the no-count process is governed by a pseudomaster equation; (3) The probability for the m-count process is the Poisson transform of the initial P function of the cavity radiation; and (4) the nonreferring measurement process is governed by a master equation.

Physical Review A•Jun 1, 1994•17 citations

Quantum photodetection distributions with ‘nonlinear’ quantum jump superoperators

Alexandre V. Dodonov, Salomon Sylvain Mizrahi, V. V. Dodonov

We address the issue of the detection and counting of photons. We assume an electromagnetic field enclosed in an ideal cavity, which together with the detector constitute a closed system, so no photon is lost to the environment. Basing ourselves on a microscopic model consisting of a set of two-level atoms (the detector) interacting with the field, we derive a 'nonlinear' jump superoperator. We compare the count statistics calculated within our model with those obtained from previous models, such as the coincidence probability density , two-count conditional probability density , waiting times and the second order correlation function , for several field states.

Journal of Optics B Quantum and Semiclassical Optics•Mar 10, 2005•18 citations

Microscopic models of quantum-jump superoperators

Alexandre V. Dodonov, Salomon Sylvain Mizrahi, V. V. Dodonov

We discuss the quantum-jump operation in an open system and show that jump superoperators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with two-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that the derived quantum-jump superoperators have a ``nonlinear'' form $J\ensuremath{\rho}=\ensuremath{\gamma}\phantom{\rule{0.2em}{0ex}}\mathrm{diag}[F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})a\ensuremath{\rho}{a}^{\ifmmode\dagger\else\textdagger\fi{}}F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})]$, where the concrete form of the function $F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})$ depends on assumptions made about the interaction between the system and detector. Under certain conditions the asymptotical power-law dependence $F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})={(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}+1)}^{\ensuremath{-}\ensuremath{\beta}}$ is obtained. A continuous transition to the standard Srinivas-Davies form of the quantum-jump superoperator (corresponding to $\ensuremath{\beta}=0$) is shown.

arXiv:quant-ph/0506118•Physical Review A•Aug 16, 2005•17 citations

Unified quantum jump superoperator for optical fields from the weak- to the strong-coupling limit

Teppo Häyrynen, Jani Oksanen, Jukka Tulkki

We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigate how the setup operates at the close proximity of the lasing threshold.

Physical Review A•Jun 3, 2010•6 citations

Continuous photodetection model: quantum jumps engineering and hints for experimental verification

Alexandre V. Dodonov, Salomon Sylvain Mizrahi, V. V. Dodonov

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.

arXiv:quant-ph/0612067•Journal of Physics Conference Series•Oct 1, 2007•0 citations
Time development of electromagnetic fields in closed cavities under continuous detection of photons continues to be a subject of confusing controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued that their model of quantum superoperators (E model) invalidates some of the predictions of the previously introduced photon counting model of Srinivas and Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models are based on two postulated quantum jump superoperators: (1) the one-count operator corresponding to the absorption of a single photon and (2) the no-count operator. In this work we develop a stochastic difference equation that describes the dissipative coupling of the cavity field and the detector. The difference equation is based on non-perturbative treatment of the cavity-detector coupling. In spite of being non-integrable due to the coupling of the detector with an external reservoir it can be used to derive the exact forms of the quantum jump superoperators. When applied to a particular photon counting measurement our theory gives predictions identical with those of the SD model which should be considered a non-perturbative and ab-initio result. It is pointed out that available experimental results coincide with the results given by the ab-initio SD model. We summarize some of the key characteristics of cavity fields and photon counting processes to demonstrate that the results given by the SD model are consistent with the principles of quantum mechanics while those given by the E model are not.
The theory of photon correlation is an established part of quantum electronics. However, recently reported divergences in the theory of time correlated detection of photons show that important details of cavity photon statistics are still incompletely understood. The quantum jump superoperators of the SD photon counting model given by Srinivas and Davies (1981 J. Mod. Opt. 28 981–96 ) do not fulfil the assumption of the bounded interaction rate. This has raised doubts about the consistency of the SD photon counting model and especially about the existence of coincidence probability density (CPD) functions (Dodonov et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 99–108). In this work, we start from the first principles of the quantum trajectory theory and show how the different coincidence probability densities and coincidence probabilities (CPs) have to be calculated. CPDs derived by us are well defined, and CPs are finite and correctly normalized for all fields with finite photon number expectation value. Furthermore, we show that the SD model reproduces photon bunching and antibunching phenomena when consistent derivation for the second-order coherence degree is used.
The external photodetection of cavity radiation is considered as a continuous quantum measurement in the sense of Srinivas and Davies [Opt. Acta 28, 981 (1981)]. It is analyzed in terms of three elementary processes: the no-leak process, the one-leak-undetected process, and the one-leak-detected process. The first two form a no-count process and the last one, a one-count process. Superoperators for these elementary processes are postulated, following the examples of Srinivas and Davies. The superoperators for the one-count process, the no-count process, the m-count process, and the nonreferring process are then derived based on the postulates. The following implications of these superoperators are found: (1) the change of average photon number due to the one-count process is identical to the well-known Q parameter introduced by Mandel [Opt. Lett. 4, 205 (1979)]; (2) the no-count process is governed by a pseudomaster equation; (3) The probability for the m-count process is the Poisson transform of the initial P function of the cavity radiation; and (4) the nonreferring measurement process is governed by a master equation.
We address the issue of the detection and counting of photons. We assume an electromagnetic field enclosed in an ideal cavity, which together with the detector constitute a closed system, so no photon is lost to the environment. Basing ourselves on a microscopic model consisting of a set of two-level atoms (the detector) interacting with the field, we derive a 'nonlinear' jump superoperator. We compare the count statistics calculated within our model with those obtained from previous models, such as the coincidence probability density , two-count conditional probability density , waiting times and the second order correlation function , for several field states.
We discuss the quantum-jump operation in an open system and show that jump superoperators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with two-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that the derived quantum-jump superoperators have a ``nonlinear'' form $J\ensuremath{\rho}=\ensuremath{\gamma}\phantom{\rule{0.2em}{0ex}}\mathrm{diag}[F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})a\ensuremath{\rho}{a}^{\ifmmode\dagger\else\textdagger\fi{}}F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})]$, where the concrete form of the function $F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})$ depends on assumptions made about the interaction between the system and detector. Under certain conditions the asymptotical power-law dependence $F(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n})={(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}+1)}^{\ensuremath{-}\ensuremath{\beta}}$ is obtained. A continuous transition to the standard Srinivas-Davies form of the quantum-jump superoperator (corresponding to $\ensuremath{\beta}=0$) is shown.
We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigate how the setup operates at the close proximity of the lasing threshold.
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.