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arXiv:quant-ph/0607215 · Physical Review A

Inclusion of nonidealities in the continuous photodetection model

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

Published Jan 10, 2007• 13 citations
arXivHTMLPDF

Abstract

Some nonideal effects as nonunit quantum efficiency, dark counts, dead time, and cavity losses that occur in experiments are incorporated within the continuous photodetection model by using the analytical quantum trajectories approach. We show that in standard photocounting experiments the validity of the model can be verified and the formal expression for the quantum jump superoperator can also be checked.

DOI
10.1103/physreva.75.013806

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Some nonideal effects as nonunit quantum efficiency, dark counts, dead time, and cavity losses that occur in experiments are incorporated within the continuous photodetection model by using the analytical quantum trajectories approach. We show that in standard photocounting experiments the validity of the model can be verified and the formal expression for the quantum jump superoperator can also be checked.
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.
Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as, by an ideal photodetector. Here we derive (non-Markovian) quantum trajectories for realistic photodetection, including the effects of efficiency, dead time, bandwidth, electronic noise, and dark counts. We apply our theory to a realistic cavity QED scenario and investigate the impact of such detector imperfections on the conditional evolution of the system state. A practical theory of quantum trajectories with realistic detection will be essential for experimental and technological applications of quantum feedback in many areas.
Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. In practice an experimenter has access to an output filtered through various electronic devices, rather than the microscopic states of the detector. This introduces several imperfections into the measurement process, of which only inefficiency has previously been incorporated into quantum trajectory theory. However, all electronic devices have finite bandwidths, and the consequent delay in conveying the output signal to the observer implies that the evolution of the conditional state of the quantum system must be non-Markovian. We present a general method of describing this evolution and apply it to avalanche photodiodes and to photoreceivers. We include the effects of efficiency, dead time, bandwidth, electronic noise and dark counts. The essential idea is to treat the quantum system and classical detector jointly, and to average over the latter to obtain the conditional quantum state. The significance of our theory is that quantum trajectories for realistic detection are necessary for sophisticated approaches to quantum feedback, and our approach could be applied in many areas of physics.
We study the back action of a single-photon detector on the electromagnetic field upon a photodetection by considering a microscopic model in which the detector is constituted of a sensor and an amplification mechanism. Using the quantum trajectories approach we determine the quantum jump superoperator (QJS) that describes the action of the detector on the field state immediately after the photocount. The resulting QJS consists of two parts: the bright-count term, representing the real photoabsorptions, and the dark-count term, representing the amplification of intrinsic excitations inside the detector. First we compare our results for the counting rates to experimental data, showing good agreement. Then we point out that by modifying the field frequency one can engineer the form of the QJS, obtaining the QJS's proposed previously in an ad hoc manner.
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.