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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Measurements with on-off detector systems

Jan Sperling, W. Vogel, G. S. Agarwal

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We study systems of on-off detectors. For coherent light, such kinds of measurements reveal a binomial statistics rather than a Poisson one. Hence, nonclassicality may be determined by a sub-binomial click statistics.
DOI
10.1364/cqo.2013.m6.31

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The click statistics from on-off detector systems is quite different from the counting statistics of the more traditional detectors. This necessitates the introduction of new parameters to characterize the nonclassicality of fields from measurements using on-off detectors. To properly replace the Mandel Q(M) parameter, we introduce a parameter Q(B). A negative value represents a sub-binomial statistics. This is possible only for quantum fields, even for super-Poisson light. It eliminates the problems encountered in discerning nonclassicality using Mandel's Q(M) for on-off data.
Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Distinguishing nonclassical states from those that can be described without invoking quantum mechanics is both a necessary practical task and of fundamental interest. In general, signatures of nonclassicality arise from apparently pathological behaviour of the quasi-probability distributions used to describe the states. While tomographic reconstruction of the state is therefore sufficient to show nonclassicality, it is often more convenient to probe photon-counting statistics of on-off detectors directly. This is formalised by the Mandel Q-parameter QM= 〈Δn〉 / 〈n〉 - 1, which is negative for sub-Poissonian statistics arising from nonclassical states. However, the Mandel Q-parameter can fail when using a multiplexed array of on-off detectors to measure states with several photons; splitting in this manner can corrupt its original statistics. A new parameter, QB= N 〈(Δ c) 2 〉 / 〈 c 〉 (N - 〈 c 〉) can be used to witness nonclassicality directly from such click statistics. For QB<; 0, such statistics are thus deemed sub-binomial and therefore arise from a nonclassical state.
We introduce a general parameter QPB{Q}_{\mathrm{PB}}QPB​ that provides an experimentally accessible nonclassicality measure for light. The parameter is quantified by the click statistics obtained from on-off detectors in a general multiplexing detection setup. Sub-Poisson-binomial statistics, observed by QPB<0{Q}_{\mathrm{PB}}<0QPB​<0, indicates that a given state of light is nonclassical. Our parameter replaces the binomial parameter QB{Q}_{\mathrm{B}}QB​ for more general cases, where any unbalance among the multiplexed modes is allowed, thus enabling the use of arbitrary multiplexing schemes. The significance of the parameter QPB{Q}_{\mathrm{PB}}QPB​ is theoretically examined in a measurement setup that only consists of a ring resonator and a single on-off detector. The proposed setup exploits minimal experimental resources and is geared towards a fully integrated quantum nanophotonic circuit. The results show that nonclassical features remain noticeable even in the presence of significant losses, rendering our nonclassicality test more practical and sufficiently flexible to be used in various nanophotonic platforms.