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arXiv:2303.14246 · Physical Review A

Photocounting measurements with dead time and afterpulses in the continuous-wave regime

А. А. Семенов, J. Samelin, Chris Boldt, Melanie Schünemann, C. Reiher, W. Vogel, Boris Hage

Published Jan 4, 2024• 9 citations
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Abstract

The widely used experimental technique of continuous-wave detection assumes counting pulses of photocurrent from a click-type detector inside a given measurement time window. With such a procedure we miss out the photons detected after each photocurrent pulse during the detector dead time. Additionally, each pulse may initialize a so-called afterpulse, which is not associated with the real photons. We derive the corresponding quantum photocounting formula and experimentally verify its validity. Statistics of photocurrent pulses appears to be nonlinear with respect to the quantum state, which is explained by the memory effect of the previous measurement time windows. Expressions---in general, nonlinear---connecting statistics of photons and pulses are derived for different measurement scenarios. We also consider an application of the obtained results to quantum state reconstruction with unbalanced homodyne detection.

DOI
10.1103/physreva.109.013701

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The widely used experimental technique of continuous-wave detection assumes counting pulses of photocurrent from a click-type detector inside a given measurement time window. With such a procedure we miss out the photons detected after each photocurrent pulse during the detector dead time. Additionally, each pulse may initialize a so-called afterpulse, which is not associated with the real photons. We derive the corresponding quantum photocounting formula and experimentally verify its validity. Statistics of photocurrent pulses appears to be nonlinear with respect to the quantum state, which is explained by the memory effect of the previous measurement time windows. Expressions---in general, nonlinear---connecting statistics of photons and pulses are derived for different measurement scenarios. We also consider an application of the obtained results to quantum state reconstruction with unbalanced homodyne detection.
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Abstract Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.
We derive a closed photocounting formula, including noise counts and a finite quantum efficiency, for photon-number-resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photocounting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indispensable for the correct interpretation of quantum effects observed with such devices.
Abstract Photon counting provides a valuable tool for measuring quantum properties of light. Unavoidable imperfections of photon detectors lead to discrepancies between the statistics of photons and statistics of photon counts. Here we consider dead-time corrections and influence of intensity fluctuations for simulated Poissonian statistics of photo counts for the pulsed or continuous wave coherent light sources. We analyse dependence between the statistical moments of corrected distribution and the mean photon number, dead-time, and level of intensity fluctuations.
A novel technique for photon correlation measurements, based on the excitation of a resonant system by photon-detector single pulses, analog/digital sampling, and deconvolution, has been developed and analyzed experimentally and by computer simulations. The measured correlation function is expressed by a convolution of the true photon correlation function of the optical field and a well-defined, noiseless resonator correlation function. The effect of detector statistics is reduced to the contribution of two integral parameters—the total single-pulse charge and the jitter of single-pulse centers. Good performance of this technique is demonstrated at high photon rates and resolutions, where the well-known photon-counting or single-quantum methods are ineffective. The novel technique offers linear recording of photocount time series without dead-time effects. The temporal resolution is defined by the sampling step of the analog/digital converter. The retrieval error does not exceed 1 to 3% at count rates higher than 1 GHz and single-pulse durations larger than the resolution cell. This technique can be effectively applied in photon correlation measurements of high dynamic optical fields.
We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitatively describes the measurement backaction of photon-counting on the homodyne output. The obtained results are applied to typical initial states --- coherent, number, thermal, and squeezed states. Monte Carlo simulations of the measurement processes are also presented to demonstrate the dynamics of the combined measurement process.