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arXiv:quant-ph/0310161 · Journal of Modern Optics

Towards photostatistics from photon-number discriminating detectors

Hwang Lee, Ulvi Yurtsever, Pieter Kok, G. Hockney, Christoph Adami, Samuel L. Braunstein, Jonathan P. Dowling

Published Jan 1, 2004• 48 citations
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Abstract

We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.

DOI
10.1080/09500340408235289

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We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.
In quantum optical computing and quantum cryptography a very important problem is that of developing an efficient photon-number resolving detector. Such a device is critical for the development of linear optical quantum computing (LOQC) [1], and can be also used in quantum cryptography [2]. A recent paper claims to have demonstrated the operation of a superconducting, number-resolving photon detector, developed by a group at NIST [3]. However, this device operates with a quantum efficiency of only about 20%, and we show here that it cannot discriminate photon number, even in principal. However, the NIST device has a very low dark-count rate, much less than 1%, which means that it can quite efficiently discriminate against the absence of photons of particular numbers. We call such a device a number-discriminating non-photon detector. Interestingly enough, even though this detector cannot yield photon number—its ability to discriminate against photons of certain numbers allows it to be used, under suitable assumptions, to reconstruct the ensemble photostatistics of the incoming photon field. However, such a low-efficiency device cannot be used, say, in LOQC, where single-shot photon number discrimination is required.
The output of a photodetector consists of a current pulse whose charge has the statistical distribution of the actual photon numbers convolved with a Bernoulli distribution. Photodetectors are characterized by a nonunit quantum efficiency, i.e., not all the photons lead to a charge, and by a finite resolution, i.e., a different number of detected photons leads to a discriminable values of the charge only up to a maximum value. We present a detailed comparison, based on Monte Carlo simulated experiments and real data, among the performances of detectors with different upper limits of counting capability. In our scheme the inversion of Bernoulli convolution is performed by maximum-likelihood methods assisted by measurements taken at different quantum efficiencies. We show that detectors that are only able to discriminate between zero, one and more than one detected photons are generally enough to provide a reliable reconstruction of the photon number distribution for single-peaked distributions, while detectors with higher resolution limits do not lead to further improvements. In addition, we demonstrate that, for semiclassical states, even on/off detectors are enough to provide a good reconstruction. Finally, we show that a reliable reconstruction of multipeaked distributions requires either higher quantum efficiency or higher resolution.
Photon-number resolving detectors are a fundamental building-block of optical quantum information processing protocols. A loop detector, combined with appropriate statistical processing, can be used to convert a binary on/off photon counter into a photon-number-resolving detector. Here we describe the idea of a signature of photon-counts, which may be used to more robustly reconstruct the photon number distribution of a quantum state. The methodology is applied experimentally in a 9-port loop detector operating at a telecommunications wavelength and compared directly to the approach whereby only the number of photon-counts is used to reconstruct the input distribution. The signature approach is shown to be more robust against calibration errors, exhibit reduced statistical uncertainty, and reduced reliance on a-priori assumptions about the input state.
Any single on-off photocounter, which can only detect the presence or absence of photons without discriminating their number, is not capable of identifying nonclassical nature of light. This limitation arises because any photocounting statistics obtained with such a detector can be easily reproduced with coherent states of a light mode. We show that a simple modification of an on-off detector -- introducing controlled attenuation as a tunable setting -- enables such detectors to reveal nonclassical properties of radiation fields.
We investigate the possibility of using linear detectors that exhibit a response to dark just resolved from that corresponding to a single detected photon to reconstruct the photon-number statistics of pulsed fields containing sizeable numbers of photons per pulse. We demonstrate that by applying a self-consistent procedure to analyze the output pulses of such detectors, we can properly measure statistical distributions of the number of detected photons and photon number correlations. The lack of fulfillment of such minimal requirements impairs the possibility of reliable shot-by-shot determinations of photon numbers.
Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters.