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OSA Continuum

Photon statistics without coincidence counting using an unbalanced beam-splitter

Hamed Pourbeyram, Cody Bassett, Arash Mafi

Published Feb 4, 2019• 0 citations
Publisher

Abstract

We have developed a new method to determine the photon statistics of a light source without the need for coincidence counting. Our method relies on using an asymmetric beam-splitter with intentional asymmetrical losses in a non-photon-number resolving detection system. We observe that the counts from one arm of the beam-splitter, when plotted as a function of the counts from the other arm, follow universal single-parameter curves that hint to the statistics of the photon source. We make a series of measurements on single photons detected from an attenuated laser source and show that the data clearly conforms to the universal curve established exclusively for coherent sources. We also show that the data cannot be fitted to the universal curve for thermal and photon-number sources.

DOI
10.1364/osac.2.000370

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We have developed a new method to determine the photon statistics of a light source without the need for coincidence counting. Our method relies on using an asymmetric beam-splitter with intentional asymmetrical losses in a non-photon-number resolving detection system. We observe that the counts from one arm of the beam-splitter, when plotted as a function of the counts from the other arm, follow universal single-parameter curves that hint to the statistics of the photon source. We make a series of measurements on single photons detected from an attenuated laser source and show that the data clearly conforms to the universal curve established exclusively for coherent sources. We also show that the data cannot be fitted to the universal curve for thermal and photon-number sources.
Theoretical research on the record of every incident output of the single-molecule photon source responded by two SPCM with standard Hanbury-Brown-Twiss technique is presented.The photon statistic measurement of a single molecule photon source based on the HBT configuration with an unbalanced detection system is studied.The photon counting statistics character of the real single molecular photon source with a Poisson statistics background is theoretically investigated.It is shown that the unbalanced detectors,the unbalanced beam-splitter and the unbalanced linear propagation efficiencies will cause the single event Mandel parameter to be less than that of balance system.In addition,the correction expression to the Mandel parameter based on unbalanced detection is given.
In this work, we present a comprehensive analytical study of a lossless quantum beam splitter (BS) with transmission coefficient T and reflection coefficient R. Using the unitary operator representation and binomial expansion, we derive the exact probability distribution P_k for detecting k photons in one output port when the input ports are prepared in Fock states |N>_0 |M>_1. The balanced configuration R = T = 1/2 and N = M is examined in detail: we prove that destructive quantum interference suppresses all odd photon numbers at the outputs, leaving only even photon counts. The special case N = M = 1 reproduces the famous Hong-Ou-Mandel (HOM) dip with P_1 = 0. Beyond photon statistics, we demonstrate that the beam splitter functions as a deterministic, tunable source of photon-number entanglement. By tracing over one output mode, we construct the reduced density matrix rho_2 and compute the von Neumann entropy S = - sum_k P_k log2 P_k, a direct measure of entanglement between the two output ports. For the balanced case with N = M = 1, we obtain S = 1 ebit, i.e., maximal Bell-state entanglement. For larger equal photon numbers, the entropy increases monotonically. Our results transform the passive beam splitter into a deterministic source of photon-number entanglement, with direct applications in optical quantum computing, interferometry, and quantum information processing. Numerical three-dimensional plots of the probability distribution are provided, and all derivations are supported by rigorous algebra and a full appendix.
This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.
A method for calibration of single-photon detectors without the need of input photon flux calibration is presented. The method relies on the use of waveguide-coupled single photon detectors and a series of photon-counting measurements using a single-photon source. It is shown that the method can yield relative uncertainties of less than 1% including counting statistics and fiber splice loss uncertainties with a total measurement time of about 1 h under the assumptions that the fractional losses of the waveguide-coupled detectors are known or zero and the loss along the waveguide is constant. It is also shown that the fractional losses of the waveguide-coupled detectors can be determined if they are equal. However, in this case an input photon flux calibration is required.
Abstract A method for calibration of single-photon detectors without the need of input photon flux calibration is presented. The method relies on the use of waveguide-coupled single photon detectors and a series of photon-counting measurements using a single-photon source. It is shown that the method can yield relative uncertainties of less than 1% including counting statistics and fiber splice loss uncertainties with a total measurement time of about 1 h under the assumptions that the fractional losses of the waveguide-coupled detectors are known or zero and the loss along the waveguide is constant. It is also shown that the fractional losses of the waveguide-coupled detectors can be determined if they are equal. However, in this case an input photon flux calibration is required.