Photocount Distribution Research Articles

Preparation and properties of a non-Gaussian state by quantum catalysis with thermal state input

We theoretically introduce a new kind of non-Gaussian state, namely, the mixture of multiphoton added thermal states, achieved through multiphoton measurements at one output port of the beam splitter (termed multiphoton catalysis) for thermal state input. We discuss the success probabilities of detection (the normalization factors). Furthermore, we investigate their nonclassical properties based on the nonclassical depth, photon number distribution, and photocount distribution. It is shown that the multiphoton catalysis presents a better nonclassical performance by controlling the thermal parameter, catalyzed photon number and the transmissivity of the beam splitter. In addition, the nonclassicality is further examined through the partial negativity of the Wigner function, which reveals that multiphoton catalysis operation can prepare highly nonclassical quantum states. These results indicate that the preparation of a non-Gaussian states may have potential applications in the realms of quantum information processing and quantum metrology.

Non-Gaussian quantum states generated via quantum catalysis and their statistical properties

Abstract A new kind of non-Gaussian quantum catalyzed state is proposed via multiphoton measurements and two-mode squeezing as an input of thermal state. The characteristics of generating multiphoton catalysis output state depends on the thermal parameter, catalyzed photon number and squeezing parameter. We then analyze the nonclassical properties by examining the photon number distribution, photocount distribution and partial negativity of the Wigner function. Our findings indicate that nonclassicality can be achieved through the implementation of multiphoton catalysis operations, and modulated by the thermal parameter, catalyzed photon number and squeezing parameter.

Photon-counting schemes for MIMO underwater wireless optical communication with arrayed PMTs.

Underwater wireless optical communication (UWOC) is a promising means of realizing large capacity and high rate in aquatic media. In this paper, a photomultiplier tube (PMT)-based multiple-input multiple-output (MIMO) UWOC system is investigated. Photon counting is an effective technique used to detect very low-level light. A PMT with an excellent photon-counting mode is adopted, and the performance in terms of the bit error rate is discussed. The received optical power can be predicted based on the detected photocount in each symbol period, and the received photocount distribution may be simulated through MATLAB. Furthermore, the optical link model and energy per bit with on-off keying are evaluated for different water types at a 10 m optical link distance. This MIMO-UWOC system combines the advantages of PMTs and the MIMO scheme and has the potential to realize long-distance optical link transmission.

Nonclassicality of photon–modulated spin coherent states in the Holstein-Primakoff realization

Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein–Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

Recursive method for solving the inverse problem of photocount statistics

An analytical recursive method for solving the inverse problem of photocount statistics, that is, for reconstructing the photon-number distribution from the photocount distribution, is proposed for few-photon light. It is shown that if the inverse problem is represented as a system of linear equations, then for finite distributions one can obtain a recurrence formula relating the photocount distribution and the photon-number distribution without restrictions on the quantum efficiency of photodetection.

Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors. II. Criteria based on probabilities

Numerous non-classicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the non-classicality from different points of view ('local' non-classicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the non-classicality. Quantification of the non-classicality using the Lee non-classicality depth and the non-classicality counting parameter is discussed. The used number of field's modes is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its s-ordered form, needed for the determination of the non-classicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.

Non-classicality of optical fields as observed in photocount and photon-number distributions.

Non-classicality criteria for optical fields based on the probabilities of photocount and photon-number distributions are derived. Relations among the criteria obtained by the applied methods are revealed. Redundant criteria are identified. The performance of the fundamental criteria is tested on a set of potentially sub-Poissonian fields generated by photon-number-resolved post-selection from a mesoscopic twin beam. The corresponding non-classicality depths are determined to quantitatively compare the used criteria.

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.

The Bit Error Performance and Information Transfer Rate of SPAD Array Optical Receivers

In this paper the photon counting characteristics, the information rate and the bit error performance of single-photon avalanche diode (SPAD) arrays are investigated. It is shown that for sufficiently large arrays, the photocount distribution is well approximated by a Gaussian distribution with dead-time-dependent mean and variance. Because of dead time, the SPAD array channel is subject to counting losses, part of which are due to inter-slot interference (ISI) distortions. Consequently, this channel has memory. The information rate of this channel is assessed. Two auxiliary discrete memoryless channels (DMCs) are proposed which provide upper and lower bounds on the SPAD array information rate. It is shown that in sufficiently large arrays, ISI is negligible and the bounds are tight. Under such conditions, the SPAD array channel is precisely modelled as a memoryless channel. A discrete-time Gaussian channel with input-dependent mean and variance is adopted and the properties of the capacity-achieving input distributions are studied. Using a numerical algorithm, the information rate and the capacity-achieving input distributions, subject to peak and average power constraints are obtained. Furthermore, the bit error performance of a SPAD-based system with on-off keying (OOK) is evaluated for various array sizes, dead times and background count levels.

A photocounting distribution formula for a laser channel

For a laser channel governed by the master equation of the density operator which involves both photon gain and loss parameters, g and κ, we derive a new formula for the photocount distribution at time t for an initial density operator ρ0. The formula brings convenience, since we need not derive the density operator ρt at time t. Moreover, this formula is applied to the case of a damping channel and a diffusion channel, respectively.

Statistical Modeling of Single-Photon Avalanche Diode Receivers for Optical Wireless Communications

In this paper, a comprehensive analytical approach is presented for modeling the counting statistics of active quenching and passive quenching single-photon avalanche diode (SPAD) detectors. It is shown that, unlike ideal photon counting receiver for which the detection process is described by a Poisson arrival process, photon counts in practical SPAD receivers do not follow a Poisson distribution and are highly affected by the dead time caused by the quenching circuit. Using the concepts of renewal theory, the exact expressions for the probability distribution and moments (mean and variance) of photocounts in the presence of dead time are derived for both active quenching and passive quenching SPADs. The derived probability distributions are validated through Monte Carlo simulations and it is demonstrated that the moments match with the existing empirical models for the moments of SPAD photocounts. Furthermore, an optical communication system with on–off keying and binary pulse position modulation is considered and the bit error performance of the system for different dead time values and background count levels is evaluated.

Poisson pre-processing of nonstationary photonic signals: Signals with equality between mean and variance.

Photonic signals are broadly exploited in communication and sensing and they typically exhibit Poisson-like statistics. In a common scenario where the intensity of the photonic signals is low and one needs to remove a nonstationary trend of the signals for any further analysis, one faces an obstacle: due to the dependence between the mean and variance typical for a Poisson-like process, information about the trend remains in the variance even after the trend has been subtracted, possibly yielding artifactual results in further analyses. Commonly available detrending or normalizing methods cannot cope with this issue. To alleviate this issue we developed a suitable pre-processing method for the signals that originate from a Poisson-like process. In this paper, a Poisson pre-processing method for nonstationary time series with Poisson distribution is developed and tested on computer-generated model data and experimental data of chemiluminescence from human neutrophils and mung seeds. The presented method transforms a nonstationary Poisson signal into a stationary signal with a Poisson distribution while preserving the type of photocount distribution and phase-space structure of the signal. The importance of the suggested pre-processing method is shown in Fano factor and Hurst exponent analysis of both computer-generated model signals and experimental photonic signals. It is demonstrated that our pre-processing method is superior to standard detrending-based methods whenever further signal analysis is sensitive to variance of the signal.

Noise Reduction in Photon Counting by Exploiting Spatial Correlations

Sometimes you need a steady drip, not a torrent---as in certain optics experiments, where the precise number of photons in each ``drip'' of a faint beam is important. The authors use an intensified charge-coupled device as a photon-number-resolving detector with spatial resolution, to study at once the joint photocount distributions and spatial correlations of weak twin beams of light. Compared to the usual analysis of photocount distributions, their spatially resolved analysis provides additional information about the statistical properties of the beams, and allows noise reduction.

Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors

Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well as the Cauchy-Schwarz inequality. Different approaches for deriving these inequalities are compared. Using the experimental photocount histogram generated by a weak noisy twin beam monitored by a photon-number-resolving iCCD camera the performance of the derived inequalities is compared. A basic set of ten inequalities suitable for monitoring the entanglement of a twin beam is suggested. Inequalities involving moments of photocounts (photon numbers) as well as those containing directly the elements of photocount (photon-number) distributions are also discussed as a tool for revealing nonclassicality.

Higher-order sub-Poissonian-like nonclassical fields: Theoretical and experimental comparison

Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order non-classicality is observed in the latter case.

Dynamical modeling of pulsed two-photon interference

Single-photon sources are at the heart of quantum-optical networks, with their uniquely quantum emission and phenomenon of two-photon interference allowing for the generation and transfer of nonclassical states. Although a few analytical methods have been briefly investigated for describing pulsed single-photon sources, these methods apply only to either perfectly ideal or at least extremely idealized sources. Here, we present the first complete picture of pulsed single-photon sources by elaborating how to numerically and fully characterize non-ideal single-photon sources operating in a pulsed regime. In order to achieve this result, we make the connection between quantum Monte-Carlo simulations, experimental characterizations, and an extended form of the quantum regression theorem. We elaborate on how an ideal pulsed single-photon source is connected to its photocount distribution and its measured degree of second- and first-order optical coherence. By doing so, we provide a description of the relationship between instantaneous source correlations and the typical experimental interferometers (Hanbury-Brown and Twiss, Hong–Ou–Mandel, and Mach–Zehnder) used to characterize such sources. Then, we use these techniques to explore several prototypical quantum systems and their non-ideal behaviors. As an example numerical result, we show that for the most popular single-photon source—a resonantly excited two-level system—its error probability is directly related to its excitation pulse length. We believe that the intuition gained from these representative systems and characters can be used to interpret future results with more complicated source Hamiltonians and behaviors. Finally, we have thoroughly documented our simulation methods with contributions to the Quantum Optics Toolbox in Python in order to make our work easily accessible to other scientists and engineers.

Photocount statistics of ultra-weak photon emission from germinating mung bean

Ultra-weak photon emission (UPE) is an endogenous bioluminescence phenomenon present in all biological samples with an active oxidative metabolism, even without an external pre-illumination. To verify the potential of UPE for non-invasive monitoring of metabolism and growth in germinating plants, the aim of this study was to investigate the UPE from a model system - germinating mung bean seedlings (Vigna radiata) - and analyze the statistical properties of UPE during the growth in two different conditions of imbibition (pure water and 1% sucrose). We found that in all days and in both conditions, photocount distributions of UPE time series follow the negative binomial distribution whose parameters changed during the growth due to the increasing ratio of signal-to-detector dark count. Correspondingly for both groups, the mean values of UPE increased during the seedlings growth, while the values of Fano factor show a decreasing trend towards 1 during the 6day period. While our results do not show any significant difference in hypocotyl length and weight gain between the two groups of mung seedlings, there is an indication of a tiny suppressing effect of sucrose on UPE intensity. We believe that UPE can be exploited for a sensitive non-invasive analysis of oxidative metabolism during the plant development and growth with potential applications in agricultural research.

On photon statistics parametrized by a non-central Wishart random matrix

In order to tackle parameter estimation of photocounting distributions, polykays of acting intensities are proposed as a new tool for computing photon statistics. As unbiased estimators of cumulants, polykays are computationally feasible thanks to a symbolic method recently developed in dealing with sequences of moments. This method includes the so-called method of moments for random matrices and results to be particularly suited to deal with convolutions or random summations of random vectors. The overall photocounting effect on a deterministic number of pixels is introduced. A random number of pixels is also considered. The role played by spectral statistics of random matrices is highlighted in approximating the overall photocounting distribution when acting intensities are modeled by a non-central Wishart random matrix. Generalized complete Bell polynomials are used in order to compute joint moments and joint cumulants of multivariate photocounters. Multivariate polykays can be successfully employed in order to approximate the multivariate Poisson–Mandel transform. Open problems are addressed at the end of the paper.

M Times Photon Subtraction-Addition Coherent Superposition Operated Odd-Schrődinger-cat State: Nonclassicality and Decoherence

We introduce a new non-Gaussian state (MCSO-OSCS), generated by m times coherent superposition operation acos θ + a †sin θ (MCSO) on odd-Schrődinger-cat state |α 0〉 − | − α 0〉(OSCS), whose normalized constant is shown to be related to Hermite polynomials. We investigate the nonclassical properties of the MCSO-OSCS through Mandel’s Q-parameter, quadrature squeezing, the photocount distribution and Wigner function (WF), which is turned out to be influenced by parameters m, θ and α 0. Especially the volume of negative region of WF could increase through controlling the parameters m, θ and α 0. We also investigate the decoherence of the MCSO-OSCS in terms of the fadeaway of the negativity of WF in a thermal environment.

On Realization of a Cavity-QED Laser Emitting a Highly Sub-Poissonian, Anti-Bunched Beam of Photons in a CW Fashion

We propose a feedback scheme to control the photon statistics in a micromaser/laser cavity, using the system output as the control signal, which generates a highly nonclassical field whose Mandel-Q parameter is even lower than −0.9 and mean photon number much greater than unity. We demonstrate that the so-obtained system constitutes a continuous-wave (CW) quasi-Fock state source, the emission of which exhibits a sub-Poissonian photocount distribution as well as the photon anti-bunching property.