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Physica Scripta

Modeling memory function of entangled photon and classical laser photon-count fluctuations using white noise integral analysis

Lian Seng Tey, Sithi Vinayakam Muniandy, Wu Yi Chong

Published Dec 2, 2024• 3 citations
Publisher

Abstract

Abstract This study investigates photon-count fluctuation dynamics of two light sources, namely a spontaneous parametric down-conversion (SPDC) light source and a 780 nm attenuated laser diode (LD). White noise integral with customizable memory function is used to model the mean square displacements (MSDs) and the probability density functions (PDFs) for both light sources. This approach overcomes the limitation of monofractal scaling of fractional Brownian motion (fBm) model characterized by a single Hurst exponent. The memory function used has an exponential-tempered power-law relation, parametrized by μ and β, where β modulates the extent of memory parameter μ. Although optical losses and detector inefficiencies degrade photon statistics to Poissonian at post-detection, our findings reveal notable memory effects at higher mean photon counts, especially in the SPDC source with memory parameter μ ⪆ 1.00, compared to the classical LD, which remained relatively constant at μ ⪅ 1.00. Both light sources shared similar correction parameters β, which indicates they have identical photon-count fluctuations at short time but diverge significantly at longer time. This work highlights the need for models beyond fBm, capable of capturing complex MSD behaviors of photon-count fluctuations.

DOI
10.1088/1402-4896/ad9960

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Abstract This study investigates photon-count fluctuation dynamics of two light sources, namely a spontaneous parametric down-conversion (SPDC) light source and a 780 nm attenuated laser diode (LD). White noise integral with customizable memory function is used to model the mean square displacements (MSDs) and the probability density functions (PDFs) for both light sources. This approach overcomes the limitation of monofractal scaling of fractional Brownian motion (fBm) model characterized by a single Hurst exponent. The memory function used has an exponential-tempered power-law relation, parametrized by μ and β, where β modulates the extent of memory parameter μ. Although optical losses and detector inefficiencies degrade photon statistics to Poissonian at post-detection, our findings reveal notable memory effects at higher mean photon counts, especially in the SPDC source with memory parameter μ ⪆ 1.00, compared to the classical LD, which remained relatively constant at μ ⪅ 1.00. Both light sources shared similar correction parameters β, which indicates they have identical photon-count fluctuations at short time but diverge significantly at longer time. This work highlights the need for models beyond fBm, capable of capturing complex MSD behaviors of photon-count fluctuations.
Understanding photon-count dynamics is crucial for applications such as quantum random number generators and quantum key distributions, where random and memoryless photon-count arrival processes are essential for performance and security. We investigated the fluctuation dynamics of aggregated photon-count time series for two distinct light sources: a 780-nm laser diode and a spontaneous parametric down-conversion source, using detrended fluctuation analysis (DFA) and the index of dispersion for intervals (IDI). Despite the degradation of photon statistics to Poissonian due to optical losses and detector inefficiencies, our analysis reveals significant long-range dependence at large timescales. The DFA scaling exponents α[over ¯]>0.75 and IDI values c_{k}^{2}>1 at high mean photon count and large aggregation timescales indicate photon-count fluctuations deviated from Poisson model. Our findings underscore the necessity of models beyond Poisson statistics to accurately describe the photon-count dynamics over extended timescales.
We investigate the fluctuation dynamics of photons generated by spontaneous parametric down conversion (SPDC) using detrended fluctuation analysis (DFA). SPDC photon pairs were generated via a periodically poled potassium titanyl phosphate waveguide, pumped by a 405 nm continuous-wave laser. The scaling exponents obtained from DFA reveal that SPDC photons exhibit long-range correlations at high pump power regimes. The average scaling exponent of DFA increases from 0.67 to 0.97 as the laser diode drive current increases, indicating the existence of long-range correlations. Our analysis concluded that the scaling exponent of aggregated time series is correlated to the number of SPDC photon pairs.
Time-correlated photons can be used to demonstrate emerging technical applications such as ghost imaging, and they can demonstrate quantum-based phenomena in order to interest undergraduate students in engineering applications involving optics and quantum mechanics. In this work, we use spontaneous parametric down-conversion to generate time-correlated photons. To achieve this, we simulated laboratory parameters with MATLAB and designed optical and electrical setups. Specifically, we used a 405 nm diode laser, various common optical components, and a nonlinear crystal designed to generate time-correlated photons, and we used single-photon detectors, time-to-amplitude converters, custom flash-conversion analog-to-digital converters, a Teensy 4.1 microcontroller, and the Arduino IDE to detect the time-correlated photons. We present two significant results. First, we measured >100,000 counts per second 5 ± 1° on either side of our input laser which was within our theoretical expectations of 4–9° and much greater than our < 2000 dark counts per second. Our second major result was finding 15.8 ± 0.7 time-correlated counts per second with an SNR of 2.7. We also outline future extensions of our work including ghost imaging and generating polarization-entangled photons.
Abstract The photon statistics of spontaneous parametric down-conversion (SPDC) exhibit dependencies on wavelength, pump power, and coincidence time. Notably, the average photon numbers were found to asymmetrically increase with increasing pump power around the degenerate wavelength of emission. We employ a four-detector Hanbury Brown and Twiss interferometer to study the photon statistics of the signal beam. Coupling the detection scheme to a spectrometer enabled the dynamic probing of different bandwidths within the broadband emission. Spectrally resolving the photon statistics revealed that shorter wavelengths increased nonlinearly with pump power, while longer wavelengths showed more linear behavior, indicating a wavelength-dependent efficiency in the generation of the SPDC. The detection and characterization of complex light sources has wide ranging applications in the fields of quantum metrology, quantum communications, and quantum computing, more specifically, a system that is sensitive to wavelength and photon number distribution.
Nowadays, with the continuous development of optical quantum sensor technology, the importance of the quantum entanglement source is increasing day by day. As an indispensable part of optical quantum systems, the quantum entanglement source has a wide prospect of application in quantum communication, quantum imaging, quantum computing, life science and so on. However, the current power consumption and preparation cost of quantum entanglement sources are relatively huge, which impedes further integration and expansion. In view of these problems, we establish a quantum entanglement source model pumped by a low-power laser diode based on spontaneous parametric down-conversion (SPDC) theory and phase matching technology, to effectively analyze the influence of components and characteristics of each module of quantum entanglement source on its performance. Furthermore, we prepare a quantum entanglement source with a 10mW laser diode and a typical type-II barium metaborate (BBO) crystal to conduct experiment whose result is 2053 counts per second in average which is in desirable agreement with the model. To some extent, the low-power and low-cost goal of quantum entanglement source has been achieved, which has made a significant contribution to the practical application of quantum entanglement lighting, and is conducive to the popularization of optical quantum systems in the future.
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.