Higher-order photon correlations in pulsed photonic crystal nanolasers
D. Elvira, X. Hachair, V. B. Verma, Rémy Braive, G. Beaudoin, Isabelle Robert-Philip, Isabelle Sagnes, Burm Baek, S. W. Nam, Eric A. Dauler, Izo I. Abram, Martin J. Stevens, A. Beveratos
We report on the higher-order photon correlations of a high-$\ensuremath{\beta}$ nanolaser under pulsed excitation at room temperature. Using a multiplexed four-element superconducting single-photon detector we measured ${g}^{(n)}(\stackrel{P\vec}{0})$ with $n=2,3,4$. All orders of correlation display partially chaotic statistics, even at four times the threshold excitation power. We show that this departure from coherence and Poisson statistics is due to the quantum fluctuations associated with the small number of photons at the lasing threshold.
We report on the higher-order photon correlations of a high-\ensuremathβ nanolaser under pulsed excitation at room temperature. Using a multiplexed four-element superconducting single-photon detector we measured {g}^{(n)}(\stackrel{P\vec}{0}) with n=2,3,4. All orders of correlation display partially chaotic statistics, even at four times the threshold excitation power. We show that this departure from coherence and Poisson statistics is due to the quantum fluctuations associated with the small number of photons at the lasing threshold.
We demonstrate a new approach to measuring high-order temporal coherences that uses a four-element superconducting nanowire single-photon detector. The four independent, interleaved single-photon-sensitive elements parse a single spatial mode of an optical beam over dimensions smaller than the minimum diffraction-limited spot size. Integrating this device with four-channel time-tagging electronics to generate multi-start, multi-stop histograms enables measurement of temporal coherences up to fourth order for a continuous range of all associated time delays. We observe high-order photon bunching from a chaotic, pseudo-thermal light source, measuring maximum third- and fourth-order coherence values of 5.87 +/- 0.17 and 23.1 +/- 1.8, respectively, in agreement with the theoretically predicted values of 3! = 6 and 4! = 24. Laser light, by contrast, is confirmed to have coherence values of approximately 1 for second, third and fourth orders at all time delays.
The Siegert relation connects the first- and second-order coherence properties of light. Although strictly valid only in the thermal regime and in the absence of correlations, this relation is routinely extended to the partially coherent regime in the study of high-β nanolasers, where it aids in the identification of the lasing threshold. We re-evaluate the use of a generalized Siegert relation in different device regimes. A full two-time quantum-optical theory is derived as a reference for obtaining first- and second-order correlation functions g(1)(τ) and g(2)(τ) in the steady state. We find that even in the partially coherent regime, the generalized Siegert relation is well suited as an approximation to g(2)(τ) as long as emitter correlations are negligible but does not apply well in the quantum regime of few-emitter nanolasers or to devices featuring sub- and super-radiant emission.
Quantum universal invariants of a Gaussian state's covariance matrix, which can be derived from intensity correlation moments, have been adopted to characterize the entanglement properties of Gaussian states via the positive partial transpose criterion, also known as the Peres-Horodecki separability criterion. Such intensity correlation moments enable the extraction of information about the covariance matrix without the need for a coherent local oscillator. Here, we experimentally detect the entanglement properties of multimode Gaussian states using high-order\,(up to sixth-order) intensity correlation moments. These multimode Gaussian states are prepared via spontaneous and cascaded parametric down-conversion pumped by a high-peak-energy pulsed laser. Their intensity correlation moments are measured using a pseudo-photon-number-resolving detector constructed through spatial multiplexing of 32 threshold superconducting nanowire single photon detectors. This method is successfully demonstrated for two-mode and three-mode Gaussian states and can be extended to N-mode Gaussian states with N>3.
Abstract We present an experimental technique that can accurately measure the high-order photon correlations of various light fields based on double Hanbury Brown–Twiss scheme. The system consists of four conventional binary response single-photon counting modules which are non-photon-number-resolving detectors. We theoretically analyze the effects of the experimental conditions on the high-order photon correlations of coherent, chaotic thermal, Fock and squeezed vacuum states with considering the overall efficiency and background noise. In experiment, we determine the proper resolution time from 2 9 = 512 ns to 2 11 = 2048 ns and counting rate from 10 kc s −1 to 100 kc s −1 for characterizing the exact second-, third- and fourth-order photon correlations of chaotic thermal state. At complete time delays, we also observe the third- and fourth-order photon correlations of chaotic thermal state, with the maximum high-order correlation values of 5.99 ± 0.02 and 23.9 ± 0.2 respectively, which are in good agreement with the theoretical values of 6 and 24. The demonstrated experimental technique with high accuracy is a promising tool for investigating quantum optical coherence and ghost imaging.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.
High-order photon correlations of light fields are important for characterizing the quantum nature. Since Hanbury Brown and Twiss conducted the pioneering experiments in the 1950s, the HBT effect has inspired extensive research on high-order photon correlation in quantum optics, quantum information, and quantum imaging. The Single-photon counting module is one of the most widely used single-photon detectors. Due to its high detection efficiency and low dark counts in the visible and near-infrared region, it is reasonably chosen for basic research on quantum mechanics. Many researches have demonstrated that the maximum value of second-order photon correlation g(2)(τ) at zero delay (τ = 0) can be used to distinguish different light fields. Therefore, the HBT scheme containing two single photon detectors have been widely used in many advanced studies, such as space interference, ghost imaging, single photon detection with high efficiency, etc. However, higher-order photon correlations g(n) (n > 2) can reveal more measurable characteristics of light fields, such as information about the non-Gaussian scattering process, the skewness and kurtosis of photon number distribution, etc. When the extended HBT scheme is used to measure higher-order photon correlations, the experimental conditions including quantum efficiency and background noise greatly affect the photon correlation measurement. The influences of the counting rate and resolution time of the detection system on the measurements are also very important and cannot be ignored. Therefore, the comprehensive considering of various influence factors is necessary for accurately measuring the high-order photon correlations and also a challenge. In this paper, we present a method based on double Hanbury Brown-Twiss scheme for the accurate measuring of high-order photon correlations g(n) (n > 2). The system consists of four single photon counting modules and is used to detect and analyze the joint distribution probability of temporal photon correlation. Considering the effects of the background noise and overall efficiency, theoretically, we analyze the correlations of the third- and fourth-order photon with the incident light intensity, squeezing parameter and photon number respectively for thermal state, coherent state, squeezed vacuum state, and Fock state. Meanwhile, experimentally we study the influences of resolution time and counting rate on correlations of the coherent state and thermal state with third- and fourth-order photon. On condition that the resolution time is 210 ns and the counting rate is 80 kc/s, the correlations of third and fourth-order photon with the thermal state at zero time delay are accurately measured, and the relative statistical deviations of the measured vales from the theoretical values are 0.3% and 0.8%, respectively. In addition, the third- and fourth-order photon correlations of the thermal state at different delay times are also observed. It is demonstrated that the high-order photon correlations of light fields are measured accurately by comprehensively analyzing various influencing factors. This technique provides a promising and useful tool to investigate quantum correlated imaging and quantum coherence of light fields.