Autocorrelation functions: a useful tool for both state and detector characterisation

With the advancement of non-classical light sources such as single-photon and entangled-photon sources, innovative microscopy based on quantum principles has been proposed for traditional microscopy. This paper introduces the experimental demonstration of a quantum polarization microscopic technique that incorporates a quantum-entangled photon source. Although the point that employs the variation in polarization angle due to reflection or transmission at the sample is similar to classical polarization microscopy, the method for constructing the image contrast is significantly different. The image contrast is constructed by the coincidence count of signal and idler photons. In the case that the coincidence count is recorded from both the signal and idler photons, the photon statistics resemble a thermal state, similar to the blackbody radiation, but with a significantly higher peak intensity in the second-order autocorrelation function at zero delay that is derived from the coincidence count, while, when the coincidence count is taken from either the signal or idler photon only, although the photon state exhibits a thermal state again, the photon statistics become more dispersive and result in a lower peak intensity of the autocorrelation function. These different thermal states can be switched by slightly changing the photon polarization, which is suddenly aroused within a narrow range of the analyzer angle. The autocorrelation function g2(0) at the thermal state exhibits a sensitivity that is three times higher compared to the classical coincidence count rate, and this concept can be effectively utilized to enhance the contrast of the image. One of the key achievements of our proposed method is ensuring a low power of illumination (in the order of Pico-joules) for constructing the image. In addition, the robustness without any precise setup is also favorable for practical use. This polarization microscopic technique can provide a superior imaging technique compared to the classical method, opening a new frontier for research in material sciences, biology, and other fields requiring high-resolution imaging.

The stream of photons emitted by a single quantum system such as a molecule or a nanocrystal is often statistically characterized by the distribution of delays between consecutive photons, or by the autocorrelation function of the intensity, or by the distributions of on- and off-times. We derive and discuss general relations between their Laplace transforms, addressing the influence of detection yield and background. Our analytical treatment applies to any distribution of delays and to random telegraph signals, including nonexponential distributions. We examine the special case of systems switching between two states characterized by different distributions of delays, where the switching can obey various statistics. We show that the second-order autocorrelation function keeps track of long-time fluctuations which are obviously lost in averaging the distributions of delays. We apply our formalism to random telegraphs, in particular to those with power-law distributions of on- and/or of off-times, which are encountered in the blinking of single semiconductor nanocrystals.

Measured and calculated results are presented for the emission properties of a new class of emitters operating in the cavity quantum electrodynamics regime. The structures are based on high-finesse GaAs/AlAs micropillar cavities, each with an active medium consisting of a layer of InGaAs quantum dots (QDs) and the distinguishing feature of having a substantial fraction of spontaneous emission channeled into one cavity mode (high β-factor). This paper demonstrates that the usual criterion for lasing with a conventional (low β-factor) cavity, that is, a sharp non-linearity in the input–output curve accompanied by noticeable linewidth narrowing, has to be reinforced by the equal-time second-order photon autocorrelation function to confirm lasing. The paper also shows that the equal-time second-order photon autocorrelation function is useful for recognizing superradiance, a manifestation of the correlations possible in high-β microcavities operating with QDs. In terms of consolidating the collected data and identifying the physics underlying laser action, both theory and experiment suggest a sole dependence on intracavity photon number. Evidence for this assertion comes from all our measured and calculated data on emission coherence and fluctuation, for devices ranging from light-emitting diodes (LEDs) and cavity-enhanced LEDs to lasers, lying on the same two curves: one for linewidth narrowing versus intracavity photon number and the other for g(2)(0) versus intracavity photon number.

We investigate the effect of multiphoton emission on polarization-entangled photon pairs from a coherently driven quantum dot by comparing quantum state tomography and second-order autocorrelation measurements as a function of the excitation power. We observe that the relative (absolute) multiphoton emission probability is as low as ${p}_{m}\phantom{\rule{4pt}{0ex}}=(5.6\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}[{p}_{2}=(1.5\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}]$ at the maximum source brightness, with a negligible effect on the degree of entanglement. In contrast with probabilistic sources of entangled photons, the multiphoton emission probability and the degree of entanglement remain practically unchanged against the excitation power over multiple Rabi cycles, while observing oscillations in the second-order autocorrelation function by more than one order of magnitude. Our results, explained by a model which links the second-order autocorrelation function to the actual multiphoton contribution in the two-photon density matrix, highlight that quantum dots can be regarded as a multipair-free source of entangled photons in the solid state.

This paper contains a detailed analysis of the statistical properties of the Rayleigh backscatter signal from a single-mode optical fiber. Derivations of the first- and second-order statistics, autocorrelation function, and power spectral density of the backscatter wave are given. The probability density functions of the amplitude and intensity of the backscatter signal are also calculated.

We employ a master equation approach to study the second-order quantum\nautocorrelation functions for up to two independent quantum dot excitons,\ncoupled to an off-resonant cavity in a photonic crystal - single quantum dot\nsystem. For a single coupled off-resonant exciton, we observe novel oscillatory\nbehaviour in the early-time dynamics of the cavity autocorrelation function,\nwhich leads to decreased antibunching relative to the exciton mode. With a\nsecond coupled exciton in the system, we find that the magnitude and the\nlifetime of these oscillations greatly increases, since the cavity is then able\nto exchange photons with multiple excitonic resonances. We unambiguously show\nthat this spoils the antibunching characteristics of the cavity quasi-mode,\nwhile the autocorrelation of the first exciton is unaffected. We also examine\nthe effects of detector time resolution and make a direct connection to a\nseries of recent experiments.\n

The properties of a heralded single-photon source with temporal and spatial multiplexing are studied with the aim to maximize its efficiency for a given value of the second-order zero-time autocorrelation function. We show that the variable time delay, which is used for temporal multiplexing, can be optimized so that the mean number of photon passes through the switches and the total number of switches are respectively reduced to ∼ log2N and ∼ (1/2)log2N, where N is the temporal multiplexing degree. The total efficiency of such an optimized source is calculated for typical switching losses and the autocorrelation function is calculated in the presence of the detector dark-count noise.

Structural and dynamical properties of HCl dissolved in CCl 4. A molecular dynamics study

We demonstrate the emission of photons from a single molecule into a hybrid gap plasmon waveguide. Crystals of anthracene, doped with dibenzoterrylene (DBT), are grown on top of the waveguides. We investigate a single DBT molecule coupled to the plasmonic region of one of the guides and determine its in-plane orientation, excited state lifetime, and saturation intensity. The molecule emits light into the guide, which is remotely out-coupled by a grating. The second-order autocorrelation and cross-correlation functions show that the emitter is a single molecule and that the light emerging from the grating comes from that molecule. The coupling efficiency is found to be βWG = 11.6(1.5)%. This type of structure is promising for building new functionality into quantum-photonic circuits, where localized regions of strong emitter-guide coupling can be interconnected by low-loss dielectric guides.

We analyse how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, nonphoton-number resolving detections on the Cauchy–Schwarz parameter, on the second-order auto-correlation and cross-correlation functions, and on the visibilities of both Hong–Ou–Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.

Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.

Magnon statistical properties in multiphoton-catalyzed optomagnonics

A correlator for constructing the second-order autocorrelation function g(2)(τ) implemented on a field-programmable gate array (FPGA) is presented. The device is intended for high-precision recording of time intervals between photons emitted by single emitters. Using an FPGA made it possible to achieve a temporal resolution of 185 ps and real-time event processing. Experimental data confirming the achievement of photon antibunching with g(2)(0) < 0.5, which is typical for single quantum emitters, are demonstrated. The device can be used for analyzing photon correlations in tasks of quantum optics and when working with single quantum emitters.

A research on the demodulation performance of second-order cyclic autocorrelation and spectral density function of the frequency modulated (FM) signals with cyclostationarity properties was done. A comprehensive analysis was made to interpret the spectrum domain slice map and the cyclic spectral domain slice map for the three-dimensional cycle spectral diagram of the original signal. Then the modulation frequency was extracted from the FM signal. Simulation and experimental studies show that the proposed method can be effectively applied to detect the early bearing failure.

Optically induced ultrafast switching of single photons is demonstrated by rotating the photon polarization via the Kerr effect in a commercially available single-mode fiber. A switching efficiency of 97% is achieved with a ∼1.7 ps switching time and signal-to-noise ratio of ∼800. Preservation of the single-photon properties is confirmed by measuring no significant increase in the second-order autocorrelation function g(2)(0). These values are attained with only nanojoule-level pump energies that are produced by a laser oscillator with 80MHz repetition rate. The results highlight a simple device capable of both high-bandwidth operations and preservation of single-photon properties for applications in photonic quantum processing and ultrafast time-gating or switching.