Degree Of Second-order Coherence Research Articles

Time evolution of coherent state’s photon number statistics in laser channel gained via cumulant calculation

In this paper, by using the method of integration within the ordered product of operators and entangled state representation, the degree of second-order coherence of coherent state evolving in a laser channel is derived for the first time, which exhibits its anti-bunching property. The master equation of the laser channel is solved by entangled state representation, and the cumulant for deriving mean and mean-square photon numbers is evaluated.

Higher-order mean-field theory of chiral waveguide QED

Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.

Experimental Verification of Heralded Single Photon Generation by Second Order Degree of Coherence

Experimental Verification of Heralded Single Photon Generation by Second Order Degree of Coherence

Determination of weakly squeezed vacuum states through photon statistics measurement

Weakly squeezed vacuum light, especially when resonant with an atomic transition, plays an important role in quantum storage and the generation of various quantum sources. However, achieving a weak squeezing measurement with a precision better than 0.01 dB by means of typical homodyne detection (HD) is still very challenging due to the low signal-to-noise ratio and the limited resolution of HD systems. Here, we provide an alternative method based on photon statistics measurement to determine the weak squeezing of the squeezed vacuum light generated from an optical parametric oscillator (OPO) working far below the threshold, and we establish the relationship between the squeezing parameter and the second-order degree of coherence. The experimental results agree well with the theoretical analysis. The advantages of this method are that it provides a feasible and reliable experimental measure to determine weak squeezing with high precision and that the measurement is independent of the detection efficiency. This method can be used to measure other quantum features for various quantum states with extremely weak nonclassicality.

Nth-order nonlinear intensity fluctuation amplifier

Stronger light intensity fluctuations are pursued by related applications such as optical resolution, image enhancement, and beam positioning. In this paper, an Nth-order light intensity fluctuation amplifier is proposed, which was demonstrated by a four-wave mixing process with different statistical distribution coupling lights. Firstly, its amplification mechanism is revealed both theoretically and experimentally. The ratio R of statistical distributions and the degree of second-order coherence g(2)(0) of beams are used to characterize the affected modulations and the increased light intensity fluctuations through the four-wave mixing process. The results show that the amplification of light intensity fluctuations is caused by not only the fluctuating light fields of incident coupling beams, but also the fluctuating nonlinear coefficient of interaction. At last, we highlight the potentiality of applying such amplifier to other Nth-order nonlinear optical effects.

Identification and generation of different statistical distributions of light using Gamma modeling

Correlation measurement or calculation is typically used to classify the antibunched, bunched, or superbunched light with the degree of second-order coherence. However, it cannot characterize and identify the statistical distribution type of light. Since the statistical distributions of many classical light sources can be characterized by the generalized Gamma distribution, here we propose a new method to directly identify and generate classical light with different correlation properties by Gamma modeling from statistics rather than correlation. Experimental verification of beams from a four-wave mixing process agrees with this method, and the influences of temperature and laser detuning on the measured results are investigated. The proposal demonstrates an efficient approach to classifying and identifying classical light sources using Gamma modeling. More importantly, it can flexibly design and generate the required correlated lights meeting various optical applications according to the presented rules.

Simple and efficient way to generate superbunching pseudothermal light

By modulating the intensity of laser light before rotating groundglass, the well-known pseudothermal light source can be modified into superbunching pseudothermal light source, in which the degree of second-order coherence of scattered light is larger than 2. With the modulated intensities following binary distribution, we experimentally observed the degree of second- and third-order coherence equaling 20.45 and 227.07, which is much larger than the value of thermal or pseudothermal light, 2 and 6, respectively. Numerical simulation predicts that the degree of second-order coherence can be further improved by tuning the parameters of binary distribution. It is also predicted that the quality of temporal ghost imaging can be improved with this type of superbunching pseudothermal light. This simple and efficient superbunching pseudothermal light source provides an interesting alternative to study the second- and higher-order interference of light in these scenarios where thermal or pseudothermal light source were employed.

Non-Rayleigh photon statistics of superbunching pseudothermal light

Superbunching pseudothermal light has important applications in studying the second- and higher-order interference of light in quantum optics. Unlike the photon statistics of thermal or pseudothermal light is well understood, the photon statistics of superbunching pseudothermal light has not been studied yet. In this paper, we will employ single-photon detectors to measure the photon statistics of superbunching pseudothermal light and calculate the degree of second-order coherence. It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The results are helpful to understand the physics of two-photon superbunching with classical light. It is suggested that superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles.

Pairwise Mode Locking in Dynamically Coupled Parametric Oscillators.

Mode locking in lasers is a collective effect, where due to a weak coupling a large number of frequency modes lock their phases to oscillate in unison, forming an ultrashort pulse in time. We demonstrate an analogous collective effect in coupled parametric oscillators, which we term "pairwise mode locking," where many pairs of modes with twin frequencies (symmetric around the center carrier) oscillate simultaneously with a locked phase sum, while the phases of individual modes remain undefined. Thus, despite being broadband and multimode, the emission is not pulsed and lacks first-order coherence, while possessing a very high degree of second-order coherence. Our configuration comprises two coupled parametric oscillators within identical multimode cavities, where the coupling between the oscillators is modulated in time at the repetition rate of the cavity modes, with some analogy to active mode locking in lasers. We demonstrate pairwise mode locking in a radio-frequency experiment, covering over an octave of bandwidth with approximately 20 resonant mode-locked pairs, filling most of the available bandwidth between dc and the pump frequency. We accompany our experiment with an analytic model that accounts for the properties of the coupled parametric oscillators near threshold.

Two-photon superbunching effect of broadband chaotic light at the femtosecond timescale based on a cascaded Michelson interferometer

It is challenging to observe the superbunching effect with true chaotic light. Here we propose and demonstrate a method to achieve the superbunching effect of ${g}^{(2)}(0)=2.42\ifmmode\pm\else\textpm\fi{}0.02$ with broadband stationary chaotic light based on a cascaded Michelson interferometer (CMI), exceeding the theoretical upper limit of 2 for the two-photon bunching effect of chaotic light. The superbunching correlation peak is measured with an ultrafast two-photon absorption detector whose full width at half-maximum reaches about 95 fs. Two-photon superbunching theory in a CMI is developed to interpret the effect and is in agreement with experimental results. The theory also predicts that the degree of second-order coherence can be much greater than 2 if chaotic light propagates $N$ times in a CMI. Finally, a type of weak signal detection setup that employs broadband chaotic light circulating in a CMI is proposed. Theoretically, it can increase the detection sensitivity of weak signals 79 times after the chaotic light circulates 100 times in the CMI.

Ghost imaging normalized by second-order coherence.

Towards improvements in the quality of reconstructed images, the errors in the point spread function of a ghost imaging system caused by a limited number of samplings and imperfect illumination are discussed. We propose an algorithm by normalizing with the second-order coherence of the illumination field, with which the errors caused by imperfect illumination can be reduced, such as non-uniform spatial distribution of the average intensity, spatially varying profile of the second-order degree of coherence, or power fluctuation.

Stimulated emission of relic gravitons and their super-Poissonian statistics

The degree of second-order coherence of the relic gravitons produced from the vacuum is super-Poissonian and larger than in the case of a chaotic source characterized by a Bose–Einstein distribution. If the initial state does not minimize the tensor Hamiltonian and has a dispersion smaller than its averaged multiplicity, the overall statistics is by definition sub-Poissonian. Depending on the nature of the sub-Poissonian initial state, the final degree of second-order coherence of the quanta produced by stimulated emission may diminish (possibly even below the characteristic value of a chaotic source) but it always remains larger than one (i.e. super-Poissonian). When the initial statistics is Poissonian (like in the case of a coherent state or for a mixed state weighted by a Poisson distribution) the degree of second-order coherence of the produced gravitons is still super-Poissonian. Even though the quantum origin of the relic gravitons inside the Hubble radius can be effectively disambiguated by looking at the corresponding Hanbury Brown–Twiss correlations, the final distributions caused by different initial states maintain their super-Poissonian character which cannot be altered.

Photon statistics and bunching of a chaotic semiconductor laser.

The photon statistics and bunching of a semiconductor laser with external optical feedback are investigated experimentally and theoretically. In a chaotic regime, the photon number distribution is measured and undergoes a transition from Bose-Einstein distribution to Poisson distribution with increasing the mean photon number. The second order degree of coherence decreases gradually from 2 to 1. Based on Hanbury Brown-Twiss scheme, pronounced photon bunching is observed experimentally for various injection currents and feedback strengths, which indicates the randomness of the associated emission light. Near-threshold injection currents and strong feedback strengths modify exactly the laser performance to be more bunched. The macroscopic chaotic dynamics is confirmed simultaneously by high-speed analog detection. The theoretical results qualitatively agree with the experimental results. It is potentially useful to extract randomness and achieve desired entropy source for random number generator and imaging science by quantifying the control parameters.

High visibility temporal ghost imaging with classical light

High visibility temporal ghost imaging with classical light is possible when superbunching pseudothermal light is employed. In the numerical simulation, the visibility of temporal ghost imaging with pseudothermal light, equaling (4.7±0.2)%, can be increased to (75±8)% in the same scheme with superbunching pseudothermal light. The reasons for that the retrieved images are different for superbunching pseudothermal light with different values of degree of second-order coherence are discussed in detail. It is concluded that high visibility and high quality temporal ghost image can be obtained by collecting sufficient number of data points. The results are helpful to understand the difference between ghost imaging with classical light and entangled photon pairs. The superbunching pseudothermal light can be employed to improve the image quality in ghost imaging applications.

Squeezed relic photons beyond the horizon

Owing to the analogy with the ordinary photons in the visible range of the electromagnetic spectrum, the Glauber theory is generalized to address the quantum coherence of the gauge field fluctuations parametrically amplified during an inflationary stage of expansion. The first and second degrees of quantum coherence of relic photons are then computed beyond the effective horizon defined by the evolution of the susceptibility. In the zero-delay limit the Hanbury Brown-Twiss correlations exhibit a super-Poissonian statistics which is however different from the conventional results of the single-mode approximation customarily employed, in quantum optics, to classify the coherence properties of visible light. While in the case of large-scale curvature perturbations the degrees of quantum coherence coincide with the naive expectation of the single-mode approximation, the net degree of second-order coherence computed for the relic photons diminishes thanks to the effect of the polarizations. We suggest that the Hanbury Brown-twiss correlations are probably the only tool to assess the quantum or classical origin of the large-scale magnetic fluctuations and of the corresponding curvature perturbations.

Quantum coherence of cosmological perturbations

In this paper, the degrees of quantum coherence of cosmological perturbations of different spins are computed in the large-scale limit and compared with the standard results holding for a single mode of the electromagnetic field in an optical cavity. The degree of second-order coherence of curvature inhomogeneities (and, more generally, of the scalar modes of the geometry) reproduces faithfully the optical limit. For the vector and tensor fluctuations, the numerical values of the normalized degrees of second-order coherence in the zero time-delay limit are always larger than unity (which is the Poisson benchmark value) but differ from the corresponding expressions obtainable in the framework of the single-mode approximation. General lessons are drawn on the quantum coherence of large-scale cosmological fluctuations.

Scattering of sphere coherent state by an absorptive and dispersive dielectric slab

In this paper, we examine the modification of specific nonclassical properties of the sphere coherent state upon perpendicular propagation through an absorptive and dispersive dielectric slab at finite temperature. To achieve this purpose, by describing the dielectric dispersion of the slab by Lorentz model, the quadrature squeezing and the Mandel parameter are evaluated for the transmitted state. A generalization of the single-mode sphere coherent state to a continuum-mode is considered. The degree of second-order coherence is calculated for a continuum sphere coherent state, and the quantum noise effects produced by transmission through the slab on the antibunching feature are examined. We find that near the medium resonance the detrimental effect of the loss and thermal fluctuations of the slab are not compensated with increasing the physical space curvature of the incident state.

Second-order coherence properties of amplified spontaneous emission from a high-power tapered superluminescent diode

We study the degree of second-order coherence of the emission of a high-power multi-quantum well superluminescent diode with a lateral tapered amplifier section with and without optical feedback. When operated in an external cavity, the degree of second-order coherence changed from the almost thermal case of towards the mostly coherent case of when the injection current at the tapered section was increased. We found good agreement with semi-classical laser theory near and below threshold while above laser threshold a slightly higher g(2)(0) was observed. As a free running device, the superluminescent diode yielded more than 400 mW of optical output power with good spatial beam quality of . In this case, the degree of second-order coherence dropped only slightly from 1.9 at low powers to 1.6 at the maximum output power. To our knowledge, this is the first investigation of a high-power tapered superluminescent diode concerning the degree of second-order coherence. Such a device might be useful for real-world applications probing the second order coherence function, such as ghost imaging.

Indistinguishability-induced classical-to-nonclassical transition of photon statistics

Photon statistics is one of the key properties of the photon state for the study of quantum coherence and quantum information techniques. Here, we discuss the photon indistinguishability induced bunching effect which can significantly change photon statistics. Through the measurement of the second-order degree of coherence of a mixed photon state composed of a single-photon state and a weak coherent state, the statistical transition from a classical behavior to a nonclassical behavior is experimentally demonstrated by modifying the indistinguishability of the two-photon states. The study will help us to understand and control the photon statistics with a method for quantum optical coherence and quantum information applications. It also indicates that the photon indistinguishability is a key parameter for multipartite quantum coherence.

Thermo vacuum state for Gaussian-enhanced chaotic light

In nature, there exists superposition of Gaussian light and chaotic light, so we introduce the density operator for describing the Gaussian-enhanced chaotic light (GECL). By virtue of the method of integration within ordered product (IWOP) of operators, we derive its normalization constant. Then, by virtue of the partial trace method, we derive its thermo vacuum state and this may greatly simplify the calculation of photon number average and quantum fluctuation in GECL. It is demonstrated that the second-order degree of coherence of GECL is larger than 2.