Second-order Correlation Research Articles

Femtosecond Dynamics of a Polariton Bosonic Cascade at Room Temperature.

Whispering gallery modes in a microwire are characterized by a nearly equidistant energy spectrum. In the strong exciton-photon coupling regime, this system represents a bosonic cascade: a ladder of discrete energy levels that sustains stimulated transitions between neighboring steps. Here, by using a femtosecond angle-resolved spectroscopic imaging technique, the ultrafast dynamics of polaritons in a bosonic cascade based on a one-dimensional ZnO whispering gallery microcavity are explicitly visualized. Clear ladder-form build-up processes from higher to lower energy branches of the polariton condensates are observed, which are well reproduced by modeling using rate equations. Remarkably, a pronounced superbunching feature, which could serve as solid evidence for bosonic cascades, is demonstrated by the measured second-order time correlation factor. In addition, the nonlinear polariton parametric scattering dynamics on a time scale of hundreds of femtoseconds are revealed. Our understandings pave the way toward ultrafast coherent control of polaritons at room temperature.

Mixedness, Coherence and Entanglement in a Family of Three-Qubit States.

We consider a family of states describing three-qubit systems. We derived formulas showing the relations between linear entropy and measures of coherence such as degree of coherence, first- and second-order correlation functions. We show that qubit–qubit states are strongly entangled when linear entropy reaches some range of values. For such states, we derived the conditions determining boundary values of linear entropy parametrized by measures of coherence.

Antibunching and superbunching photon correlations in pseudo-natural light

Since Hanbury Brown and Twiss revealed the photon bunching effect of a thermal light source in 1956, almost all studies in correlation optics have been based on light’s intensity fluctuation, regardless of fact that the polarization fluctuation is a basic attribute of natural light. In this work, we uncover the veil of the polarization fluctuation and corresponding photon correlations by proposing a new light source model, termed pseudo-natural light, embodying both intensity and polarization fluctuations. Unexpectedly, the strong antibunching and superbunching effects can be simultaneously realized in such a new source, whose second-order correlation coefficient g ( 2 ) can be continuously modulated across 1. For the symmetric Bernoulli distribution of the polarization fluctuation, particularly, g ( 2 ) can be in principle from 0 to unlimitedly large. In pseudo-natural light, while the bunching effects of both intensity and polarization fluctuations enhance the bunching to superbunching photon correlation, the antibunching correlation of the polarization fluctuation can also be extracted through the procedure of division operation in the experiment. The antibunching effect and the combination with the bunching one will arouse new applications in quantum imaging. As heuristic examples, we carry out high-quality positive or negative ghost imaging, and devise high-efficiency polarization-sensitive and edge-enhanced imaging. This work, therefore, sheds light on the development of multiple and broad correlation functions for natural light.

Noncentrosymmetric far-zone spectral density induced by light scattering with random media having parity-time symmetry

We study the scattering property of a normally incident plane wave scattered by random media whose second-order potential correlation function has parity-time $(\mathcal{PT})$ or classical symmetry. Based on the weak-potential-scattering theory, we show analytically that when the random media have classical symmetry, the far-zone spectral density is centrosymmetric. However, the spectral density becomes asymmetric for the $\mathcal{PT}$ random scatterer. The reason is the odd-symmetric distribution of the phase in the potential correlation function of the $\mathcal{PT}$ random media. We demonstrate numerically the asymmetric far-zone spectral density with two types of potential correlations, i.e., Schell-model-correlated and nonuniform-correlated correlations.

A study of a nonlinear interaction between a two-mode cavity field and ♢-type four-level with field damping

In this paper, the effects of the field damping and Kerr-like medium on a system of a four-level atom in the [Formula: see text]-type interacting nonlinearly with a two-mode field are studied. Analytical solution of the system of differential equations resulting from the Schrödinger equation is obtained. The effects of detuning parameters, Kerr-like parameter, coupling function and damping rate are discussed for atomic population inversion, the second-order correlation function, Shannon information entropy, and linear entropy. Under justifiable all conditions, extreme entanglement states may appear periodically with the evolution of time. The arrival of the quantum system to a pure state can be controlled by variations of the Kerr medium and the damping parameters. The results also exhibit that the periods of strong and weak entanglement between the parts of the system are achieved during the periods of collapses and revivals of the atomic population inversion. Moreover, the photon distribution changes from non-classical to classical by increasing the damping rate.

Cascaded frequency up-conversion of bright squeezed vacuum: spectral and correlation properties.

High-gain parametric down-conversion (PDC) is inevitably accompanied by cascaded up-conversion (CUpC) of PDC radiation in a nonlinear crystal even if CUpC is nonphase matched. Here we study experimentally and theoretically the spectral properties of broadband phase-matched and nonphase-matched CUpC radiation in a beta barium borate (BBO) crystal. Our calculations of the normalized second-order correlation function predict the super-bunching of CUpC radiation.

Optomechanical strong coupling between a single photon and a single atom

Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of ‘single-photon strong coupling’, where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.

On the free vibrations of FG-GPLRC folded plates using GDQE procedure

The present study theoretically investigates the performance of the generalized differential quadrature element (GDQE) method to obtain the free vibration response of folded plates. The considered folded plate is assumed as a laminated functionally graded composite augmented with graphene platelets (GPLs). This kind of composite is identified as the FG-GPLRC structure. Each lamina is strengthened with randomly oriented and uniformly distributed GPLs. The GPL weight fraction of each layer changes based on several functionally graded (FG) models. The effective Young modulus of each ply is calculated utilizing a second-order correlation homogenization technique called Halpin–Tsai. Based on the GDQE method, the folded plate is split into two plate elements. The motion equations of each element are derived based on the first-order shear deformation theory and utilizing Hamilton’s principle. Equations of motion for each element are solved by employing the conventional GDQ method. After that, the suitable continuity conditions are applied to the common boundaries of the two elements. In this research, the influences of plate dimensions, crank angle, FG patterns, boundary conditions, and GPL weight fraction on the natural frequencies and corresponding mode shapes are examined.

Two-Phonon Blockade in Quadratically Coupled Optomechanical Systems

We propose a scheme to realize the two-phonon blockade effect in a quadratically coupled optomechanical system. We consider the case that the optical cavity is simultaneously driven by a strong pumping field and a weak driving field. By strongly driving the optical cavity, the nonlinear interaction between the optical mode and the mechanical resonator can be significantly enhanced and an effective second-order nonlinearity between photons and phonons is induced. Based on this effectively strong nonlinearity, the two-phonon blockade effect can be achieved when a weak driving field is applied into the optical cavity. By contrast, we study the case of weakly driving the mechanical resonator. In this case, the single-phonon blockade is generated, while the two-phonon blockade cannot be observed. By numerically calculating the second-order and third-order correlation function, we investigate the statistical characteristics of phonons. In addition, we also study the influence of the thermal noise on the achieved two-phonon blockade effect. Our work provides an alternative approach for implementing multiphonon blockade and has potential applications in quantum information processing.

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second-order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity’s motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.

Bright squeezed vacuum for two-photon spectroscopy: simultaneously high resolution in time and frequency, space and wavevector

Entangled photons offer two advantages for two-photon absorption spectroscopy. One of them, the linear scaling of two-photon absorption rate with the input photon flux, is valid only at very low photon fluxes and is therefore impractical. The other is the overcoming of the classical constraints for simultaneous resolution in time-frequency and in space-wavevector. Here we consider bright squeezed vacuum (BSV) as an alternative to entangled photons. The efficiency increase it offers in comparison with coherent light is modest, but it does not depend on the photon flux. Moreover, and this is what we show in this work, BSV also provides simultaneously high resolution in time and frequency, and in space and wavevector. In our experiment, we measure the widths of the second-order correlation functions in space, time, frequency, and angle and demonstrate the violation of the constraint given by the Fourier transformation, in the case of photon pairs, known as the Mancini criterion of entanglement.

Cryogenic integrated spontaneous parametric down-conversion

Scalable quantum photonics relies on interfacing many optical components under mutually compatible operating conditions. To that end, we demonstrate that spontaneous parametric down-conversion (SPDC) in nonlinear waveguides, a standard technology for generating entangled photon pairs, squeezed states, and heralded single photons, is fully compatible with cryogenic operating conditions required for superconducting detectors. This is necessary for the proliferation of integrated quantum photonics in integration platforms exploiting quasi-phase-matched second-order nonlinear interactions. We investigate how cryogenic operation at 4 K affects the SPDC process by comparing the heralding efficiency, second-order correlation function, and spectral properties with operation at room temperature.

Regularized second-order correlation methods for extended systems.

Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.

Retrieval of photon blockade effect in the dispersive Jaynes-Cummings model

We propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems.

Higher-order photon antibunching of phase-variable squeezed coherent state

<sec>Squeezed state has important applications in quantum communication, quantum computing, and precision measurement. It has been used to improve the sensitivity and measurement accuracy of gravitational wave detectors. Currently, squeezed state can be prepared by optical parametric oscillators, four-wave mixing, and atom–optomechanical coupling. As a typical non-classical light, the photon statistics of squeezed state usually shows obvious bunching effect, but it can also present photon antibunching effect through interference or photon subtraction operation. More importantly, squeezed coherent state is prepared by performing displacement operation on the squeezed state. In the case of certain displacement and squeezing operations, squeezed coherent state with obvious antibunching effect can be produced. The squeezed coherent state with photon antibunching effect can be employed to achieve super-resolution imaging beyond the diffraction limit, and the state exhibits good particle features which can suppress the multiphoton emission. Then it has become a focus for studying the antibunching effect and quantum statistical properties of squeezed coherent state at a single-photon level.</sec><sec>The photon antibunching effect can be characterized by the second-order photon correlation <i>g</i><sup>(2)</sup>(τ), which is introduced by Glauber to determine the non-classical properties of the light field. Namely, the second-order photon correlation <i>g</i><sup>(2)</sup> can be used as a metric to distinguish different lights. Hanbury Brown-Twiss (HBT) scheme is used to measure the second-order photon correlation experimentally. However, the second-order photon correlation <i>g</i><sup>(2)</sup> can reflect only the variance of the photon-number statistical distribution. In order to obtain more information about the photon statistical distribution and non-classical features, it is necessary to measure higher-order photon correlations. Then the higher-order photon correlations for different light fields are studied by extending the traditional HBT scheme and combining with multiplex single-photon detection technology. This method can be applied to ghost imaging, characterization of single-photon detectors, research of exciton dynamics, and analysis of NV center fluorescence emission. However, the research on photon statistics of the squeezed state focuses mainly on the second-order photon correlation and the effect of displacement amplitude on the statistical properties. The effect of squeezed phase on photon antibunching and higher-order photon correlation of squeezed coherent states, with background noise and detection efficiency taken into consideration, have not been investigated.</sec><sec>In this paper, we study high-order photon correlations and antibunching effect of phase-variable squeezed coherent state based on an extended HBT scheme. The photon statistics of the squeezed coherent state manifests prominent antibunching effect by adjusting the squeezing parameter r, displacement amplitude <i>α</i> and squeezing phase <i>θ</i>. The antibunching effect of the state can be obtained in a wide range of <i>α</i>-<i>r</i> parameter space when squeezing phase <i>θ</i>∈[0,π/2]. In an ideal case, the minimum antibunching values of the squeezed coherent state are <i>g</i><sup>(2)</sup> = 4.006 × 10<sup>–4</sup>, <i>g</i><sup>(3)</sup> = 1.3594 × 10<sup>–4</sup> and <i>g</i><sup>(4)</sup> = 6.6352 × 10<sup>–5</sup>. When the detection efficiency <i>η</i> = 0.1 and background noise <i>γ</i> = 10<sup>–6</sup>, the strong antibunching effect can still be observed, specifically, <i>g</i><sup>(2)</sup> = 0.1740, <i>g</i><sup>(3)</sup> = 0.0432, <i>g</i><sup>(4)</sup> = 0.0149. The results indicate that the antibunching effect of higher-order photon correlation has strong robustness against the experimental environment. In addition, the antibunching effect of the phase-variable squeezed coherent state is studied as a function of the measured mean photon number <<i>n</i>> and the squeezing degree S. When the measured mean photon number is much less than 1 and the squeezing parameter is less than 10<sup>–4</sup>, a prominent photon anti-bunching effect of <i>g</i><sup>(<i>n</i>)</sup> <inline-formula><tex-math id="Z-20220921173504">\begin{document}$\ll $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20220574_Z-20220921173504.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="19-20220574_Z-20220921173504.png"/></alternatives></inline-formula> 0.5 can still be obtained. The results show that the control of the squeezing phase <i>θ</i> can be used to prepare the squeezed coherent state with obvious antibunching effect, which has potentially important applications in quantum metrology and secure communication.</sec>

A Stellar Ranging Scheme Based on the Second-order Correlation Measurement

Stellar ranging is the basis for stellar dynamics research and in-depth research on astrophysics. The parallax method is the most widely used and important basic method for stellar ranging. However, it needs to perform high-precision measurement of the parallax angle and the baseline length together. We aim to propose a new stellar ranging scheme based on second-order correlation that does not require a parallax angle measurement. We hope our solution can be as basic as the parallax method. We propose a new stellar ranging scheme by using the offset of second-order correlation curve signals. The optical path difference between the stars and different base stations is determined by the offset of the second-order correlation curve signals. Then the distance of the stars could be determined by the geometric relation. With the distance to stars out to 10 kpc away, our astrometric precision can be better compared to Gaia by simulation. We also design an experiment and successfully demonstrate the feasibility of this scheme. This stellar ranging scheme enables further and more accurate stellar ranging without requiring any prior information or angle measurement.

Correlations between Distribution of Producer Services and Urban Built Environment in Metro Station Areas: A Case of Xi’an, China

Since impacts of rail transit on urban industries and space most obviously appear in metro station areas, correlations between the spatial distribution of producer services and urban built environment in metro station areas are studied in Xi’an, China. At first, the scope determining methods of a metro station area were separately proposed for both single‐line station and multiline transfer station based on their construction and transportation modes. Then, when the producer services were divided into 6 categories of business, POI numbers of enterprises of each category in metro station areas were collected and weighted to calculate the distribution intensity for categories. Finally, on condition that the urban built environment of a metro station area included job and residence space, outdoor activity space, and municipal road space, correlation performances between the distribution intensity of categories and indexes representing 3 space elements of the built environment were calculated through second‐order partial correlation analysis, while the corresponding mechanisms of correlations were explained too. The main conclusions of this paper indicate that there are significant positive correlations between the distribution intensity and the diversity index of job and residence space for most categories, whereas significant negative correlations between it and the openness index of outdoor activity space for most categories. Moreover, positive but weak correlations were appeared between the distribution intensity and the street network density index of municipal road space only for categories of intermediary consulting and leasing.

The photon blockade effect of a complete Buck-Sukumar model

The Buck-Sukumar (BS) model, with a nonlinear coupling between the atom and the light field, is well defined only when its coupling strength is lower than a critical coupling. Its energy collapses at a critical coupling and is unbounded beyond that value. In other words, the BS model is incomplete. We introduce a simple and a complete BS model by adding a nonlinear photon term into the initial BS model. Considering the rotating wave approximation, this complete BS model conserves the excited number and the parity. By expanding it in the subspace of the product state between the atom and the field, we solve the time-independent SchrÖdinger equation to obtain the eigenenergy and eigenstate. Furthermore, we explore the influence of the nonlinear photon term on the energy spectrum and the photon blockade effect for the complete BS model by calculating the excited number and second-order correlation function. Our study shows that, the nonlinear photon term not only eliminates the energy spectral collapse but also makes it well-defined and complete in all the coupling regime. When at the resonance between the atomic and the field frequency, the nonlinear photon term breaks the harmonicity of the energy spectrum and produces a ladder of the excited number in the ground state. Because the larger nonlinear photon term inhibits the photon transition from an energy level to the higher one, it produces the single-photon projection state in the larger coupling region. Accordingly, we find that the nonlinear photon term promotes photon blockade by calculating the second-order correlation function. When at the non-resonant region, the nonlinear photon term enlarges the originally anharmonic energy ladder. For a complete BS model with the fixed nonlinear photon coupling strength and the fixed detuning, the energy level for the positive detuning is lower than that with the negative detuning, and more energy is required to overcome the absorption of a photon. Therefore, the positive detuning promotes the photon blockade. For the negative detuning, the system is more likely to absorb a photon and jump to a higher energy level, and therefore, suppresses the photon blockade.

The photon blockade effect of a complete Buck-Sukumar model

<sec>The Buck-Sukumar (BS) model, with a nonlinear coupling between the atom and the light field, is well defined only when its coupling strength is lower than a critical coupling. Its energy collapses at a critical coupling and is unbounded beyond that value. In other words, the BS model is incomplete. We introduce a simple and complete BS model by adding a nonlinear photon term into the initial BS model. Considering the rotating wave approximation, this complete BS model conserves the excited number and the parity. By expanding it in the subspace of the product state between the atom and the field, we solve the time-independent Schrödinger equation to obtain the eigenenergy and eigenstate. Furthermore, we explore the influence of the nonlinear photon term on the energy spectrum and the photon blockade effect for the complete BS model by calculating the excited number and second-order correlation function.</sec><sec>Our study shows that, the nonlinear photon term not only eliminates the energy spectral collapse but also makes it well-defined and complete in all the coupling regime. When at the resonance between the atomic and the field frequency, the nonlinear photon term breaks the harmonicity of the energy spectrum and produces a ladder of the excited number in the ground state. Because the larger nonlinear photon term inhibits the photon transition from an energy level to the higher one, it produces the single-photon projection state in the larger coupling region. Accordingly, we find that the nonlinear photon term promotes photon blockade by calculating the second-order correlation function. When at the non-resonant region, the nonlinear photon term enlarges the originally anharmonic energy ladder. For a complete BS model with the fixed nonlinear photon coupling strength and the fixed detuning, the energy level for the positive detuning is lower than that with the negative detuning, and more energy is required to overcome the absorption of a photon. Therefore, the positive detuning promotes the photon blockade. For the negative detuning, the system is more likely to absorb a photon and jump to a higher energy level, and therefore, suppresses the photon blockade.</sec>

Энергия корреляции двухатомных молекул в пределе полного базиса из дистрибутивных гауссовых s-функций

In this paper possibilities of distributive s-Gaussian functions to estimate the second-order correlation energy (МР2) are investigated to the complete basis set limit. In contrast to standard atom-centered, the proposed bases consist of functions distributed along the molecular axis and off-axis functions. We propose and investigate the possibilities of one of the models for choosing the alignment of such functions. The model is characterized by a set of subsets of off-axis s-functions uniformly distributed along circles whose planes are perpendicular to the molecular axis. The function parameters are determined by minimizing the Hartree-Fock energy (for functions located along the molecular axis) and minimizing the Hylleraas functional (for off-axis s-functions). The resulting basis sequences, combined with known extrapolation models, are used to predict the MP2 energy in the complete basis set limit. The efficiency of the models is demonstrated by calculating the energy MP2 of simple H2 and LiH molecules.