Statistical Properties Of Photons Research Articles

Probing the Ginzburg–Landau Potential for Lasers Using Higher-order Photon Correlations

Lasing transition is known to be analogous to the second-order phase transition. Furthermore, for some cases, it is possible to define the Ginzburg-Landau (GL) potential, and the GL theory predicts the photon statistical properties of lasers. However, the GL potential for lasers is surprising, because lasers are operating far from equilibrium. In this paper, we theoretically examine the validity of the GL theory for lasers in terms of various parameters, particularly, the ratio between photon and carrier lifetimes. For this purpose, we use stochastic rate equations and higher-order photon correlation functions. With higher-order photon correlation measurements, we can check whether or not laser dynamics are described by the GL theory. We demonstrate that, for low-$\beta$ lasers, the GL theory is applicable even when the photon lifetime is comparable to the carrier lifetime and that photon-carrier relaxation oscillation is the fundamental origin of the breakdown of the GL theory, which can be understood in the framework of center manifold reduction.

Nonreciprocal photon blockade in a spinning optomechanical resonator

A scheme is presented to realize nonreciprocal photon blockade by exploiting a spinning optomechanical resonator, where the photon blockade effect appears when the spinning resonator is driven from one side but vanishes from the other side. This quantum nonreciprocity originates from the Sagnac effect and Kerr-type interaction between photons in the spinning resonator. We analyze the dynamics of the system in the weak driving regime, and discuss the photon statistical properties by calculating the second-order correlation function. Based on master-equation simulations, we also study numerical results of the steady state of the system and the validity of the analytical solution, and find that it is feasible to achieve nonreciprocal photon blockade by choosing appropriate parameters in a spinning optomechanical resonator.

Ququats as superposition of coherent states and their application in quantum information processing

Superposition of optical coherent states (SCS) [Formula: see text], possessing opposite phases, plays an important role as qubits in quantum information processing tasks like quantum computation, teleportation, key distribution, etc. and are of fundamental importance in testing quantum mechanics. Passage of such SCS from a 50:50 beam splitter leads to generation of entangled coherent states. Recently, ququats and qutrits defined in four- and three-dimensional Hilbert space, respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially requires physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with [Formula: see text] (here, [Formula: see text] or 3 and [Formula: see text]) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four-dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher-dimensional BB84 protocol to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different quantum information processing tasks.

Quantum correlation and non-classical properties in semiconductor microcavities for multi-photon excitation

We study how the interplay of weak excitation regime of quantum well confined in a semiconductor microcavity affects the dynamics of correlations and the statistical properties of photons. We discuss how the system parameters can impact the quantum entropy and Mandel’s parameter, and illustrate our concerns with numerical simulations. We have found that the enhancement of the correlations and the control of the statistical properties of photons in semiconductor microcavities for multi-photon excitation highly benefits from the combination of the strength of the field, excitonic spontaneous emission rate, cavity dissipative rate, and the coupling between the exciton and photons. Our results may have important implications not only for those specially interested in quantum optics and information, but also for the general physics community.

Interference-modulated photon statistics in whispering-gallery-mode microresonator optomechanics

Whispering-gallery-mode (WGM) microresonator optomechanical systems that can attain high quality factors, exhibit small optical mode volume, and can be excited through their evanescent field are versatile platforms for both theoretical and experimental studies in quantum and nonlinear optics. Investigating photon statistical properties in WGM microresonator optomechanical systems is an important avenue to understand their inner interaction mechanism. Here, the interference-modulated photon statistics in a three-mode coupling, i.e., a pair of counterpropagating optical cavity modes and a mechanical mode, in WGM microresonator optomechanical systems is studied. In the case that one optical mode is driven by an external field, strong antibunching photon statistics can be observed in the presence of mode coupling. When the two cavity modes are driven simultaneously, it is found that the photon statistical properties can be well steered by modulating the interference between different transition paths with the help of the amplitudes of the two input fields and their relative phase. Especially, we show in detail that the antibunching photon statistics can be optimized within the weak optomechanical coupling regime by properly adjusting the relative phase. We also find that it is necessary to prepare the mechanical resonator near to the ground state to eliminate the detrimental effect of thermal phonon number on the photon statistical properties. This investigation can deepen our understanding of the interaction between clockwise or counterclockwise light and mechanical motion as well as be useful for the construction of integrated on-chip single-photon sources.

Tunable unconventional phonon blockade in Fabry-Perot cavity and optical parametric amplifier composite system

In this paper, we present a scheme to realize an unconventional photon blockade effect in a Fabry-Perot cavity and optical parametric amplifier (OPA) composite system. The system includes a tunable phase of complex driving strength, the second-order correlation function is used to describe the photon statistical properties. The numerical simulation of the photon blockade effect is conducted with different parameters. Our calculations show that the unconventional photon blockade effect can be controlled by the tunable phase of complex driving strength. Under the weak driving condition, the exact optimal conditions for strong photon anti-bunching are analytically derived (i.e. the optimal nonlinear gain of optical parametric amplifier and the phase of the field driving for the strong photon anti-bunching are obtained), and obtain the analytic calculations of the second-order correlation function. Under the optimal conditions, we perform a numerical simulation with different parameters. The optimal conditions for strong photon anti-bunching are found by analytic calculations, which are in good agreement with the numerical results. The results provide a platform for coherently operating the photon blockade and have potential applications in quantum information processing and quantum optical devices.

Chiral microresonator assisted by Rydberg-atom ensembles

The chiral light-matter interaction, which shows great potential in applications ranging from photonic devices to quantum information processing, can be achieved with the development of recent experimental advances of the fabrication technologies on nanoscales. Traditionally, the chiral optics based on spin-momentum locking in micro- and nanophotonics could be observed only for specific optical modes, such as the transverse magnetic mode. Here in this study, we investigate that the chirality of a whispering-gallery-mode (WGM) microresonator can be well controlled with assistance from coupled Rydberg-atom ensembles. The presented asymmetric backscattering also originates from interferences between scattered optical modes in the WGM microresonator, which is proposed by Wiersig [Phys. Rev. A 84, 063828 (2011)]. Therefore the flow of light can be well controlled, and the statistical properties of photons could be changed by regulating this asymmetric coupling. Most importantly, its universal chiral property is not limited by specific optical modes which may also be used as optical diodes and routers.

Photon blockade with cross-Kerr nonlinearity in superconducting circuits

We theoretically investigate the photon statistical properties of a weakly-driven circuit quantum electrodynamic system with a cross-Kerr nonlinearity, which is built from two coupled transmon qubits through a superconducting quantum interference device (SQUID). We show that when two resonators are resonant with each other, photon blockade and sub-Poissonian photon statistics in the first superconducting transmission line resonator (TLR), TLR1, can be achieved by modulating the resonator-driving detunings and the cross-Kerr nonlinearity. Moreover, the optimal conditions for obtaining sub-Poissonian statistics are put forward through analytical derivations, which are in good agreement with those obtained by numerical simulations. We also examine the role of the resonator–resonator hopping interaction for photon statistics in TLR1 by numerically analyzing the case where the frequencies of two resonators are far detuned from each other. Due to the cutoff of the indirect transition paths in this case, the output field always acquires super-Poissonian statistics. In addition, a physical model with a SQUID embedded in TLR1 is proposed to tune the detuning between two TLRs, making it possible to demonstrate the importance of the resonator–resonator hopping interaction in obtaining a single-photon blockade. Thereby, our model of two coupled resonators with cross-Kerr nonlinearity has the potential to engineer the photon statistics through operating on the system parameters.

Tunable Photon Blockade in Coupled Second-order Nonlinear Cavities

The unconventional photon blockade with weak χ (2) nonlinearity in a system consists of two single-mode cavities driving by two external fields is studied in this paper. The photon statistical properties, described by the second-order correlation function, are discussed, and the exact optimal conditions for strong photon anti-bunching is analytically derived. The optimal frequency detuning and nonlinear interaction strength for the strong photon anti-bunching are also obtained, which are in good agreement with numerical simulations. We find that the unconventional photon blockade effect can be controlled by tuning the relative phase between two complex driving fields when the two cavity modes are driven simultaneously. Our results provide a promising scheme for the coherent manipulation of photon blockade through tuning the relative phase between the two driving fields, which makes the experimental realization more flexible.

Q-Deformed Barut–Girardello su(1, 1) coherent states and Schrödinger cat states

We define Schrodinger cat states as superpositions of q-deformed Barut–Girardello su(1, 1) coherent states with an adjustable angle φ in a q-deformed Fock space. We study the statistical properties of the q-deformed Barut–Girardello su(1, 1) coherent states and Schrodinger cat states. The statistical properties of photons are always sub-Poissonian for q-deformed Barut–Girardello su(1, 1) coherent states. For Schrodinger cat states in the cases φ = 0, π/2, π, the statistical properties of photons are always sub-Poissonian if φ = π/2, and the other cases are hard to determine because they depend on the parameters q and k. Moreover, we find some interesting properties of Schrodinger cat states in the limit |z| → 0, where z is the parameter of those states. We also derive that the statistical properties of photons are sub-Poissonian in the undeformed case where π/2 ≤ φ ≤ 3π/2.

Discorrelated quantum states

The statistical properties of photons are fundamental to investigating quantum mechanical phenomena using light. In multiphoton, two-mode systems, correlations may exist between outcomes of measurements made on each mode which exhibit useful properties. Correlation in this sense can be thought of as increasing the probability of a particular outcome of a measurement on one subsystem given a measurement on a correlated subsystem. Here, we show a statistical property we call “discorrelation”, in which the probability of a particular outcome of one subsystem is reduced to zero, given a measurement on a discorrelated subsystem. We show how such a state can be constructed using readily available building blocks of quantum optics, namely coherent states, single photons, beam splitters and projective measurement. We present a variety of discorrelated states, show that they are entangled, and study their sensitivity to loss.

Single-photon nonlinearities in a strongly driven optomechanical system with quadratic coupling

Optical nonlinearities at the single-photon level are explored in a quadratically coupled optomechanical system, where the cavity frequency is coupled to the square of the mechanical displacement. The effective nonlinear interaction between photons and phonons is enhanced by a strong driving field, which allows one to implement the single-photon nonlinearities even if the single-photon coupling strength ${g}_{0}$ is much lower than the cavity decay rate $\ensuremath{\kappa}$. The photon statistical properties are discussed by calculating the second-order correlation function both analytically and numerically. The results show that the single-photon nonlinearities are robust against mechanical thermal noise in the strong-coupling and sideband-resolved regime, and photon blockade and photon-induced tunneling can be realized with experimentally accessible parameters.

Photon statistical properties emitted from single molecule derived from generating function method

Photon statistical properties emitted from single molecule derived from generating function method

Photon Statistical Properties of Single Terrylene Molecules in P-Terphenyl Crystals**Supported by the Project of Xuzhou Institute of Technology under Grant No XKY2014309, and the National Natural Science Foundation of China under Grant Nos 11304266 and 11447149.

We consider the photon emission statistical properties of a single molecule under pump-probe field driving, using the generating function method. The first- and second-order moments of statistical quantities are presented. Derived from the first-order moment, the line shapes are in good agreement with the experimental results. Derived from the second-order moment, Mandel's Q parameters show an obvious quantum effect of photon statistical distribution, i.e., the anti-bunching effect.

Quantum-discord-triggered superradiance and subradiance in a system of two separated atoms

We investigate collective radiant properties of two separated atoms in X-type quantum states. We show that quantum correlations measured by quantum discord (QD) can trigger and enhance superradiance and subradiance in the two-atom system even though in the absence of interatomic quantum entanglement. We also explore quantum statistical properties of photons in the superradiance and subradiance by addressing the second-order correlation function. In particular, when the initial state of the two separated atoms is the Werner state with nonzero QD, we find that radiation photons in the superradiant region exhibit the nonclassical sub-Poissonian statistics and the degree of the sub-Poissonian statistics increases with increasing of the QD amount, while radiation photons in the subradiant region have either the sub-Poissonian or super-Poissonian statistics depending on the amount of QD and the directional angle. In the subradiant regime, we predict the QD-triggered photon statistics transition from the super-Poissonian to sub-Poissonian statistics. These results shed a new light on applications of QD as a quantum resource.

Study of s-exciton and p-exciton pump on the lasing generation of biexciton quantum dot–cavity system

The quantum dot (QD)–cavity system with deep confinement potential is usually studied by either non-resonant or quasi-resonant p-exciton pump (PEP) with the s-exciton pump (SEP) ignored. In this paper, we investigate the effect of an SEP on the emission properties of a QD–cavity system with deep confinement potential by comparing the different incoherent excitation schemes, including pumping with both s- and p-exciton pump and with PEP only. The investigation reveals that the steady-state properties such as photon statistical properties and emission spectra of the QD–cavity system are significantly affected. More importantly, after taking SEP into consideration, the lasing and self-quenching regime of the entire system will be reached at a much lower pump rate than that of the only PEP scheme.

Photon counting statistics of a single molecule under pump–probe fields

We consider the photon statistical properties emitted from a two-level quantum system under pump–probe driving. The line shapes and Mandel's Q parameters are studied for a single quantum system based on the generating function method developed recently. The control of photon emission from a single quantum system driven simultaneously by a driven field and a tunable probe field is investigated. Our theoretical results and the experimental results are in good agreement.

Photon statistical properties of photon-added two-mode squeezed coherent states

We investigate photon statistical properties of the multiple-photon-added two-mode squeezed coherent states (PA-TMSCS). We find that the photon statistical properties are sensitive to the compound phase involved in the TMSCS. Our numerical analyses show that the photon addition can enhance the cross-correlation and anti-bunching effects of the PA-TMSCS. Compared with that of the TMSCS, the photon number distribution of the PA-TMSCS is modulated by a factor that is a monotonically increasing function of the numbers of adding photons to each mode; further, that the photon addition essentially shifts the photon number distribution.

Photon statistical properties of multiple-photon-subtracted two-mode squeezed coherent states

We investigate how the combination of photon subtraction and coherent displacement affects the photon statistical properties of the multiple-photon-subtracted two-mode squeezed coherent states (PS-TMSCS). We find that the photon statistical properties are sensitive to the compound phase involved in the TMSCS. Our numerical analysis shows that the photon subtraction can enhance the cross-correlation and anti-bunching effects of the PS-TMSCS. Compared with that of the TMSCS, the photon number distribution of the PS-TMSCS is modulated by a factor that is a monotonically increasing function of the numbers of subtracting photons from each mode. And the photon subtraction essentially shifts the photon number distribution.

Photon counting ghost imaging using non-Poisson light source

We show theoretically that photon counting technique can be used to obtain ghost imaging as long as the number distribution of photon source is non-Poissonian; the visibility of image could be either negative or positive, depending on the photon statistical properties. The visibility of photon counting ghost imaging can be enhanced using higher order correlations. With taking advantage of high speed photon counting CCD and detector, fast imaging can be achieved.