Second-order Coherence Function Research Articles

Effective factors in improving lasing performance in an atom-cavity system in the steady state regime

The behavior of a three-level atom in a V configuration with a multi-photon transition enclosed in a single-mode Fabry–Perot optical cavity is examined theoretically. To solve the describing equations of the atom-cavity system, a matrix continued fractions method has been used in the steady state. On the one hand, the effects of the number of transitions have been discussed over quantities involving population inversion, mean photon number and second-order correlation function. On the other hand, the changes of the coupling constant have been investigated on observables consisting atom-cavity correlation, the mean photon number and the second-order coherence function for different transitions. The influences of the number of transitions and the variations of the coupling constant are discussed separately on the improving lasing action in both cases. Finally, the transformation circumstances of the given three-level atom to an effective two-level one have been analyzed for various transitions. The results of the three-level atomic simulations appropriately confirm the correctness of several special conditions applied in the two-level atomic pattern.

Coherence of vortex pseudo-Bessel beams in turbulent atmosphere

Theoretical research of coherent properties of vortex conic waves propagating in a turbulent atmosphere was developed. The analysis was based on the analytical solution of the equation for the transverse second-order mutual coherence function of a light field. The following characteristics of coherence of vortex conic waves were considered: the coherence degree, the coherence radius, the root-mean-square and the integral scale of coherence degree. Dependence of these characteristics on the parameters of optical radiation and turbulent atmosphere was analyzed. Unlike the coherence radius, the root-mean-square and integral scales of the coherence degree of vortex conic waves were found to be highly sensitive to the influence of atmospheric turbulence.

Light emission properties in a double quantum dot molecule immersed in a cavity: Phonon-assisted tunneling

Two main mechanisms dictate the tunneling process in a double quantum dot: overlap of excited wave functions, effectively described as a tunneling rate, and phonon-assisted tunneling. In this paper, we study different regimes of tunneling that arise from the competition between these two mechanisms in a double quantum dot molecule immersed in a unimodal optical cavity. We show how such regimes affect the mean number of excitations in each quantum dot and in the cavity, the spectroscopic resolution and emission peaks of the photoluminescence spectrum, and the second-order coherence function which is an indicator of the quantumness of emitted light from the cavity.

Fluctuation dynamics of an open photon Bose-Einstein condensate

Bosonic gases coupled to a particle reservoir have proven to support a regime of operation where Bose-Einstein condensation coexists with unusually large particle-number fluctuations. Experimentally, this situation has been realized with two-dimensional photon gases in a dye-filled optical microcavity. Here, we investigate theoretically and experimentally the open-system dynamics of a grand canonical Bose-Einstein condensate of photons. We identify a regime with temporal oscillations of the second-order coherence function $g^{(2)}(\tau)$, even though the energy spectrum closely matches the predictions for an equilibrium Bose-Einstein distribution and the system is operated deeply in the regime of weak light-matter coupling. The observed temporal oscillations are attributed to the nonlinear, weakly driven-dissipative nature of the system which leads to time-reversal symmetry breaking.

Second-order coherence function of a plasmonic nanoantenna fed by a single-photon source.

We study the second-order coherence function of a plasmonic nanoantenna fed by near-field of a single-photon source incoherently pumped in the continuous wave regime. We consider the case of a strong Purcell effect, when the single-photon source radiates almost entirely in the mode of a nanoantenna. We show that when the energy of thermal fluctuations, kT, of the nanoantenna is much smaller than the interaction energy between the electromagnetic field of the nanoantenna mode and the single-photon source, ℏΩR, the statistics of the emission is close to that of thermal radiation. In the opposite limit, ℏΩR>>kT, the nanoantenna radiates single photons. In the last case, we demonstrate the possibility of overcoming the radiation intensity of an individual single-photon source. This result opens the possibility of creating a high-intensity single-photon source.

Lasing action in low-resistance nanolasers based on tunnel junctions

We experimentally demonstrate the lasing action of a new nanolaser design with a tunnel junction. By using a heavily doped tunnel junction for hole injection, we can replace the p-type contact material of a conventional nanolaser diode with a low-resistance n-type contact layer. This leads to a significant reduction of the device resistance and lowers the threshold voltage from 5V to around 0.95V at 77K. The lasing behavior is verified by the light output versus the injection current (L-I) characterization and second-order coherence function measurements. Because of less Joule heating during current injection, the nanolaser can be operated at temperatures as high as 180K under CW pumping. The incorporation of heavily doped tunnel junctions may pave the way for other nanoscale cavity design for improved heat management.

Spin Current Cross-Correlations as a Probe of Magnon Coherence.

Motivated by the important role of the normalized second-order coherence function, often called g^{(2)}, in the field of quantum optics, we propose a method to determine magnon coherence in solid-state devices. Namely, we show that the cross-correlations of pure spin currents injected by a ferromagnet into two metal leads, normalized by their dc value, replicate the behavior of g^{(2)} when magnons are driven far from equilibrium. We consider two scenarios: driving by ferromagnetic resonance, which leads to the coherent occupation of a single mode, and driving by heating of the magnons, which leads to an excess of incoherent magnons. We find an enhanced normalized cross-correlation in the latter case, thereby demonstrating bunching of nonequilibrium thermal magnons due to their bosonic statistics. Our results contribute to the burgeoning field of quantum magnonics, which seeks to explore and exploit the quantum nature of magnons.

Second-order coherence properties of amplified spontaneous emission.

Properties of light sources based on amplified spontaneous emission (ASE) are similar to the properties of lasers in many regards. However, even though ASE has been widely studied, its photon statistics have not been settled. There are no reliable theoretical estimates or unambiguous experimental data for the second-order coherence function of photons that characterizes the coherence properties of a light source. Our computer simulation clearly establishes that, independently of pump power, the light produced by ASE is similar to that of a thermal source. This result lays bare the fundamental difference between ASE radiation and laser radiation.

Cross density of states and mode connectivity: Probing wave localization in complex media

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the second-order coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves.

Quantum stabilization of photonic spatial correlations

The driven, dissipative Bose–Hubbard model (BHM) provides a generic description of collective phases of interacting photons in cavity arrays. In the limit of strong optical nonlinearities (hard-core limit), the BHM maps on the dissipative, transverse-field XY model (XYM). The steady-state of the XYM can be analyzed using mean-field theory, which reveals a plethora of interesting dynamical phenomena. For example, strong hopping combined with a blue-detuned drive, leads to an instability of the homogeneous steady-state with respect to antiferromagnetic fluctuations. In this paper, we address the question whether such an antiferromagnetic instability survives in the presence of quantum correlations beyond the mean-field approximation. For that purpose, we employ a self-consistent 1/z expansion for the density matrix, where z is the lattice coordination number, i.e. the number of nearest neighbors for each site. We show that quantum fluctuations stabilize a new homogeneous steady-state with antiferromagnetic correlations in agreement with exact numerical simulations for finite lattices. The latter manifests itself as short-ranged oscillations of the first and second-order spatial coherence functions of the photons emitted by the array.

Coherence of Pseudo-Bessel Beams in a Turbulent Atmosphere

Coherent properties of nondiffracting pseudo-Bessel optical beams propagating in a turbulent atmosphere are studied theoretically. The solution of the equation formulated based on the paraxial approximation of the scalar wave equation for the second-order transverse mutual coherence function of the optical radiation field is analyzed. The behavior of the modulus and phase of the complex degree of coherence, coherence radius, and integral scale of the coherence degree of the Bessel-Gaussian optical beam and conical optical wave obtained by cone focusing of the optical beam by an axicon is studied as a function of optical beam parameters and characteristics of a turbulent atmosphere. Significant qualitative and quantitative distinctions between the studied coherence characteristics for cases of a Bessel-Gaussian optical beam and conical optical wave have been revealed. In general, under similar conditions of propagation in a turbulent atmosphere, the coherence of a conical optical wave is higher than that of a Bessel-Gaussian optical beam.

Entangled nonlinear displaced number states

Entangled nonlinear displaced number states are defined as the superposition of separable two-mode nonlinear displaced number states. In this paper, the nonlinear functions related to the harmonious states and trapped ion motion in center of mass system are considered. Considering the importance of non-classical states in quantum information theory, the non-classical properties of these states, such as photon statistics and entanglement, will be studied. Photon statistics of the entangled nonlinear displaced number states is evaluated by calculating the Mandel parameter and second order coherence function; the entanglement of the states is also examined by calculating concurrence. According to calculations, all of the introduced states have sub-Poissonian photon statistics in some range of coherent amplitude where this range becomes larger by increasing the number of the photons, n. It was also observed that the quantum second-order coherence function of the maximally entangled states represent photon antibunching effect in all values of the related parameters.

Excitation on the para-Bose states: Nonclassical properties

In this paper, we use a para-Bose operator to construct new kinds of excited para-Bose states. These states may be considered as appropriate and linear combinations of the para-Bose Fock states. We prove that these states satisfy a closure relation that is expressed uniquely in terms of the Meijer G -function. We examine the nonclassical properties of these states, by evaluating para-Bose Fock state distribution, Mandel’s parameter, second-order coherence function and quadrature squeezing. It results that the introduced excited para-Bose states show both the nonclassical and semiclassical statistics on their Fock state distribution. We also show that these states lack second-order coherence, i.e. they are not full coherent. Interestingly, the non-classicality of these states is controlled by the deformation parameter and number of excitation, where both parameters might be feasible for fine tuning in the trapped-ion quantum simulation.

The effects of atom–cavity coupling constant on physical observables for different transitions

The aim of this work is to investigate the changing effects of the atom–cavity coupling constant on an atom–cavity system. A three-level atom in the Λ configuration with q-photon transition between levels 2 and 3 is confined in a single-mode Fabry–Pérot optical cavity. To solve the master equation of this system in the steady-state by using the appropriate physical quantities, the matrix continued fractions method for recurrence equations is applied. The behavior of physical observables including atom–field correlation, mean photon number, and second-order coherence function is discussed. The effect of altering the atom–cavity coupling constant for different transitions on these observables is fully considered. The results of calculations show that by increasing this coupling constant, the range of atom–cavity correlation becomes longer, the maximum value of the output mean photon number from the cavity remains almost constant, the broadening in the curves of the mean photon number increases and the lasing process is amplified in the system. Finally, the transformation of the three-level atom into a two-level one under several specific conditions in a four-photon transition case has been studied. The obtained results of the two-level atomic pattern are adequately confirmed by the simulations related to the three-level atom.

Strong photon antibunching in weakly nonlinear two-dimensional exciton-polaritons

A deterministic and scalable array of single photon nonlinearities in the solid state holds great potential for both fundamental physics and technological applications, but its realization has proved extremely challenging. Despite significant advances, leading candidates such as quantum dots and group III-V quantum wells have yet to overcome their respective bottlenecks in random positioning and weak nonlinearity. Here we consider a hybrid light-matter platform, marrying an atomically thin two-dimensional material to a photonic crystal cavity, and analyze its second-order coherence function. We identify several mechanisms for photon antibunching under different system parameters, including one characterized by large dissipation and weak nonlinearity. Finally, we show that by patterning the two-dimensional material into different sizes, we can drive our system dynamics from a coherent state into a regime of strong antibunching with $g^{(2)}(0) \sim 10^{-3}$, opening a possible route to building scalable, on-chip quantum simulators.

The Role of Dissipation in the Two–Color Second–Order Coherence Function for Light Sources

We discuss the effect of the dissipation and pump rates in the two-photon spectrum (2PS) for different light sources. In this paper we show the second-order coherence function for the different frequencies given of the systems, we show how this measure reveals more information about the light source, and we show how it changes with dissipation and pump rates. We emphasize the importance of modelling system as an open quantum system for a more realistic description of the spectrum S(ω) and 2PS of field light

Teager–Kaiser energy methods for signal and image analysis: A review

This paper provides a review of the Teager–Kaiser (TK) energy operator and its extensions for signals and images processing. This class of operators possesses simplicity and good time-resolution and is very efficient in instantaneously estimating AM–FM signals and images. We point out the importance of the concept of energy from the point of view of the generation of the signal. More precisely, we emphasize the importance of analyzing signals from the point of view of the energy of the system needed to produce them. We show how this class of TK energy operators can be used to estimate useful features for signals and images analysis in time, space and frequency domains such as instantaneous frequency, second-order moment frequency, coherence function or spatial envelope and phase. We also show the importance of the higher derivative order of TK energy operator in terms of demodulation for both mono and multi-dimensional signals. Most of the developed tools around TK energy operators deal with real and complex-valued signals and some of them extended to multi-dimensional case. Due to their low complexity and their instantaneous-adapting nature, the class of TK energy operators offers valuable processing tools for time (space), frequency and time–frequency analysis.

On-chip photonic transistor based on the spike synchronization in circuit QED

We consider the single photon transistor in coupled cavity system of resonators interacting with multilevel superconducting artificial atom simultaneously. Effective single mode transformation is used for the diagonalization of the Hamiltonian and impedance matching in terms of the normal modes. Storage and transmission of the incident field are described by the interactions between the cavities controlling the atomic transitions of lowest lying states. Rabi splitting of vacuum-induced multiphoton transitions is considered in input/output relations by the quadrature operators in the absence of the input field. Second-order coherence functions are employed to investigate the photon blockade and delocalization–localization transitions of cavity fields. Spontaneous virtual photon conversion into real photons is investigated in localized and oscillating regimes. Reflection and transmission of cavity output fields are investigated in the presence of the multilevel transitions. Accumulation and firing of the reflected and transmitted fields are used to investigate the synchronization of the bunching spike train of transmitted field and population imbalance of cavity fields. In the presence of single photon gate field, gain enhancement is explained for transmitted regime.

Non-classical properties and polarization degree of photon-added entangled nonlinear coherent states

Photon-added states are introduced by applying creation operators of the two modes on the two-mode entangled nonlinear coherent states. These nonlinear coherent states are assumed to be harmonious. Then, non-classical properties of these states are examined by studying photon number distribution, Mandel parameter and second-order coherence function. Entanglement and quantum polarization of these states are also studied. We observe that all the states show sub-Poissonian statistics in some ranges of the parameters involved. In addition, the maximally entangled states show anti-bunching effect too. The dependence of the quantum polarization on the number of added photons and coherent amplitude is also evaluated.

Coherence of Bessel-Gaussian Beams Propagating in a Turbulent Atmosphere

Coherent properties of vortex Bessel-Gaussian beams propagating in a turbulent atmosphere are theoretically studied based on the analytical solution of the equation for the transverse second-order mutual coherence function of optical radiation field. The behavior of coherence degree, coherence length, and integral scale of coherence degree of vortex Bessel-Gaussian beams depending on beam parameters and characteristics of the turbulent atmosphere is analyzed. It is shown that the coherence length and integral scale of coherence degree of a vortex Bessel-Gaussian beam essentially depend on the topological charge of the beam. When the topological charge of a vortex beam increases, additional decreases in the above parameters become less. The given effect is small under weak and strong fluctuations of optical radiation, and it is maximal in the transition region between them.