Photon Number Distribution Research Articles

Hybrid Boson Sampling

We propose boson sampling from a system of coupled photons and Bose–Einstein condensed atoms placed inside a multi-mode cavity as a simulation process testing the quantum advantage of quantum systems over classical computers. Consider a two-level atomic transition far-detuned from photon frequency. An atom–photon scattering and interatomic collisions provide interactions that create quasiparticles and excite atoms and photons into squeezed entangled states, orthogonal to the atomic condensate and classical field driving the two-level transition, respectively. We find a joint probability distribution of atom and photon numbers within a quasi-equilibrium model via a hafnian of an extended covariance matrix. It shows a sampling statistics that is ♯P-hard for computing, even if only photon numbers are sampled. Merging cavity-QED and quantum-gas technologies into a hybrid boson sampling setup has the potential to overcome the limitations of separate, photon or atom, sampling schemes and reveal quantum advantage.

Two-mode subharmonic generating system with coherent and thermal light

The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a single-port mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} entangled.

High-harmonic generation by a bright squeezed vacuum

AbstractHigh-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 1013 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.

Efficient validation of Boson Sampling from binned photon-number distributions

In order to substantiate claims of quantum computational advantage, it is crucial to develop efficient methods for validating the experimental data. We propose a test of the correct functioning of a boson sampler with single-photon inputs that is based on how photons distribute among partitions of the output modes. Our method is versatile and encompasses previous validation tests based on bunching phenomena, marginal distributions, and even some suppression laws. We show via theoretical arguments and numerical simulations that binned-mode photon number distributions can be used in practical scenarios to efficiently distinguish ideal boson samplers from those affected by realistic imperfections, especially partial distinguishability of the photons.

Photon number distribution of squeezed light from a silicon nitride microresonator measured without photon number resolving detectors

The measurement of the photon number distribution (PND) allows one to extract metrics of non-classicality of fundamental and technological relevance, but in principle it requires the use of detectors with photon number resolving (PNR) capabilities. In this work we reconstruct the PND of two-mode pulsed squeezed light generated from a silicon nitride microresonator using threshold detectors and variable optical attenuations. The PNDs are characterized up to ∼1.2 photons per pulse, through which we extracted an on-chip squeezing level of 6.2(2) dB and a noise reduction factor of −3.8(2) dB. The PNDs are successfully reconstructed up to a Hilbert space dimension of 6 × 6. The analysis performed on the photon number basis allows us to characterize the influence of a spurious thermal background field that spoils the photon number correlations. We evaluate the impact of self- and cross-phase modulation on the generation efficiency in case of a pulsed pump, and validate the results through numerical simulations of the master equation of the system.

Estimation of photon number distribution and derivative characteristics of photon-pair sources

The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the source. The photon number distribution, however, can be altered due to spectral or spatial filtering and optical losses, leading to changes in the above characteristics. This paper theoretically describes the effects of different filterings, losses, and noise counts on the photon number distribution and related characteristics. From the theoretical description, an analytic expression for the effective mode number of the joint spectral density is also derived. Compared with previous methods for estimating the photon number distribution and characteristics, an improved methodology is introduced along with a suitable metric of accuracy for estimating the photon number distribution, focusing on photon-pair sources. We discuss the accuracy of the calculated characteristics from the estimated (or reconstructed) photon number distribution through repeated simulations and bootstrapped experimental data.

DNA Framework-Guided Self-Limiting Aggregation for Highly Luminescent Metal Cluster Nanoaggregates.

The photoluminescent properties of atomically precise metal nanoclusters (MCs) have garnered significant attention in the fields of chemical sensing and biological imaging. However, the limited brightness of single-component nanoclusters hinders their practical applications, and the conventional ligand engineering approaches have proven insufficient in enhancing the emission efficiency of MCs. Here, we present a DNA framework-guided strategy to prepare highly luminescent metal cluster nanoaggregates. Our approach involves an amphiphilic DNA framework comprising a hydrophobic alkyl core and a rigid DNA framework shell, serving as a nucleation site and providing well-defined nanoconfinements for the self-limiting aggregation of MCs. Through this method, we successfully produced homogeneous MC nanoaggregates (10.1 ± 1.2 nm) with remarkable nanoscale precision. Notably, this strategy proves adaptable to various MCs, leading to a substantial enhancement in emission and quantum yield, up to 3011- and 87-fold, respectively. Furthermore, our investigation using total internal reflection fluorescence microscopy at the single-particle level uncovered a more uniform photon number distribution and higher photostability for MC nanoaggregates compared to template-free counterparts. This DNA-templating strategy introduces a conceptually innovative approach for studying the photoluminescent properties of aggregates with nanoscale precision and holds promise for constructing highly luminescent MC nanoparticles for diverse applications.

2D‐Material‐Fused High‐Emittance Plasmo–Photonic Metasurfaces

AbstractTransition metal dichalcogenides (TMDC) are a family of atomic‐layer 2D materials (2dMs). Many researches have attempted to reinforce the unique properties by incorporating artificially designed nanostructures. Here, a highly photoluminescence (PL) enhancing platform is reported that is formed by combining high‐emittance plasmo–photonic metasurfaces with a large‐area 2dM, which is a continuous monolayer of TMDC of cm2 dimension. It is experimentally demonstrated that the 2dM‐PL intensity at room temperature is enhanced by more than 1030‐fold in comparison with that observed on the flat gold film regions. The enhancement is associated with spectral transformation indicating a resonant effect of the metasurfaces. It is moreover revealed that the confocal PL image originates from a coherent single‐mode emission that forms a photon number distribution obeying the Poisson probability distribution. Thus, the 2dM‐fused metasurfaces function as efficient coherent quantum light sources. PL decay‐time analysis also reveals the coexistence of two components in the enhanced PL. The fast component exhibits a lifetime of 18 ps whereas the slow component decays at 4.4 ns. Both components are most likely to undergo radiative processes, which indicates that metal‐induced PL quenching is suppressed on these 2dM‐fused metasurfaces. The long lifetime component is ascribed to an excitonic intervalley transition.

New angular momentum coherent states via the nonlinear Bose SU(2) generators and their nonclassical behaviors

I theoretically construct a kind of new angular momentum coherent states by virtue of the nonlinear Bose SU(2) generators, and investigate their nonclassicality by analyzing the sub-Poissonian distributions, photon number distributions, entanglement entropy and Wigner phase-space distributions. The results show that the new states always have the sub-Poissonian distributions for all of the photon number sum [Formula: see text] of two modes, the photon number distributions are subjected to the parameter q, and the entanglement always increases quickly and then decreases slowly with increasing [Formula: see text], and the new states for odd q possess more stronger nonclassicality than for even q.

Preparation and properties of a non-Gaussian state by quantum catalysis with thermal state input

We theoretically introduce a new kind of non-Gaussian state, namely, the mixture of multiphoton added thermal states, achieved through multiphoton measurements at one output port of the beam splitter (termed multiphoton catalysis) for thermal state input. We discuss the success probabilities of detection (the normalization factors). Furthermore, we investigate their nonclassical properties based on the nonclassical depth, photon number distribution, and photocount distribution. It is shown that the multiphoton catalysis presents a better nonclassical performance by controlling the thermal parameter, catalyzed photon number and the transmissivity of the beam splitter. In addition, the nonclassicality is further examined through the partial negativity of the Wigner function, which reveals that multiphoton catalysis operation can prepare highly nonclassical quantum states. These results indicate that the preparation of a non-Gaussian states may have potential applications in the realms of quantum information processing and quantum metrology.

Non-Gaussian quantum states generated via quantum catalysis and their statistical properties

Abstract A new kind of non-Gaussian quantum catalyzed state is proposed via multiphoton measurements and two-mode squeezing as an input of thermal state. The characteristics of generating multiphoton catalysis output state depends on the thermal parameter, catalyzed photon number and squeezing parameter. We then analyze the nonclassical properties by examining the photon number distribution, photocount distribution and partial negativity of the Wigner function. Our findings indicate that nonclassicality can be achieved through the implementation of multiphoton catalysis operations, and modulated by the thermal parameter, catalyzed photon number and squeezing parameter.

Nonclassicality in a dispersive atom–cavity field interaction in the presence of an external driving field

We investigate nonclassical properties of a state generated by the interaction of a three-level atom with a quantized cavity field and an external classical driving field. In this study, the fields being degenerate in frequency are highly detuned from the atom. The atom interacts with the quantized field in a dispersive manner. The experimental setup involves a three-level atom passing through a cavity and interacting dispersively with the cavity field mode. Simultaneously, the atom interacts with an external classical field that is in resonance with the cavity field. The three-level atom can enter the cavity in one of the bare states [Formula: see text], [Formula: see text] or [Formula: see text] or in a superposition of two of these states. In this paper, we consider superposition of [Formula: see text] and [Formula: see text]. In our analysis, we focus on the statistical properties of the cavity field after interacting with the atom. The state vector [Formula: see text] describes the entire atom–field system but we analyze the properties of the cavity field independently neglecting the atomic component of the system. For this the atom part is traced out from [Formula: see text] to acquire the cavity field state only, denoted by [Formula: see text]. We evaluate different nonclassical measures including photon number distribution, Mandel’s [Formula: see text] parameter, squeezing properties [Formula: see text] and [Formula: see text], Wigner distribution, [Formula: see text] function, second-order correlation function [Formula: see text], etc. for the obtained cavity field state.

Experimental characterization of multimode photon-subtracted twin beams

States obtained from multimode twin beams by symmetric as well as asymmetric photon subtraction are experimentally investigated. Using the joint photocount distributions measured by an intensified CCD camera, their joint photon-number distributions are reconstructed. Mean photon numbers, Fano factors, and noise-reduction parameters are determined for the group of states reached by subtracting up to four photocounts in each beam. Photon subtraction is monitored using the nonclassicality depths and joint quasidistributions of integrated intensities of the emerging states. The non-Gaussianity of the obtained states is also determined. The states reached by coherent photon subtraction are also analyzed. The investigations represent an important step towards the use of photon-subtracted twin beams in sub-shot-noise metrology and imaging. Published by the American Physical Society 2024

Reduction of g2(0) value in heralded spontaneous parametric down-conversion sources using photon number resolving detectors

Single Photon Sources (SPSs) play a pivotal role in fields such as quantum communication and quantum cryptography by generating information in a secure manner. However, realizing the ideal emission of single photons with high efficiency is still a theoretical model. This leads to the presence of multiphoton components in SPSs, which could potentially compromise security. This study focuses on enhancing the purity of a class of sources by characterizing their photon number distribution and mitigating the impact of the multiphoton components. We propose the use of Photon Number Resolving Detectors (PNRD) as a technique to exclude multiphoton contributions, particularly in sources like Spontaneous Parametric Down Conversion sources, where emitted photons can be represented as Two-Mode Squeezed Vacuum states. By analyzing the second-order cross-correlation function, g2(0), using either PNRD or Single Photon Detectors, we can quantify the reduction in multiphoton contributions.

Analysis of quantum properties of two-mode coupled Harmonic Oscillator based on the entangled state representation

The quantum oscillator model plays a significant role in quantum optics and quantum information and has been one of the hot research topics in related fields. Inspired by the single-mode linear harmonic oscillator and the two-mode entangled state representation, this paper constructs a two-mode coupled harmonic oscillator. Different from the quantum transformation method used in previous literature, this paper directly uses the entangled state representation to solve its energy eigenvalues ​​and eigenfunctions easily. Compared with the one-mode harmonic oscillator, the energy eigenvalues ​​and eigenfunctions of this two-mode coupled harmonic oscillator are continuous.<br>Using the matrix theory of quantum operators, we derive the transformation and inverse transformation of the time evolution operator corresponding to the two-mode coupled harmonic oscillator. In addition, using the entangled state representation, the specific form of the time evolution of the two-mode vacuum state under the action of the oscillator is obtained. Through the analysis of quantum fidelity, it is found that the fidelity of the output quantum state decreases with the increase of the oscillator frequency, and the fidelity eventually tends to zero with the increase of time.<br>When analyzing the orthogonal squeezing properties of the output quantum state, this type of two-mode oscillator does not have the orthogonal squeezing effect, but instead has a strong quantum dissipation effect. This conclusion is further verified by the quasi-probability distribution Q function of the quantum state phase space. Therefore, the two-mode coupled harmonic oscillator has a major reference value in quantum control such as quantum decoherence and quantum information transmission.<br>Like the two-mode squeezed vacuum state, the photon distribution of the output quantum light field corresponding to the two-mode harmonic oscillator presents a super-Poisson distribution, and the photons exhibit a strong anti-bunching effect. Using the three-dimensional discrete plot of the photon number distribution, the super-Poisson distribution and quantum dissipation effect of the output quantum state are intuitively demonstrated.<br>Finally, the SV entanglement criterion is used to determine that the output quantum state has a high degree of entanglement. Further numerical analysis shows that the degree of entanglement increases with the action time and the oscillator frequency.<br>In summary, the two-mode coupled harmonic oscillator constructed in this paper can be used to prepare highly entangled quantum states through a complete quantum dissipation process. This provides theoretical support for the experimental preparation of quantum entangled states based on dissipative mechanisms.

Generalized sub-Poissonian states of two-beam fields.

Two-beam states obtained by partial photon-number-resolving detection in one beam of a multi-mode twin beam are experimentally investigated using an intensified CCD camera. In these states, sub-Poissonian photon-number distributions in one beam are accompanied by sub-shot-noise fluctuations in the photon-number difference of both beams. Multi-mode character of the twin beam implying the beam nearly Poissonian statistics is critical for reaching sub-Poissonian photon-number distributions, which contrasts with the use of a two-mode squeezed vacuum state. Relative intensities of both nonclassical effects as they depend on the generation conditions are investigated both theoretically and experimentally using photon-number distributions of these fields. Fano factor, noise-reduction parameter, local and global nonclassicality depths, degree of photon-number coherence, mutual entropy as a non-Gaussianity quantifier, and negative quasi-distributions of integrated intensities are used to characterize these fields. Spatial photon-pair correlations as means for improving the field properties are employed. These states are appealing for quantum metrology and imaging including the virtual-state entangled-photon spectroscopy.

Quantum second harmonic generation in terms of elementary processes

We address the quantum dynamics of second harmonic generation with a perturbative approach. By inspecting the Taylor expansion of the unitary evolution, we identify the subsequent application of annihilation and creation operators as elementary processes and find out how the expansion of the second-harmonic photon-number probability distribution can be expressed in terms of the interplay of these processes. We show that overlaps between the output states of different elementary processes contribute to the expansion of the probability distribution and provide a diagrammatic technique to analytically retrieve terms of the distribution expansion at any order.

Tomography of Detectors Taking Dead Time into Account

Using numerical simulation methods that take into account the dead time effect, algorithms are developed to calculate the detector’s response for photon fluxes with different photon number distributions, including the Poisson, Fock, and thermal distributions. Based on the results obtained, a detector tomography method is developed, as well as an algorithm for identifying the corresponding elements of a positive operator-valued measure (POVM). Experimental studies using coherent states demonstrate close agreement between the calculation results and experimental data.

Noise-induced dynamics and photon statistics in bimodal quantum-dot micropillar lasers

Emission characteristics of quantum-dot micropillar lasers (QDMLs) are located at the intersection of nanophotonics and nonlinear dynamics, which provides an ideal platform for studying the optical interface between classical and quantum systems. In this work, a noise-induced bimodal QDML with orthogonal dual-mode outputs is modeled, and nonlinear dynamics, stochastic mode jumping and quantum statistics with the variation of stochastic noise intensity are investigated. Noise-induced effects lead to the emergence of two intensity bifurcation points for the strong and the weak mode, and the maximum output power of the strong mode becomes larger as the noise intensity increases. The anti-correlation of the two modes reaches the maximum at the second intensity bifurcation point. The dual-mode stochastic jumping frequency and effective bandwidth can exceed 100 GHz and 30 GHz under the noise-induced effect. Moreover, the noise-induced photon correlations of both modes simultaneously exhibit super-thermal bunching effects () in the low injection current region. The -value of the strong mode can reach over 6 in the high injection current region. Photon bunching () of both modes is observed over a wide range of noise intensities and injection currents. In the presence of the noise-induced effect, the photon number distribution of the strong or the weak mode is a mixture of Bose–Einstein and Poisson distributions. As the noise intensity increases, the photon number distribution of the strong mode is dominated by the Bose–Einstein distribution, and the proportion of the Poisson distribution is increased in the high injection current region, while that of the weak mode is reduced. Our results contribute to the development preparation of super-bunching quantum integrated light sources for improving the spatiotemporal resolution of quantum sensing measurements and enhancing the security of optical communication.

Tomography of Detectors Taking Dead Time into Account

Using numerical simulation methods that take into account the dead time effect, algorithms are developed to calculate the detector’s response for photon fluxes with different photon number distributions, including the Poisson, Fock, and thermal distributions. Based on the results obtained, a detector tomography method is developed, as well as an algorithm for identifying the corresponding elements of a positive opera-tor-valued measure (POVM). Experimental studies using coherent states demonstrate close agreement between the calculation results and experimental data.