We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q-parameter and Wigner function that the statistics of oscillatory excitation number is drastically changed in order-to chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime the system exhibits the range of sub- and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed.
We propose a method to prepare different non-Poissonian signal pulses from sources of Poissonian photon number distribution using only linear optical elements and threshold photon detectors. This method allows a simple passive preparation of decoy states for quantum key distribution. We show that the resulting key rates are comparable to the performance of active choices of intensities of Poissonian signals.
We report the direct observation of sub-Poissonian number fluctuation for a degenerate Bose gas confined in an optical trap. Reduction of number fluctuations below the Poissonian limit is observed for average numbers that range from 300 to 60 atoms.
A derivation of the coarse grained dynamical equation for a maser with periodic injection of atoms suggested by Briegel and Englert [Phys.Rev.A. {\bf 52}, 2361 (1995)] from the microscopic masterequation is presented.
We have measured the photon statistics of pump and probe beams after interaction with Rb atoms in a situation of Electromagnetically Induced Transparency. Both fields present super-poissonian statistics and their intensities become correlated, in good qualitative agreement with theoretical predictions in which both fields are treated quantum-mechanically. The intensity correlations measured are a first step towards the observation of entanglement between the fields.
A simple method for the production of ultrashort light pulses (USPs) with suppressed photon fluctuations is considered. The method is based on self-phase modulation (SPM) of an USP in a nonlinear medium (optical fibre) and subsequent transmission of pulse through a dispersive optical element.
Measurement-based feedback as a flexible tool to control non-Poissonian photon statistics
Shenzhen International Quantum Academy（深圳国际量子学院）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学深圳量子科学与工程学院）；Department of Physics, Zhejiang University of Science and Technology（浙江科技学院物理系）
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 induce 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 non-zero QD, we find that radiation photons in the superradia…
We use majorization and confidence intervals as a convenient tool to compare the uncertainty in photon number for different quantum light states. To this end majorization is formulated in terms of confidence intervals. As a suitable case study we apply this tool to sub- and super-Posissonian behavior and bunching and anti- bunching effects. We focus on the most significant classical and nonclassical states, such as Glauber coherent, thermal, photon number, and squeezed states. We show that majorization provides a more complete analysis that in some relevant situations contradicts the predictio…
We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with time-dependent parameters and take place for the regimes of long time intervals exceeding dissipation time and for macroscopic levels of oscillatory excitation numbers. Two schemas of time modulation: (i) periodic variation of the strength of the χ(3) nonlinearity; (ii) periodic modulation of the amplitude of the driving force, are considered. These effects are obtai…
In this work we study an optomechanical system in which there is a purely quadratic optomechanical coupling between the optical and mechanical modes. The optical mode is pumped by three coherent fields and the mechanical mode is parametrically driven. We show that if the frequencies and amplitudes of both optical and mechanical drivings are properly chosen, the optomechanical interaction gives rise to an effective interaction, which, in the presence of optical damping and in the absence of mechanical damping, has the squeezed vacuum state and the squeezed one phonon state as dark states of the…
Heralded single photon sources (HSPS) from spontaneous parametric down-conversion are widely used as single photon sources. We study the photon number statistics of an HSPS carrying orbital angular momentum in our laboratory and observe the sub-Poissonian statistics using only photo detectors and an oscilloscope.
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories that the probability distributions and variances of oscillatory number states are strongly transformed in the order-to-chaos transition. The nonclassical, sub-Poissonian statistics of oscillatory excitation numbers is established for chaotic dissipative dynamics in the framework of Fano factor and Wigner functions. These results are proposed for testing and …
Using the theoretical model of the optical beam-splitter, the interference of the self-phase modulated ultrashort light pulse (SPM-USP) with the coherent one is investigated. It is found that, the choice of the coefficient of transmission of the beam-splitter allows one to get the spectra of quadrature fluctuations with forms of interest to us. It is shown that the choice of the geometrical phase gives one the control of the position of the ellipse of squeezing in the quadrature space XY. The extended Mandel parameter is introduced and the photon statistics is scanned at all frequencies. It is…
Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation …
Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become…
Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in t…
We elucidate generally the interference of independent Bose fields in view of the conditional probability for the particle number measurements, and clarify its relation to the source number statistics. Despite lack of intrinsic phases, the interference phase can be inferred from the particle number registered at one detector by using the classical mean fields. If the conditional number distributions for the other detectors, given the outcome of the first detector, exhibit sufficiently narrow peaks around the values specified by the estimated phases, the mean field description is valid in a sin…
This paper discusses the effect of saturated absorption on the quantum features of a sub-Poissonian laser. It is shown that when both media (laser and absorbing) are saturated, the appearance of an additional element in the cavity does not lead to the demolition of the quantum properties (regular statistics of photons and quadrature squeezing) of laser radiation.
From the microscopic quantum Langevin equations (QLEs) we derive the effective semiconductor QLEs and the associated noise correlations which are valid at a low-injection level and in real devices. Applying the semiconductor QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula for the Fano factor of photons which gives the photon-number statistics as a function of the pump statistics and several parameters of LEDs. Key ingredients are non-radiative processes, carrier-number dependence of the radiative and non-radiative lifetimes, and multimodeness of LEDs. The formula i…
The speed of quantum random number generators is a major concern for practical quantum applications. However, the bit extraction process limits the final bit rate due to lack of comparably fast electronics. Here we introduce optical scattering as a method to perform optical bit extraction. Scattering is a probabilistic phenomenon and it increases the chaotic behaviour of coherent sources. As a result, it broadens the distribution of photon statistics and makes it super-Poissonian. We show that the raw signal of the sources with super-Poissonian distribution have better randomness compared to P…
Sub-Poissonian light generation in the non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q-functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behavior are obtained analytically by applying the classical tra…
A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in two-mode squeezed vacuum state generated in optical parametric amplifier. A quadrature component of the idler mode is measured in balanced homodyne detector and only those experimental runs where the absolute value of the measured quadrature is higher than certain threshold are accepted. If the threshold is large enough then the conditional output state of signal mode exhibits reduction of photon-number fluctuat…
Non-classical correlations in optical beams offer the unprecedented opportunity of surpassing conventional limits of sensitivity and resolution in optical measurements and imaging, especially but not only, when a low photon flux down to the single photons are measured. We review the principles of quantum imaging and sensing techniques which exploit sub-Poissonian photon statistics and non-classical photon number correlation, presenting some state-of-the-art achievements in the field. These quantum photonics protocols have the potential to trigger major steps in many applications, such as micro…
Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly-excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of …
We investigate the photon statistics of a single-photon source that operates under non-stationary conditions. The photons are emitted by shining a periodic sequence of laser pulses on single atoms falling randomly through a high-finesse optical cavity. Strong antibunching is found in the intensity correlation of the emitted light, demonstrating that a single atom emits photons one-by-one. However, the number of atoms interacting with the cavity follows a Poissonian statistics so that, on average, no sub-Poissonian photon statistics is obtained, unless the measurement is conditioned on the pres…
The optical interference constitutes a paramount resource in modern physics. At the scale of individual atoms and photons, it is a diverse concept that causes different coherent phenomena. We present the experimental characterization of both coherent and statistical properties of light emitted from ensembles of trapped ions increasing with a number of contributing phase-incoherent independent atomic particles ranging from a single to up to several hundreds. It conclusively demonstrates how super-Poissonian quantum statistics non-trivially arises purely from the finite number of indistinguishab…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the distribution of the number of excitations departs from the Poisson statistics according to combinations of stretched exponen…
We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission properties, power spectrum, the full counting statistics and the entanglement entropy of transmitted and reflected states of light. Our approach takes into account spatial parameters of an incident coherent pulse as well as waiting and counting times of a detector. We describe time evolution of the power spectrum as well as observe deviations from the Poissonian sta…
Interfacing light and matter at the quantum level is at the heart of modern atomic and optical physics and enables new quantum technologies involving the manipulation of single photons and atoms. A prototypical atom-light interface is electromagnetically induced transparency, in which quantum interference gives rise to hybrid states of photons and atoms called dark-state polaritons. We have observed individual dark-state polaritons as they propagate through an ultracold atomic gas involving Rydberg states. Strong long-range interactions between Rydberg atoms give rise to an effective interacti…
We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson-Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations, and obtain an exact analytical formula for the line shape and Mandel's Q parameter. The line shape exhibits well known behaviors, including motional narrowing when the stochastic modulation is fast, and power broad…
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) analytical formulas for the level spacing distribution function have been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P$\rightarrow$GUE, P$\rightarrow$GOE, and …
Lasers essentially consist of single-mode optical cavities containing two-level atoms with a supply of energy called the pump and a sink of energy, perhaps an optical detector. The latter converts the light energy into a sequence of electrical pulses corresponding to photo-detection events. It was predicted in 1984 on the basis of Quantum Optics and verified experimentally shortly thereafter that when the pump is non-fluctuating the emitted light does not fluctuate much. Precisely, this means that the variance of the number of photo-detection events observed over a sufficiently long period of …
In the present work the model of a single-atom laser generating in the regime when incoherent pumping rate coincides with the cavity decay rate is theoretically investigated. Using the stationary equation for the phase averaged Glauber P function the analytical expressions for mean number of photons and its dispersion are obtained. In the limiting case of the strong-coupling regime the exact expression for the photon number distribution function is found. Obtained results describe the sub-Poissonian photon statistics and show an increase in mean number of photons to non-zero value when the pum…
Motivated by the hyperfine interaction of electron spins with surrounding nuclei, we investigate systems of central spins coupled to a bath of noninteracting spins in the framework of random matrix theory. With increasing number of central spins a transition from Poissonian statistics to the Gaussian orthogonal ensemble occurs which can be described by a generalized Brody distribution. These observations are unaltered upon applying an external magnetic field. In the transition region, the classical counterparts of the models studied have mixed phase space.
A complete characterization of quantum fluctuations in many-body systems is accessible through the full counting statistics. We present an exact computation of statistical properties of light in a basic model of light-matter interaction: a multimode photonic field coupled to a single two-level emitter. We mostly consider an initial coherent state in a given mode and demonstrate how the original Poissonian statistics gets modified because of quantum many-body scattering effects leading to non-Poissonian distributions. We argue that measuring this statistics in a simple quantum optical setup pro…
We propose to use the resonant enhancement of the parametric instability in an optomechanical system of two optical modes coupled to a mechanical oscillator to prepare mechanical states with sub-Poissonian phonon statistics. Strong single photon coupling is not required. The requirements regarding sideband resolution, circulating cavity power and environmental temperature are in reach with state of the art parameters of optomechanical crystals. Phonon antibunching can be verfied in a Hanburry-Brown-Twiss measurement on the output field of the optomechanical cavity.
The nonclassicality of primordial gravitational waves (PGWs) is characterized in terms of sub-Poissonian graviton statistics. The sub-Poissonian statistics are realized when quantum states are squeezed coherent states. In the presence of matter fields, the Universe experiences the squeezed coherent state during inflation. The condition to realize the sub-Poissonian graviton statistics is translated into the frequency range of gravitational waves. If the initial state is the Bunch-Davies vacuum, there is another necessary condition between phases of squeezing and coherent parameters. Here, we e…
The arithmetic triangular billiards are classically chaotic but have Poissonian energy level statistics, in ostensible violation of the BGS conjecture. We show that the length spectra of their periodic orbits divides into subspectra differing by the parity of the number of reflections from the triangle sides; in the quantum treatment that parity defines the reflection phase of the orbit contribution to the Gutzwiller formula for the energy level density. We apply these results to all 85 arithmetic triangles and establish the boundary conditions under which the quantum billiard is \textquotedbl…
High-flux sub-Poissonian twin fields generation from warm atomic vapor
FAMU–FSU College of Engineering, Florida State University（佛罗里达州立大学 FAMU-FSU 工程学院）；University of Tennessee, Chattanooga（田纳西大学查塔努加分校）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
We propose and experimentally demonstrate a device for generating light with arbitrary classical photon-number distribution. We use programmable acousto-optical modulation to control the intensity of light within the dynamic range of more than 30 dB and inter-level transitions faster than 500 ns. We propose a universal method that allows high-fidelity generation of user-defined photon statistics. Extremely high precision <0.001 can be reached for lower photon numbers, and faithful tail behavior can be reached for very high photon numbers. We demonstrate arbitrary statistics generation for up t…
When laser diodes are driven by high-impedance electrical sources the variance of the number of photo-detection events counted over large time durations is less than the average number of events (sub-Poissonian light). The paper presents a Monte Carlo simulation that keeps track of each level occupancy (0 or 1) in the conduction and valence bands, and of the number of light quanta in the optical cavity. When there is good electron-lattice thermal contact the electron and hole temperatures remain equal to that of the lattice. In that case, elementary laser-diode noise theory results are accurat…
As the energy relaxation time of superconducting qubits steadily improves, non-equilibrium quasiparticle excitations above the superconducting gap emerge as an increasingly relevant limit for qubit coherence. We measure fluctuations in the number of quasiparticle excitations by continuously monitoring the spontaneous quantum jumps between the states of a fluxonium qubit, in conditions where relaxation is dominated by quasiparticle loss. Resolution on the scale of a single quasiparticle is obtained by performing quantum non-demolition projective measurements within a time interval much shorter …
Developments in quantum technologies lead to new applications that require radiation sources with specific photon statistics. A widely used Poissonian statistics are easily produced by lasers; however, some applications require super- or sub-Poissonian statistics. Statistical properties of a light source are characterized by the second-order coherence function g^(2)(0). This function distinguishes stimulated radiation of lasers with g^(2)(0)=1 from light of other sources. For example, g^(2)(0)=2 for black-body radiation, and g^(2)(0)=0 for single-photon emission. One of the applications requir…
Single-shot qubit readout typically combines high readout contrast with long-lived readout signals, leading to large signal-to-noise ratios and high readout fidelities. In recent years, it has been demonstrated that both readout contrast and readout signal lifetime, and thus the signal-to-noise ratio, can be enhanced by forcing the qubit state to transition through intermediate states. In this work, we demonstrate that the sub-Poissonian relaxation statistics introduced by intermediate states can reduce the single-shot readout error rate by orders of magnitude even when there is no increase in…
Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）
We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the classical system and its signatures in the corresponding quantum dynamics. By introducing a symmetry-breaking term we tune the classical dynamics from integrable to strongly chaotic which we demonstrate by calculating Poincaré sections and Lyapunov exponents. The corresponding quantum system features level statistics that change from Poissonian in the integrable t…
