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 time is much smaller than the average number of events. Light having that property is said to be ``sub-Poissonian''. The theory presented rests on the concept introduced by Einstein around 1905, asserting that matter may exchange energy with a wave at angular frequency $ω$ only by multiples of $\hbarω$. The optical field energy may only vary by integral multiples of $\hbarω$ as a result of matter quantization and conservation of energy. A number of important results relating to isolated optical cavities containing two-level atoms are first established on the basis of the laws of Statistical Mechanics. Next, the laser system with a pump and an absorber of radiation is treated. The expression of the photo-current spectral density found in that manner coincides with the Quantum Optics result. The concepts employed in this paper are intuitive and the algebra is elementary. The paper supplements a previous OQE tutorial paper in establishing a connection between the theory of laser noise and Statistical Mechanics.
In this study, we demonstrate the possibility of the implementation of universal Gaussian computation on a two-node cluster state ensemble. We consider the phase-locked sub-Poissonian lasers, which radiate the bright light with squeezed quadrature, as the resource to generate these states.
We consider sub-Poissonian single-mode laser with external synchronization and analyze its applicability to the problems of quantum information. Using Heisenberg-Langevin theory we calculate the quadrature variances of the field emitted by this laser. It is shown that such systems can demonstrate strong quadrature squeezing. Taking into account that the emitted field is temporally multi-mode the application of such sources to multichannel quantum teleportation and dense coding protocols is discussed.
Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. The purpose of this paper is to show that, as long as the laser-detector system is strictly stationary, quantization of the optical field is not required to explain such phenomena. The theory presented here is semi-classical, yet exact. Previous theories considering excited-state atoms regularly-injected in resonators, on the other hand, do require in principle light quantizat…
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.
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…
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…
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…
We consider three- and four-level atomic lasers that are either incoherently (unidirectionally) or coherently (bidirectionally) pumped, the single-mode cavity being resonant with the laser transition. The intra-cavity Fano factor and the photo-current spectral density are evaluated on the basis of rate equations. According to that approach, fluctuations are caused by jumps in active and detecting atoms. The algebra is considerably simpler than the one required by Quantum-Optics treatments. Whenever a comparison can be made, the expressions obtained coincide. The conditions under which the outp…
This article is the shorten version of quant-phys/0610106 with a supplemented theory and new results concerning a single-electron laser driven by a constant-potentiel battery. "Quiet (or sub-Poissonian) oscillators generate a number of dissipation events whose variance is less than the mean. It was shown in 1984 by Golubev and Sokolov that lasers driven by regular pumps are quiet in that sense. We consider in the present paper two oscillators that should exhibit in principle the same property. First, a reflex klystron, a vacuum tube operating in the microwave range of frequency. Second a laser…
The statistics of the light emitted by two-level lasers is evaluated on the basis of generalized rate equations. According to that approach, all fluctuations are interpreted as being caused by the jumps that occur in active and detecting atoms. The intra-cavity Fano factor and the photo-current spectral density are obtained analytically for Poissonian and quiet pumps. The algebra is simple and the formulas hold for small as well as large pumping rates. Lasers exhibit excess noise at low pumping levels.
Here we demonstrate that photocurrent noise reduction below the standard quantum limit and modal anticorrelation can arise in two mode coupled two-VECSEL system with common pump. This effect occurs due to correlated loss of laser modes. It is possible to suppress noise below the standard quantum limit even for Poissonian coherent pumping, whereas the regularity of the pump can be harmful for non-classicality.
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.
We generate nonclassical conditional states by exploiting the quantum correlations of multi-mode twin-beam states endowed with a sizeable number of photons. A strong relation between the sub-shot-noise correlations exhibited by twin beams and the sub-Poissonian character of the conditional states is experimentally revealed. It determines optimal conditions for sub-Poissonian light generation.
We propose an implementation of a source of strongly sub-Poissonian light in a system consisting of a quantum dot coupled to both modes of a lossy bimodal optical cavity. When one mode of the cavity is resonantly driven with coherent light, the system will act as an efficient photon number filter, and the transmitted light will have a strongly sub-Poissonian character. In addition to numerical simulations demonstrating this effect, we present a physical explanation of the underlying mechanism. In particular, we show that the effect results from an interference between the coherent light transm…
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 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.
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-Poiss…
Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of…
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…
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…
We present a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to g…
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…
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…
We report the first experimental demonstration of conditional preparation of a non classical state of light in the continuous variable regime. Starting from a non degenerate OPO which generates above threshold quantum intensity correlated signal and idler "twin beams", we keep the recorded values of the signal intensity only when the idler falls inside a band of values narrower than its standard deviation. By this very simple technique, we generate a sub-Poissonian state 4.4dB below shot noise from twin beams exhibiting 7.5dB of noise reduction in the intensity difference.
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…
A method is proposed to produce atomic ensembles with sub-Poissonian atom number distributions. The method consists of removing the excess atoms using the interatomic interactions induced by Rydberg dressing. The selective removal of atoms occurs via spontaneous decay into untrapped states using an electromagnetically induced transparency scheme. Ensembles with the desired number of atoms can be produced almost deterministically. Numerical simulations predict a strong reduction of the atom number fluctuations, with the variance twenty times less than the Poisson noise level (the predicted Fano…
In a direct detection scheme we observed 7.8 dB of twin-beam squeezing for multi-mode two-color squeezed vacuum generated via parametric down conversion. Applying post-selection, we conditionally prepared a sub-Poissonian state of light containing $6.3\cdot10^5$ photons per pulse on the average with the Fano factor $0.63\pm0.01$. The scheme can be considered as the heralded preparation of pulses with the mean energy varying between tens and hundreds of fJ and the uncertainty considerably below the shot-noise level. Such pulses can be used in metrology (for instance, for radiometers calibration…
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 consider ultracold atoms in a far detuned optical lattice orientated across a high-Q optical resonator. Applying an external driving laser to the atoms, which is red detuned from the cavity mode by one vibrational quantum, induces cavity-enhanced sideband cooling. For a dense and cold enough atomic ensemble we predict an oscillation threshold for optical Raman sideband lasing concurrent with coherent matter-wave amplification. Above this oscillation threshold photons and atoms in the lowest band are dominantly created pairwise via stimulated emission with a strong suppression of competing s…
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical fields for many thermal, coherent or squeezed states. Here, we use time-domain optical homodyne tomography for the quantum state recognition and reconstruction of the femtosecond optical field from a nonequilibrium superradiant coherent electron-hole state formed in a semiconductor laser structure. We observe severe deviations from the Poissonian statistics of…
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 …
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…
A theory for the photon statistics of a random laser is presented. Noise is described by Langevin operators, where both fluctuations of the electromagnetic field and of the medium are included. The theory is valid for all lasers with small outcoupling when the laser cavity is large compared to the wavelength of the radiation. The theory is applied to a chaotic laser cavity with a small opening. It is known that a large number of modes can be above threshold simultaneously in such a cavity. It is shown the amount of fluctuations is increased compared to the Poissonian value by an amount that de…
Despite the enormous technological interest in micro and nanolasers, surprisingly, no class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In class-B lasers $-$applicable for most solid-state lasers at room temperature$-$, the macroscopic polarization decay rate is larger than the cavity damping rate which, in turn, exceeds the upper level population decay rate. Here we carry out a density-matrix theoretical approach for generic class-B lasers, and provide closed equations for the photonic and ato…
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.
Advances in quantum physics and computational complexity threaten the security of present day cryptographic systems and have driven the development of quantum key distribution (QKD). Entangled quantum key distribution (EQKD) is a secure protocol that is based on fundamental quantum mechanics and is not vulnerable to these threats. The primary figure of merit for QKD systems is ability to generate secret bits. However, to date, methods that have been developed to simulate the secret bit rate generation for EQKD systems have been limited by techniques that do not provide a complete description o…
We calculate the emission spectra, the Glauber $g^{(2)}$ function, and the entanglement of formation for a few two-level emitters coupled to a single cavity mode and subject to an external laser-excitation. To evaluate these quantities we couple the system to environmental degrees of freedom which leads to dissipative dynamics. Because of the periodic time-dependence of the system Hamiltonian, the coefficients of the (Markovian) master equation are constant if Floquet states are used as the computational basis. Studying the emission spectra we show that the dynamic Stark effect, i.e., the shif…
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）
Sub-Poisson field with much reduced fluctuations in a cavity can boost quantum precision measurements via cavity-enhanced light-matter interactions. Strong coupling between an atom and a cavity mode has been utilized to generate highly sub-Poisson fields. However, a macroscopic number of optical intracavity photons with more than 3dB variance reduction in a setting of laser has not been possible. Here, we report sub-Poisson field lasing in a microlaser operating with hundreds of atoms with well-regulated atom-cavity coupling and interaction time. Its photon-number variance was 4dB below the st…
The concept of an acoustical analog of the optical laser has been developed recently both in theoretical as well as experimental works. We discuss here a model of a coherent phonon generator with a direct signature of quantum properties of the sound vibrations. The considered setup is made of a laser driven quantum dot (QD) embedded in an acoustical nanocavity. The system's dynamics is solved for a single phonon mode in the steady-state and in the strong QD-phonon coupling regime beyond the secular approximation. We demonstrate that the phonon statistics exhibits quantum features, i.e. sub-Poi…
In the paper a model of a single-atom laser with incoherent pumping is theoretically investigated. In the stationary case, a linear homogeneous differential equation for the phase-averaged Hussimi Q-function is derived from the equation for the density operator of the system. In the regime when the coupling of the field with an atom is many times stronger than the coupling of the field with the reservoir providing its decay, an asymptotic solution of this equation is found. This solution makes it possible to describe some statistical features of a single-atom laser, in particular the weak sub-…
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…
Although conventional lasers operate with a large number of intracavity atoms, the lasing properties of a single atom in a resonant cavity have been theoretically investigated for more than a decade. Here we report the experimental realization of such a one-atom laser operated in a regime of strong coupling. Our experiment exploits recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. In this regime the observed characteristics of the atom-cavity system are qual…
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 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.
We have simulated the time evolution of the photon number distribution in a semiconductor quantum dot-microcavity system driven by chirped laser pulses and compare with unchirped results. When phonon interactions with the dot are disregarded - thus corresponding to the limit of atomic cavity systems - chirped pulses generate photon number distributions that change their shape drastically in the course of time. Phonons have a strong and qualitative impact on the photon statistics. The asymmetry between phonon absorption and emission destroys the symmetry of the photon distributions obtained for…
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…
We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance $-14$ dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of $\pm 8$ atoms on an ensemble of some $10^3$ atoms in a one-dimensional trap. The method is ver…
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…
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…
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 …
