sub-Poissonian Photon Statistics Research Articles

The Mth nonlinear coherent states

Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times nˆM on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.

Optimized laser models with Heisenberg-limited coherence and sub-Poissonian beam photon statistics

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [1]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In Ref. [2], we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this Paper, we provide details of the calculations in Ref. [2], and introduce three new families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, $p$, with $p=4$ corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of $p$, where for $p>3$, each family of models exhibits Heisenberg-limited beam coherence, while for $p<3$, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulae for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact $p\approx4.15$, not $p=4$.

The Quantum Features of Correlated Photons with the Effect of Phase Fluctuation

We theoretically investigate the effect of phase fluctuations on correlated photons resulting from nondegenerate three-level atoms under the cavity radiation. The photon statistics, photon number correlation, and entanglement properties of the system have been calculated employing the dynamical equation of the system. It is shown that, for the sub-Poissonian photon statistics, the degree of correlation increases with the atomic pumping rate, and the entanglement varies with phase fluctuations, rather than with the atomic pumping rate. The proposed system is well suitable for the quantum information processing.

Two-mode photon added Schrödinger cat states: nonclassicality and entanglement

The concept of a photon added two-mode Schrödinger cat state in which both modes are independent is introduced, and their nonclassical properties and entanglement are studied. The introduced states emerge as eigenstates of f 1 f 2 a 1 a 2 , where f 1 , f 2 are nonlinear functions of the number operator, and a 1 , a 2 are annihilation operators. We study the evolution of these states under canonical transformation using the parity operator for the case of standard coherent states of the harmonic oscillator. The nonclassical properties of these states are evaluated especially by considering sub-Poissonian photon statistics and photon number distribution. Interestingly, the addition of photons leads to shifting the region in which photon number distribution shows oscillatory behavior. In addition, the entanglement of introduced states is quantitatively analyzed using concurrence. We observe that the state approaches maximum entanglement more rapidly after the addition of photons.

Q Function for a Single-Atom Laser Operating in the “Classical” Regime

A model of single-atom laser with incoherent pumping is investigated theoretically. In the stationary case, a linear homogeneous differential equation for the phase-averaged Husimi Q function is derived from the equation for the density operator of the system. In the regime in which the coupling of the cavity mode with an atom is much stronger than the coupling of the mode with the reservoir ensuring its damping, the asymptotic solution is obtained to this equation. This solution makes it possible to describe some statistical features of the single-atom laser (in particular, the weak sub-Poissonian photon statistics).

The “Squeeze Laser”

The level of quantum noise in measurements is bounded from below by the Heisenberg uncertainty principle, but it can be unequally distributed between two non-commuting observables — it can be “squeezed”. Since 2019, all gravitational-wave observatories have been using squeezed light for increasing the astronomical reach. Squeezed laser light is efficiently produced by degenerate parametric down-conversion in a nonlinear crystal located inside an optical resonator. A spontaneously generated initial pair of indistinguishable photons is amplified to a squeezed vacuum state. Overlapped with bright coherent light, the photo electric measurement shows a sub-Poissonian photon statistics. Squeezed states have ample applications in nonlocal quantum sensing, device-independent quantum key distribution, and quantum computing. Here, we present our continuous-wave 1550 nm ‘squeeze laser’ with a footprint of 80 cm × 80 cm. The well-defined output beam has an interference contrast of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gtrsim 99\%$</tex-math></inline-formula> with an overlapped 10 mW beam being in an almost perfect TEM00 mode. The interference result shows 13 dB squeezing of the photon shot noise in balanced detection.

A comparison between higher-order nonclassicalities of superposition engineered coherent and thermal states

We consider an experimentally obtainable superposition (SUP) operator, defined by using a generalized superposition of products of field annihilation (a) and creation (a†) operators of the type A = saa† + ta†a with s2 + t2 = 1. We apply this SUP operator on coherent and thermal quantum states, and the states thus produced are referred to as SUP-operated coherent state (SOCS) and SUP-operated thermal state (SOTS), respectively. In the present work, we report a comparative study between the higher-order nonclassical properties of SOCS and SOTS. The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order anti-bunching, higher-order sub-Poissonian photon statistics, higher-order squeezing, Agarwal–Tara parameter, Klyshko’s condition). The existence of higher-order nonclassicalities in SOCS and SOTS have been investigated for the first time. In view of possible experimental verification of the proposed scheme, we present exact calculations to reveal the effect of non-unit quantum efficiency of quantum detector on higher-order nonclassicalities.

Optical feedback-induced dynamics and nonclassical photon statistics of semiconductor microcavity laser

We study a coherently driven semiconductor laser cavity containing a single quantum dot(QD) (as gain medium) with optical feedback under Markovian approximation. We have obtained coupled operator equations for the model Hamiltonian using standard input-output formalism of cavity-QED and have found that these equations do not have any finite steady state solutions. We have also used an exact numerical framework based on Matlab platform qotoolbox, to compute the temporal dynamics of the mean excitation number of laser cavity mode under high feedback coupling regime. We have further studied the photon correlations of both the cavity mode as well as external feedback mode to feedback identify the laser parameters and coupling strength that give the nonclassical sub-Poissonian photon statistics. This work is useful for coherent control of photon statistics and photon correlations in the semiconductor laser with optical feedback.

Non-classicalities exhibited by the superposition of Schrödinger’s cat state with the vacuum of the optical field

Superposition of two coherent states, the Schrodinger’s cat state, can exhibit different nonclassical properties having foundational applications in quantum information processing. We consider the ‘superposition of Schrodinger’s cat state with the vacuum state (SCVS)’ of the optical field. We discuss different witness of nonclassicality properties such as lower- and higher-order squeezing (viz., squeezing, Hong & Mandel’s fourth-order squeezing, amplitude-squared squeezing) and sub-Poissonian photon statistics. Further, we discuss the negativity of the Wigner function of SCVS indicating the nonclassicality of the state under investigation. We find that the vacuum state contribution in SCVS exhibits different nonclassicalities under some conditions stronger where the nonclassicalities exhibited by the state without vacuum state contribution are weaker.

Effects of postselected von Neumann measurement on nonclassicality of single-photon-added coherent state

The effects of von Neumann postselected measurement on nonclassicality of single-photon-added coherent state (SPACS) are studied. Explicit expressions and analytical results for various field properties of SPACS such as the photon number distribution, the Mandel Q_{m} factor and the squeezing parameter of field quadrature after postselected von Neumann measurement are investigated. The results showed that the nonclassicality of SPACS after measurement changed dramatically than initial state. The measurement let SPACS possess more strong sub-Poissonian photon statistics in some definite coupling strength regimes and large weak values which accompanied by low postselection probabilities.

Realization of Nonclassical Effects of Light and Total Noise in Coherent Anti-Stokes Raman and Hyper-Raman Scatterings Up to the First-Order Hamiltonian Interaction

In this paper, we give an overview of nonclassical effects, such as squeezing and sub-Poissonian states, of an optical field in coherent anti-Stokes Raman scattering and coherent anti-Stokes hyper-Raman scattering under the short time scale. We establish the coupled Heisenberg equations of motion of quadrature operators in terms of real and imaginary parts. We investigate the photon statistics of the pump mode in these processes and find that they are sub-Poissonian in nature. We demonstrate that squeezing and sub-Poissonian photon statistics are greater in coherent anti-Stokes hyper-Raman scattering (CAHRS) than in coherent anti-Stokes Raman scattering (CARS). The effect of the sub- Poissonian nature of an optical field in terms of total noise is also incorporated. We show that the depth of nonclassicality directly depends on the amount of total noise present in the system. This suggests that the more squeezed the state, the greater its total noise in the system.

General superposition states associated to the rotational and inversion symmetries in the phase space

The general quantum superposition states containing the irreducible representation of the n-dimensional groups associated to the rotational symmetry of the n-sided regular polygon i.e. the cyclic group (Cn) and the rotational and inversion symmetries of the polygon, i.e. the dihedral group (Dn) are defined and studied. It is shown that the resulting states form an n-dimensional orthogonal set of states which can lead to the finite representation of specific systems. The correspondence between the symmetric states and the renormalized states, resulting from the selective erasure of photon numbers from an arbitrary, noninvariant initial state, is also established. As an example, the general cyclic Gaussian states are presented. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed. Also, their use in the calculation of physical quantities as the entanglement in a bipartite system is discussed.

Two Mode Superposition of Truncated Coherent States: Entanglement and Non-Classical Properties

In this paper we consider two-mode superposition of truncated coherent states. Using this we construct quasi-Bell states and investigate the non-classical features of two-mode superposed truncated coherent states such as oscillatory and sub-Poissonian photon statistics and violation of Cauchy-Schwartz inequality.

Nonclassical properties of two families of q-coherent states in the Fock representation space of q-oscillator algebra

We clarify that the q-generalization of the simple harmonic oscillator to the Arik–Coon one leads us to obtain two different families of q-coherent states in a Fock representation space of the system. They are eigenstates of unbounded and bounded annihilation operators associated with the Arik–Coon q-oscillator. The first family satisfies the resolution of identity condition on all the complex plane and the second one on a disc in radius $$1/\sqrt{1-q}$$ . Their positive definite q-measures are different, but in the limit $$q\rightarrow 1$$ both of them convert to the measure of well-known coherent states for the simple harmonic oscillator. The first and second families of the q-coherent states are also deformed eigenstates of the bounded and unbounded annihilation operators, respectively. Thus, it is possible to study the statistical properties of both q-coherent states via both bounded and unbounded operators. The nonclassical behaviours of interest in this article are signal-to-quantum noise ratio, sub-Poissonian photon statistics, photon antibunching, quadrature squeezing effect and bipartite entanglement for the two families of the q-coherent states, as well as Hillery-type higher-order squeezing for their corresponding photon-added states.

Sub-Poissonian single-emitter laser: Coherent pump vs incoherent

We theoretically investigate the properties of a single-emitter laser with coherent pump: two-level atom interacting with a single damping cavity mode which is resonantly excited by a coherent field. With the help of numerical simulation of the master equation we show that such pumping mechanism is more preferably than incoherent pump for achieving of sub-Poissonian photon statistics.

Entangled squeezed coherent states: generation and their nonclassical properties in comparison with other entangled states

In this paper, at first we consider special type of entangled states named “entangled squeezed coherent states” by using squeezed coherent states. Next, we study the entanglement characteristics of these entangled states by evaluating concurrence. In the continuation, we investigate some of their nonclassical properties such as quantum statistics which contained sub-Poissonian photon statistics and the oscillatory photon number distribution, second-order correlation function and quadrature squeezing for different squeezing values of two modes. In addition, we compare the results of the “entangled squeezed coherent states” with those of the common entangled states such as “entangled coherent states”, “entangled squeezed vacuum states” and “entangled squeezed one-photon states”. Finally, using the proposed theoretical scheme in the previous works, we will generate the entangled squeezed coherent states with different initial conditions. In this scheme, a $$\Lambda$$-type three-level atom interacts with the two-mode quantized field in the presence of two strong classical fields.

Quantum light from a metal nanoparticle

Single-photon sources are subjected to a fundamental limitation in the speed of operation dictated by the spontaneous emission rate of quantum emitters (QEs). The current paradigm of the rate acceleration suggests coupling of a QE to a metal nanostructure, in particular, a metal nanoparticle (MNP). Here, we demonstrate that, in contrast to this approach, a MNP itself can behave as a quantum emitter. We determine both the first- and second-order correlation functions of light spontaneously emitted by a MNP strongly coupled to a QE and show that this light should exhibit sub-Poissonian photon statistics and perfect photon antibunching. This discovery opens a prospect to single-photon sources with unprecedented generation rates up to 100 THz.

Observation of scalable sub-Poissonian-field lasing in a microlaser

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 3 dB variance reduction 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 4 dB below the standard quantum limit while the intracavity mean photon number scalable up to 600. The highly sub-Poisson photon statistics were not deteriorated by simultaneous interaction of a large number of atoms. Our finding suggests an effective pathway to widely scalable near-Fock-state lasing at the macroscopic scale.

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko’s, Vogel’s, and Agarwal–Tara’s criteria as well as the criteria of lower- and higher-order antibunching, sub-Poissonian photon statistics and squeezing. In addition, phase distribution function and quantum phase fluctuation have been studied. These properties are examined for various combinations of number of photon addition and/or subtraction and Fock parameter. The examination has revealed that photon addition generally improves nonclassicality, and this advantage enhances for the large (small) values of displacement parameter using photon subtraction (Fock parameter). The higher-order sub-Poissonian photon statistics is only observed for the odd orders. In general, higher-order nonclassicality criteria are found to detect nonclassicality even in the cases when corresponding lower-order criteria failed to do so. Photon subtraction is observed to induce squeezing, but only large number of photon addition can be used to probe squeezing for large values of displacement parameter. Further, photon subtraction is found to alter the phase properties more than photon addition, while Fock parameter has an opposite effect of the photon addition/subtraction. Finally, nonclassicality and non-Gaussianity is also established using Q function.

A Molecule‐Based Single‐Photon Source Applied in Quantum Radiometry

AbstractSingle‐photon sources (SPSs) based on quantum emitters hold promise in quantum radiometry as metrology standard for photon fluxes at the low light level. Ideally this requires control over the photon flux in a wide dynamic range, sub‐Poissonian photon statistics, and narrow‐band emission spectrum. In this work, a monochromatic SPS based on an organic dye molecule is presented, whose photon flux is traceably measured to be adjustable between 144 000 and 1320 000 photons per second at a wavelength of (785.6 ± 0.1) nm, corresponding to an optical radiant flux between 36.5 and 334 fW. The high purity of the single‐photon stream is verified, with a second‐order autocorrelation function at zero time delay below 0.1 throughout the whole range. Such molecule‐based SPS is hence used for the calibration of a single‐photon avalanche detector against a low‐noise analog photodiode traceable to the primary standard for optical radiant flux (i.e., the cryogenic radiometer). Due to the narrow bandwidth of the source, corrections to the detector efficiency arising from the spectral power distribution are negligible. With this major advantage, the developed device may finally realize a low‐photon‐flux standard source for quantum radiometry.