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We consider a non-relativistic particle in a one-dimensional box with all possible quantum boundary conditions that make the kinetic-energy operator self-adjoint. We determine the Wigner functions of the corresponding eigenfunctions and analyze in detail their classical limit, governed by their behavior in the high-energy regime. We show that the quantum boundary conditions split into two classes: all local and regular boundary conditions collapse to the same classical boundary condition, while a dependence on singular non-local boundary conditions persists in the classical limit. [ABSTRACT FROM AUTHOR]

The spin-j Einstein–Podolsky–Rosen–Bohm experiment is examined in the context of how the quantum theoretic probability distributions for the spin measurement outcomes are to be coarse-grained in order to yield classical behavior in the j → ∞ limit. A coarse-graining protocol is found that can be viewed as imperfection either in the detection process or in state preparation process, and is in both viewpoints minimal in the sense that it is no more than what is needed to wash out the execess quantum correlations. In the first point of view the coarse-grained distribution can be written in terms of a Bell-type factorizable hidden variable model wherein the conditional distributions for the spin measurement outcome of each particle is not just nonnegative but actually attains the value zero for some choice of measurement axis. In the second point of view the coarse-grained distribution arises from a spin state whose Wigner function is not just nonnegative but actually attains the value zero for some spin orientations. That such a remarkable dual interpretation should be possible suggests that this type of complementary coarse graining is an intrinsic aspect of how classicality is obtained in the large j limit, but this conclusion remains speculative. [ABSTRACT FROM AUTHOR]

The quantum Rabi model (QRM) is used to describe the light-matter interaction at the quantum level in Cavity Quantum Electrodynamics (Cavity QED). It consists of a two-level system (atom or qubit) coupled to a single-mode quantum field. Introducing an atom into a cavity alters the electromagnetic mode configuration within it. In the realm of Cavity QED, a notable consequence of this alteration is the emergence of a gauge-dependent diamagnetic term referred to as the A 2 contribution. In this study, we comparatively analyze the behaviors of the QRM and the influence of the A 2 term in the light-matter quantum Hamiltonian by examining the energy spectrum properties in the strong-coupling regime. We then investigate the ground state of the system, measuring its nonclassical properties via the Wigner distribution function for different photon number distributions in Fock space. Finally, we calculate the quantum entanglement in the ground state using the Von Neumann entropy. Our findings reveal that the A 2 term and the number of cavity Fock states, N, significantly impact the amount of the quantum entanglement, highlighting their pivotal role. [ABSTRACT FROM AUTHOR]

A nonseparable wave-like integro-differential equation for the time evolution of the Wigner distribution function in phase space is educed from the corresponding separable kinetic equation. By employing the quantum hydrodynamical description, a non-local evolution wave equation is also derived by synthesizing the Hamilton-Jacobi equation with that of continuity, which predicts the generation of nonlocal and quadrupole quantum phenomena in the propagation of the spatial probability density. [ABSTRACT FROM AUTHOR]

The heart of the light field theory at finite temperatures is the introduce of a thermal vacuum state, which is also the basis for studying the statistical properties of quantum light fields. Based on Takahashi and Umezawa's thermal chaotic field dynamics theory (TFD), this paper introduces a " fictitious mode" to represent the degrees of freedom of the thermal environment, then the thermal vacuum of the displaced thermal state (DTS) is proposed and constructed by the integration within an ordered product (IWOP) in the extended space, and we obtained the expected value of the photon number, fluctuation, second-order coherence, Wigner function. Finally, it is found that the photon number of the system is decreased at a rate of κ t due to the interaction of the DTS with the surrounding thermal environment by calculating the photon number diffusion. [ABSTRACT FROM AUTHOR]

Many non-classicality indicators are used to measure the quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced regarding the amount of Wigner distribution function's negativities and interferences in phase space quantum mechanics, respectively. Kenfack’s non-classicality indicator is used for cases just in the Wigner representation, whereas Sadeghi’s non-classicality indicator is effectively, applied for some real distribution functions. In this paper, we investigate these non-classicality indicators for the entangled photon number states in the Wigner, Husimi, and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits to measure entanglement with respect to Kenfack's indicator. For the two-level entangled state, we also show a correspondence between Sadeghi's non-classicality indicator and the Von Neumann entropy. It is also shown that for the superposition of the squeezed number state and ground number state, the squeezing parameter affects the entanglement feature and Sadeghi's non-classicality indicator increases with the increase of the squeezing parameter.

We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function g(2)(0), Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, an investigation on the two-photon quantum Rabi model at the critical coupling strength as a function of a control parameter δ ∈ 0 , 1 is treated. This control parameter is introduced to interpolate between the discrete and continuous spectrum regimes. Based on the proposed model, the theoretical effective hamiltonian in the optical phase-space representation is derived by using an appropriate unitary transformation. A numerical treatment is used to better explore the obtained effective hamiltonian. We have discussed the special feature, spectral collapse, as a function of the control parameter δ at the critical coupling strength. Also, the mean photon number in the ground-state as a function of this control parameter is studied. At the last, we have used Wigner function to follow the negativity of the ground-state of the system in our proposal. [ABSTRACT FROM AUTHOR]

Covariant integral quantization with rotational SO (3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO (3) . This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform. [ABSTRACT FROM AUTHOR]

In this paper, a quantitative investigation of the non-classical and quantum non-Gaussian characters of the photon-subtracted displaced Fock state | ψ 〉 = a k D (α) | n 〉 , where k is the number of photons subtracted and n is Fock parameter, is performed by using a collection of measures like Wigner logarithmic negativity, linear entropy potential, skew information-based measure, and relative entropy of quantum non-Gaussianity. It is noticed that the number of photons subtracted (k) changes the nonclassicality and quantum non-Gaussianity in a significant amount in the regime of small values of the displacement parameter, whereas the Fock parameter (n) presents a notable change in the large regime of the displacement parameter. In this respect, the role of the Fock parameter is found to be stronger as compared to the photon subtraction number. Finally, the Wigner function dynamics considering the effects of photon loss channel is used to show that the Wigner negativity can only be detected by highly efficient detectors. [ABSTRACT FROM AUTHOR]

We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions. [ABSTRACT FROM AUTHOR]

In this article, we study the phase-space distribution of the quantum state as a framework to describe the different properties of quantum systems in continuous-variable systems. The natural approach to quantum systems is given the Gaussian Wigner representation, to unify the description of bosonic and fermionic quantum states, we study the structure of the Kahler space geometry as the geometry generated by three forms under the agreement conditions depended on the nature of the state bosonic or fermionic. Multimode light is studied, and we established that the Fock space vacuum corresponds to a certain homogeneous Gaussian state. [ABSTRACT FROM AUTHOR]

The problem of transferring the state of even coherent states from a low to a high frequency is considered theoretically using a periodically-poled nonlinear crystal. The Wigner quasi-probability distribution function is used to study the parallel realization of two nonlinear processes: parametric and the generation sum frequencies. [ABSTRACT FROM AUTHOR]

This paper investigates the behaviour of the quantum correlations for an accelerated two-qubit system during its interaction with a classical stochastic field, utilizing the Wigner function and concurrence. The non-classical behaviour is indicated by negative values of the Wigner function, while the degree of entanglement is demonstrated by the concurrence. To consider acceleration and interaction with a common or independent environment, we discard the single-mode approximation and utilize the Unruh construction of the quantum field mode in our analysis. Our results suggest that coherence suppression is caused by the acceleration effect, noise strength, and noise frequency. Through an examination of quantum concurrence, this study analyses the level of quantum entanglement that corresponds positively with negative values of the Wigner function. The findings indicate that coherence degradation in the initial system is reduced when observers interact independently with their environments, as opposed to interacting with a common environment. Additionally, the acceleration of both observers has an impact on coherence reduction. During system evolution, the Wigner function displays collapse and reappearance behaviour, while quantum entanglement undergoes local collapse and revival phenomena. Notably, common noise situations exhibit more rapid variation in both the Wigner function and entanglement compared to independent noise configurations. [ABSTRACT FROM AUTHOR]

Standard relativistic hydrodynamics has been successful in describing the properties of the strongly interacting matter produced in the heavy-ion collision experiments. Recently, there has been a significant theoretical advancement in this field to explain spin polarization of hadrons emitted in these processes. Although current models have successfully explained some of the experimental data based on the coupling between spin polarization and vorticity of the medium, they still lack a clear understanding of the differential measurements. This is commonly interpreted as an indication that the spin needs to be treated as an independent degree of freedom whose dynamics is not entirely bound to flow circulation. In particular, if the spin is a macroscopic property of the system, in equilibrium its dynamics should follow hydrodynamic laws. Here, we develop a framework of relativistic hydrodynamics which includes spin degrees of freedom from the quantum kinetic theory for Dirac fermions and use it for modeling the dynamics of matter. Following experimental observations, we assume that the polarization effects are small and derive conservation laws for the net baryon current, the energy–momentum tensor and the spin tensor based on the de Groot–van Leeuwen–van Weert definitions of these currents. We present various properties of the spin polarization tensor and its components, analyze the propagation properties of the spin polarization components, and derive the spin-wave velocity for arbitrary statistics. We find that only the transverse spin components propagate, analogously to the electromagnetic waves. Finally, using our framework, we study the space–time evolution of the spin polarization for the systems respecting certain space–time symmetries and calculate the mean spin polarization per particle, which can be compared to the experimental data. We find that, for some observables, our spin polarization results agree qualitatively with the experimental findings and other model calculations. [ABSTRACT FROM AUTHOR]

This paper examines the dynamics of a W-configuration four-level atom in a quantized cavity field and the system driven by an external classical field. By applying some canonical transformations, we derive analytical solutions to the Schrödinger equation for the corresponding Hamiltonian. We have analyzed the impact of the external field and detuning parameters on the system's relative entropy of coherence, Wigner function, and Pancharatnam phase. Our findings suggest that the external field parameter greatly affects the coherence of the system, whereas the detuning parameters may increase its maximum bounds. Furthermore, we have utilized the Wigner function as a tool to measure the quantumness and classicality of the system in its phase space. Our results indicate that the external field has a greater impact on the classicality of the system than the detuning parameters. Additionally, we have observed rapid oscillations in the dynamics of the Pancharatnam phase for large detuning values. It is worth noting that the external field reduces the number of phase jumps in the system. [ABSTRACT FROM AUTHOR]

Phase-space transforms describe spatial and angular information about light sources where one example is the Wigner functions in wave optics. Stokes parameters, on the other hand, supply information about the polarization of light beams. The generalized phase space Stokes parameters of 2D stochastic electromagnetic beams are already developed. In this article, the application of anisotropic light sources in generalized phase space Stokes parameters is theoretically investigated and numerically analyzed. There are several different ways of studying electromagnetic light beams depending on the spatial domain. But, most measure of the polarization of random light fields is carried out within the Stokes parameters context. In this account we study the electromagnetism, Stokes parameters, phase space, and the anisotropy properties of random light beams at once. We find here that when an anisotropy introduced in phase space then the cross terms of the Wigner matrix depart from the diagonal terms, which is not the same in configuration space. As a result, anisotropy has a different effect in Phase space, i.e. an anisotropic source introduces a phase and a variance change only in the cross terms of Wigner matrix. This is due to the use of anisotropy in the shifted kernel of Wigner transform. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.

Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z×S1, i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z×SO(2). In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L2(S1), is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress.

We propose a double-opto-mechanical set-up capable of generating a macroscopic entangled cat state of mechanical oscillators. Bridged by the ultra-strong coupling of light and atom, a modulation of opto-mechanical can amplify the observable displacement of the mechanical oscillators. We calculate the logarithmic negativity and joint Wigner functions to demonstrate the entanglement and quantum coherence effects between two mechanical oscillators. [ABSTRACT FROM AUTHOR]

In this paper, we test the ability of a recently proposed effective frequency theory, viz. the generalised Feynman–Kleinert effective frequency theory (GFK), for calculating the Wigner transform of the thermalised flux operator needed in reaction rate computations based on the classical Wigner model. We consider one-dimensional symmetric and asymmetric barriers at both high and low temperatures. The reaction rates obtained from the GFK theory are found to be close to the results obtained using the accurate Wigner function. The reaction rates obtained from the classical Wigner model are approximate since they are based on classical trajectories. We therefore also present a new version of the so-called effective quantum force method, that improves the classical Wigner rates. This new implementation utilises as input matrix elements of the thermalised flux operator obtained from the GFK theory. We find a significant improvement compared to the classical Wigner reaction rates. Possible extensions to multi-dimensional systems are discussed. [ABSTRACT FROM AUTHOR]

Based on the f-oscillator formalism, we introduce a nonlinear optomechanical framework which is constructed from the standard optomechanical system by deforming the single-mode photonic-field operators. Such a generalized optomechanical system describes an intensity-dependent interaction of a mechanical oscillator with a single-mode electromagnetic field. To gain insight into the effectiveness of the non-linearization processes, we investigate the role of the involving parameters especially the nonlinearity function that controls the entanglement and statistical properties of the photon-phonon state was considered. Thus, we apply the linear entropy measure and the Wigner function to quantify the entanglement and non-classical properties of this composite system and the condition in which quantum entanglement and negativity of the Wigner function can be enhanced and maximized has been identified. Thus, depending on an election of the nonlinearity function, one can observe different non-classical effects. These trends are compared with those obtained for the standard optomechanical system including photon-phonon interaction, too. [ABSTRACT FROM AUTHOR]

The hybrid architecture of the driven qubit–photon–magnon system has recently emerged as a promising candidate for novel quantum technologies. In this paper, we introduce the effective wave-function of a superconducting single qubit and a magnon mode contained within a cavity resonator and an external field. The non-classicality of the magnon and resonator modes are investigated by using the negative values of the Wigner function. Additionally, we discuss the non-classicality of the qubit state via the Wigner–Yanase skew information. We find that the mixture angle of the qubit–resonator plays a controllable role in non-classicality. However, the strength of the magnon–photon increases the non-classical behaviour of the system. [ABSTRACT FROM AUTHOR]

The quantum dynamics of the number of photons, of the quantum entropy, and the Wigner functions of field interacting modes are studied for the process of non-degenerate parametric decay in an optical cavity, where a quantum with energy decays into two photons with energies and (). It is shown that the mode with frequency can localize in a squeezed state in the region of very strong coupling between the interacting modes, and the modes with frequencies and localize in states that are statistical mixtures of Fock states regardless of the value of the coupling coefficient [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered. [ABSTRACT FROM AUTHOR]

Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z × S 1 , i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z × SO (2) . In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L 2 (S 1) , is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress. [ABSTRACT FROM AUTHOR]

Covariant integral quantization with rotational SO(3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO(3). This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform.

We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.

In this paper, we theoretically analyze the massless Dirac fermion dynamics in twodimensional monolayers of boron allotropes, 8B and 2BH − pmmn borophene, interacting with external electric and magnetic fields. We study the effect of the Dirac cone tilt in these materials, which is known as valley index, through the time evolution of probability density of coherent electron states as well as their phase-space representation obtained via the Wigner function. Our results show that the time evolution of the coherent electron states in these materials is valley dependent, which is reinforced in the presence of external electric fields.

State g n ̂ â † m α and state â † m g n ̂ α are same to state â † m g α , which is called as multi-photon-addition amplified coherent state (MPAACS) by us. Here, n ̂ , â † , α , g (≥ 1) , and m are photon number operator, creation operator, coherent state, gain factor, and an integer, respectively. We study mathematical and physical properties for these MPAACSs, including normalization, photon component analysis, Wigner function, effective gain, quadrature squeezing, and equivalent input noise. Actually, the MPAACS, which contains more nonclassicality, is an amplified version of photon-added coherent state (PACS) introduced by Agarwal and Tara [Phys. Rev. A 43, 492 (1991)]. Our work provides theoretical references for implementing amplifiers for light fields. [ABSTRACT FROM AUTHOR]

Based on the conditional double interferometers proposed by Paris, we shall generate a class of finite-dimensional nonclassical states by inputting several different states including coherent state(CS), squeezed vacuum state(SVS), and thermal state(TS). It is shown that the double interferometers with two single-photons inputs and two single-photon detections are seen as an equivalent projection operator composed of vacuum state, one-photon state and two-photon state. Then we study the detection probability of output states and the fidelity between the corresponding input state and the output state, respectively. In addition, the nonclassical characteristics of three kinds of output states has also been analyzed and compared in detail by means of intensity gain, Mandel’s Q parameter, as well as the Wigner function. These results show that for the case of the input SVS, the nonclassical characteristics of its output state is independent of phase shift and is only related to the initial squeezed parameter. However, for the cases of the input CS and TS, the output states can present strong non-classicality by modulating the input initial parameters and the internal phase shifter of interferometer. [ABSTRACT FROM AUTHOR]

We present a scheme to directly probe the Wigner function of the motional state of a neutral atom confined in an optical trap. The proposed scheme relies on the well-established fact that the Wigner function at a given point (x, p) in phase space is proportional to the expectation value of the parity operator relative to that point. In this work, we show that the expectation value of the parity operator can be directly measured using two auxiliary internal states of the atom: parity-even and parity-odd motional states are mapped to the two internal states of the atom through a Ramsey interferometry scheme. The Wigner function can thus be measured point-by-point in phase space with a single, direct measurement of the internal state population. Numerical simulations show that the scheme is robust in that it applies not only to deep, harmonic potentials but also to shallower, anharmonic traps. [ABSTRACT FROM AUTHOR]

In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel’s parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coherent states. Finally, the occurrence of the anti-bunching phenomena in this class of tripartite excited states is studied using the second-order correlation function. [ABSTRACT FROM AUTHOR]

The evolution of the classical states, as well as a quantum state under the nonlinear Hamiltonian, detaches the state from the initial state, and the evolved state wanders through various facets in the state space. In the nonlinear Kerr evolution, the number state filtered coherent state (NSFCS) derived from the coherent state (CS) is chosen as an initial state. The departure from coherence is quantified by the Hilbert–Schmidt distance between the CS and the NSFCS in the Kerr medium; it is also calculated between the CS and the photon-added coherent states (PACS) in the Kerr medium. The similarity of states between the initial state and the time-evolved NSFCS is also analyzed through the Hilbert–Schmidt distance. We show the revivals and fractional revivals of the NSFCS, in view of the expectation values of the observables, optical tomogram, and Wigner function. The NSFCS revives at the integral multiples of π. The collapse of the wave packet does not occur at an instant of π/ 2 as like the coherent states and photon-added coherent states. These features are revealed in the moments of observables and optical tomogram. Further, the distinct features of the spread of sub-packets are captured by the Wigner function. [ABSTRACT FROM AUTHOR]

The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the "preparation region", into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schrödinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The possible influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions. [ABSTRACT FROM AUTHOR]

We study the time degradation of quantum information stored in a quantum memory device under a dissipative environment in a parameter range which is experimentally relevant. The quantum memory under consideration is comprised of an optomechanical system with additional Kerr nonlinearity in the optical mode and an anharmonic mechanical oscillator with quadratic nonlinearity. Time degradation is monitored, both in terms of loss of coherence, which is analyzed with the help of Wigner functions, as well as in terms of loss of amplitude of the original state, studied as a function of time. While our time trajectories explore the degree to which the stored information degrades depending upon the variation in values of various parameters involved, we suggest a set of parameters for which the original information can be retrieved without degradation. We identify a very interesting situation where the role played by the nonlinearity is insignificant, and the system behaves as if the information is stored in a linear medium. For this case, the information retrieval is independent of the coherence revival time and can be retrieved at any instant during the time evolution. [ABSTRACT FROM AUTHOR]

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated with N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. The main characteristic of this study is to use the same complex number to express the related states that appear in a large number of literatures. [ABSTRACT FROM AUTHOR]

We tested the ability of Wigner function to reveal and capture the quantum entanglement presents in two coupled semiconductor InAs quantum dots that independently interact with dephasing reservoirs. In this respect, we analyze their evolution against the temperature parameter as well as against the dimensionless time in both Markovian and non-Markovian environments. Further, we compare their amounts and their behaviors under the Förster interaction effect. In particular, we show that for large values of dimensionless time and at higher temperature, unlike the full disappear of entanglement the positive part of Wigner function still survives. Moreover, we show that the Wigner function volume is influenced by the variation of the Förster interaction, the temperature and the non-Markovianity degree. Nevertheless, its ability to reveal the quantum entanglement presents inside two coupled semiconductor quantum dots is still kept. [ABSTRACT FROM AUTHOR]

We investigate bright and dark diffractive focusing emerging in the free propagation of specific wave profiles. These general wave phenomena manifest themselves in matter, water, and classical waves. In this article, we lay the foundations for these effects and illustrate their origin in Wigner phase space. Our theoretical studies are supported by experimental demonstrations of dark focusing in water waves. Moreover, by using different phase slits we analyze several aspects of bright and dark focusing for classical and matter waves. [ABSTRACT FROM AUTHOR]

Various phase-space distributions, from the celebrated Wigner function, to the Husimi function and the Glauber–Sudarshan distribution, have played an interesting and important role in the phase-space formulation of quantum mechanics in general, and quantum optics in particular. A unified approach to all these distributions based on the notion of the -ordered phase-space distribution was introduced by Cahill and Glauber. With the intention of illuminating the physical meaning of the parameter , we interpret the -ordered phase-space distribution as the Wigner function of a state under the Gaussian noise channel, and thus reveal an intrinsic connection between the -ordered phase-space distribution and the Gaussian noise channel, which yields a physical insight into the -ordered phase-space distribution. In this connection, the parameter (rather than the original ) acquires the role of the noise occurring in the Gaussian noise channel. An alternative representation of the Gaussian noise channel as the scaling-measurement preparation in a coherent states is illuminated. Furthermore, by exploiting the freedom in the parameter , we introduce a computable and experimentally testable quantifier for optical nonclassicality, reveal its basic properties, and illustrate it by typical examples. A simple and convenient criterion for optical nonclassicality in terms of the -ordered phase-space distribution is derived. [ABSTRACT FROM AUTHOR]