In this paper the factorization method is used in order to obtain the eigenvalues and eigenfunctions of a quantum particle confined in a one-dimensional infinite well. The output results from the mentioned approach allows us to explore an appropriate new pair of raising and lowering operators corresponding to the physical system under consideration. From the symmetrical considerations, the connection between the obtained ladder operators with $su(1,1)$ Lie algebra is explicitly established. Next, after the construction of Barut-Girardello and Gilmore-Perelomov representations of coherent states associated with the considered system, some of their important properties like the resolution of the identity including a few nonclassical features are illustrated in detail. Finally, a theoretical scheme for generation of the Gilmore-Perelomov type of coherent state via a generalized Janes-Cummings model is proposed.
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 couplin…
Simple joint measurements of pairs of observables reveal that states considered universally as classical-like, such as SU(2) spin coherent states, Glauber coherent states, and thermal states are actually nonclassical. We show that this holds because we can find a joint measurement the statistics of which is not separable. Eventually this may be extended to all states different from the maximally mixed state.
We investigate the nonclassicality of photon-added coherent states in the photon loss channel by exploring the entanglement potential and negative Wigner distribution. The total negative probability defined by the absolute value of the integral of the Wigner function over the negative distribution region reduces with the increase of decay time. The total negative probability and the entanglement potential of pure photon-added coherent states exhibit the similar dependence on the beam intensity. The reduce of the total negative probability is consistent with the behavior of entanglement potenti…
Nonclassical properties of photon added and photon subtracted squeezed coherent states have been compared with specific focus on the higher order nonclassicalities, such as higher order squeezing, higher order sub-Poissonian photon statistics, higher order antibunching. It is observed that both photon added and photon subtracted squeezed coherent states are highly nonclassical as they satisfy criteria for all of the above mentioned nonclassicalities and a set of other criteria including negativity of Wigner function, Klyshko's criterion and Agarwal's $(A_{3})$ parameter. Further, the amount of…
We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose negativities indicate nonclassicality of the process. Using this distribution, we derive a relation for predicting nonclassicality of the output states for a given input state. We experimentally demonstrat…
The Leggett-Garg inequality (LGI), based on the notions of realism and noninvasive measurability, is applied in the context of a linear harmonic oscillator. It is found that merely through observing at various instants which region of the potential well, the oscillating quantum object is in, the LGI can be violated without taking recourse to any ancillary quantum system. Strikingly, this violation reveals an unexplored nonclassicality of the state which is considered the most "classical-like" of all quantum states, namely the Schrödinger coherent state. In the macrolimit, the extent to which s…
We present a method for the experimental measurement of nonclassicality witnesses and demonstrate its application. Our proposal only requires the coherent displacement of the initial state, which can be achieved by overlapping the latter with a coherent state at a beam splitter, and subsequent photon-number resolved detection. This setup allows a complete test of nonclassicality of an arbitrary quantum state. The role of the quantum efficiency as well as statistical and systematic uncertainties are discussed. Finally, the scheme is demonstrated for a realistic example.
The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function which reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the thermal channel. For arbitrary partial negative Wigner distribution function, a generic analytical relation between the mean photon number of heat bath and the threshold value of decay time is presented…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing, coherence) can be converted into entanglement. In this work, we present a general framework, based on superposition, for structurally connecting and converting nonclassicality to entanglement. In addition to capturing the previously known results, this framework also allows us to uncover new entanglement convertibility theorems in two broad scenarios, one which…
We study the nonclassicality of the evolution of a superposition of an arbitrary number of photon-added squeezed coherent Schrödinger cat states in a nonlinear Kerr medium. The nonlinearity of the medium gives rise to the periodicities of the quantities such as the Wehrl entropy $S_{Q}$ and the negativity $δ_{W}$ of the $W$-distribution, and a series of local minima of these quantities arise at the rational submultiples of the said period. At these local minima the evolving state coincides with the transient Yurke-Stoler type of photon-added squeezed kitten states, which, for the choice of the…
We examine whether metrological resolution beyond coherent states is a nonclassical effect. We show that this is true for linear detection schemes but false for nonlinear schemes, and propose a very simple experimental setup to test it. We find a nonclassicality criterion derived from quantum Fisher information.
We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that the normalized factor is related to the two-variable Hermite polynomials. We then investigate the nonclassical properties in terms of Mandel's Q parameter, quadrature squeezing, second correlation, and the negativity of Wigner function (WF). It is shown that all these properties are related to the amplitude of coherent state, catalysis number and unbalanced b…
The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property autom…
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical behaviour of nonlinear coherent states for generalised classes of models corresponding to the generalised ladder operators. A comparative analysis among them indicates that the models with quadratic spectrum are more nonclassical than the others. Our central result is further underpinned by the comparison of the degree of nonclassicality of squeezed states of the co…
We introduce a new non-Gaussian state, generated by m times coherent superposition operation $a\cos θ+a^{\dagger }e^{iφ}\sin θ$ (MCSO) on odd-Schrodinger-cat state (OSCS). Its normalized constant is turned out to be related with the Hermite polynomial. We further investigate the nonclassical properties of the MCSO-OSCS through Mandel's Q-parameter, quadrature squeezing, the photocount distribution and Wigner function (WF). It is shown that the nonclassicality of the MCSO-OSCS is influenced by the number of times (m) of coherent superpositon operation, the angle $θ$ and the amplitude of the coh…
Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of the Hahn-Banach theorem to separate classical states from nonclassical ones. Nonclassicality linear witnesses are constructed, based on the observables available in a given physical situation. Some examples of nonclassical states are considered, with detection schemes available nowadays. Reviewing the concept of entanglement potential from a different persp…
Dynamics of nonclassicality in a generalized Tavis Cummings model with XY spin $(1/2,1)$ atomic interactions
Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院）；Centre of Physics and Mathematics, CPM, Faculty of Sciences, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院物理与数学中心）
In this paper, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz et al., and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan $P$ distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum l…
We study different representations of a many-particle system. We reveal the stunning beauty of the connections among the nonclassicalities of a many-particle, a single-mode and a two-mode systems. First, we demonstrate that (separable) atomic coherent states~(ACSs), of a many-particle system, mimic the coherent states of single-mode light. This enables the utilization of a many-particle entanglement~(MPE) criterion as a single-mode nonclassicality~(SMNc) condition via Holstein-Primakoff transformation. As an example, we show that spin-squeezing criterion, for MPE, can be transformed into the q…
Conventional coherent states (CSs) are defined in various ways. For example, CS is defined as an infinite Poissonian expansion in Fock states, as displaced vacuum state, or as an eigenket of annihilation operator. In the infinite dimensional Hilbert space, these definitions are equivalent. However, these definitions are not equivalent for the finite dimensional systems. In this work, we present a comparative description of the lower- and higher-order nonclassical properties of the finite dimensional CSs which are also referred to as qudit CSs (QCSs). For the comparison, nonclassical properties…
Using the {\it nonlinear coherent states method}, a formalism for the construction of the coherent states associated to {\it "inverse bosonic operators"} and their dual family has been proposed. Generalizing the approach, the "inverse of $f$-deformed ladder operators" corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Finally, after applying the proposal to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field co…
We show that coherently driven atomic or molecular media potentially yield strong controllable short pulses of THz radiation. The method is based on excitation of maximal quantum coherence in a gas medium by optical pulses and coherent scattering of infra-red radiation to produce pulses of THz radiation. The pulses have the energies range from several nJ to $μ$J and time durations from several fs to ns at room temperature.
We present Bell-type tests of nonclassicality and non-Gaussianity for single-mode fields employing a generalized quasiprobability function. Our nonclassicality tests are based on the observation that two orthogonal quadratures in phase space (position and momentum) behave as independent realistic variables for a coherent state. Taking four (three) points at the vertices of a rectangle (right triangle) in phase space, our tests detect every pure nonclassical Gaussian state and a range of mixed Gaussian states. These tests also set an upper bound for all Gaussian states and their mixtures, which…
The concept of photon added two-mode Schrödinger cat states in which both modes are independent is introduced, their non-classical properties and entanglement are studied. The introduced states emerge as the eigenstates of $f_1f_2a_1a_2$, 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 the canonical transformation using the parity operator for the case of standard coherent states of the harmonic oscillator. The non-classical properties of these states are evaluated especially by considering …
We propose a technique to prepare coherent superpositions of two nondegenerate quantum states in a three-state ladder system, driven by two simultaneous fields near resonance with an intermediate state. The technique, of potential application to enhancement of nonlinear processes, uses adiabatic passage assisted by dynamic Stark shifts induced by a third laser field. The method offers significant advantages over alternative techniques: (ı) it does not require laser pulses of specific shape and duration and (\ii) it requires less intense fields than schemes based on two-photon excitation with n…
The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving recurrence relations. The states generated are good candidates for the natural generalisation of the $\mathfrak{su}(2)$ coherent states of the two-dimensional isotropic oscillator. The two-dimensional non-linear generalised ladder operators lead to several chains of states which are connected in a non trivial way. The uncertainty relations of the defining chain of…
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied. Finally, using the Gazeau-Klauder coherent states approach, time evolution of some of the nonclassical properties of the coherent states corresponding to the considered physical systems are discussed.
We present a systematic analysis on coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator. Depending on the elementary particles comprising the composite particles, we gauge the resemblance between this eigenstate and traditional coherent states through typical measures of nonclassicality, such as quadrature variances and Mandel's Q parameter. Furthermore, we show that the eigenstate of the coboson annihilation operator is useful in estimating the maximum…
In this paper we construct the generalized coherent states for an electron in monolayer or bilayer graphene placed in an external magnetic field. At first we define an appropriate set of ladder operators acting on the eigenfunctions for each Hamiltonian, afterwards we derive the generalized coherent states through several definitions and analyze the commutation relationship between the ladder operators. Then we determine the conditions leading to the mutual equivalence between coherent states. Finally, some physical quantities are calculated and we study the time evolution for the generalized …
It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as coherent states today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subj…
Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and exact solutions to the associated moment problem are displayed, providi…
Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces coherent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes-Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically…
Nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower- and higher-order antibunching and sub-Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel $Q_M$ parameter,…
Generalized $ \left\{ h (1) \oplus h(1) \right\} \uplus u(2) $ commensurate anisotropic Hamiltoninan and ladder operators; energy spectrum, eigenstates and associated coherent and squeezed states
A class of states of the electromagnetic field involving superpositions of all the excited states above a specified low energy eigenstate of the electromagnetic field is introduced. These states and the photon-added coherent states are shown to be the limiting cases of a generalized photon-added coherent states. This new class of states is nonclassical, non-Gaussian and has equal uncertainties in the field quadratures. For suitable choices of parameters, these uncertainties are very close to those of the coherent states. Nevertheless, these states exhibit sub-Poissonian photon number distribut…
We introduce a new method for constructing squeezed states for the 2D isotropic harmonic oscillator. Based on the construction of coherent states in [1], we define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the SU(2) coherent states. The new ladder operators are used for generalizing the squeezing operator to 2D and the SU(2) coherent states play the role of the Fock states in the expansion of the 2D squeezed states. We discuss some properties of the 2D squeezed states.
Ladder operators for the hyperbolic Rosen-Morse (RMII) potential are realized using the shape invariance property appearing, in particular, using supersymmetric quantum mechanics. The extension of the ladder operators to a specific class of rational extensions of the RMII potential is presented and discussed. Coherent states are then constructed as almost eigenstates of the lowering operators. Some properties are analyzed and compared. The ladder operators and coherent states constructions presented are extended to the case of the trigonometric Rosen-Morse (RMI) potential using a point canonic…
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the $SU(2)$ coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density func…
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.
In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent supersymmetric transformations. We construct ladder operators for these extensions as the product of the intertwining operators of both transformations. Then, we generate families of Barut-Girardello coherent states and analyze some of their properties as temporal stability, continuity on the label, and completeness relation. Moreover, we calculate mean-energy values, time-dependent probability densities, Wigner fun…
Stimulated Raman adiabatic passage (STIRAP) offers significant advantages for coherent population transfer between un- or weakly-coupled states and has the potential of realizing efficient quantum gate, qubit entanglement, and quantum information transfer. Here we report on the realization of STIRAP in a superconducting phase qutrit - a ladder-type system in which the ground state population is coherently transferred to the second-excited state via the dark state subspace. The result agrees well with the numerical simulation of the master equation, which further demonstrates that with the stat…
We construct ladder operators, $\tilde{C}$ and $\tilde{C^\dagger}$, for a multi-step rational extension of the harmonic oscillator on the half plane, $x\ge0$. These ladder operators connect all states of the spectrum in only infinite-dimensional representations of their polynomial Heisenberg algebra. For comparison, we also construct two different classes of ladder operator acting on this system that form finite-dimensional as well as infinite-dimensional representations of their respective polynomial Heisenberg algebras. For the rational extension, we construct the position wavefunctions in t…
