Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane [Formula: see text]-oscillator. We consider in details the role of noncommutativity parameter [Formula: see text] on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.
Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane [Formula: see text]-oscillator. We consider in details the role of noncommutativity parameter [Formula: see text] on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.
We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a q-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.
In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f -deformed creation operator A = f ( n ) a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f -deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.
Abstract We construct a generalized version of the photon-subtracted squeezed vacuum states (PSSVS), which can be utilized to construct the same for nonlinear, deformed and any usual quantum mechanical models beyond the harmonic oscillator. We apply our general framework to trigonometric Pöschl–Teller potential and show that our method works accurately and produces a proper nonclassical state. We analyze the nonclassicality of the state using three different approaches, namely, quadrature squeezing, photon number squeezing and Wigner function and indicate how the standard definitions of those three techniques can be generalized and utilized to examine the nonclassicality of any generalized quantum optical states including the PSSVS. We observe that the generalized PSSVS are always more nonclassical than those arising from the harmonic oscillator. Moreover, within some quantification schemes, we find that the nonclassicality of the PSSVS increases almost proportionally with the number of photons subtracted from the generalized squeezed vacuum state. Thus, generalized PSSVS may provide an additional freedom with which one can regulate the nonclassicality and obtain an appropriate nonclassical state as per requirement.
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.
Abstract Nonclassical properties of photon added and subtracted displaced Fock states are 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 parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.
This work has focused on the violation of uncertainty relation, squeezing effect, photon antibunching and sub-Poissonian statistics for the Arik–Coon [Formula: see text]-oscillator coherent states associated with the noncommutative complex plane [Formula: see text]. It is shown that one has to use a generalized definition for the covariance between the operators [Formula: see text] and [Formula: see text]. For [Formula: see text], Heisenberg's inequality violation with two different behaviors related to the role of the deformation parameter [Formula: see text] on the variances of the position and momentum operators is illustrated. We conclude that both weak and strong squeezing effects are exhibited by the [Formula: see text]-coherent states. In particular, strong squeezing effect is a direct consequent of the violation of Heisenberg's inequality. Moreover, the photon antibunching and sub-Poissonian photon statistics are two features of the [Formula: see text]-coherent states which are realized simultaneously with the squeezing effects. Clearly, the three later behaviors are different from their corresponding counterparts in the Arik–Coon [Formula: see text]-oscillator coherent states associated with a commutative complex plane.