We present the truncated (or [Formula: see text]-deformed) para-Bose oscillator algebra of order [Formula: see text], with [Formula: see text] being a half-integer, along with its [Formula: see text]-dimensional Fock representation. The model reduces to the truncated simple harmonic oscillator and the conventional para-Bose oscillator algebras in the limiting cases where the parameters [Formula: see text] and [Formula: see text] approach zero and infinity, respectively. A Fock–Bargmann realization is constructed in such a way that the creation operator is expressed as a function of both deformation parameters [Formula: see text] and [Formula: see text]. Two-component orthogonal cat states are formulated through suitable superpositions of even and odd parity states within the Fock representation space. The corresponding positive-definite measures over the entire complex plane are derived in terms of Meijer’s [Formula: see text]-functions parameterized by [Formula: see text] and [Formula: see text]. In addition, the nonclassical properties of the even and odd cat states are analyzed, including the manifestation of sub-Poissonian statistics, photon antibunching effect, and quadrature squeezing. We further investigate how the parameters [Formula: see text] and [Formula: see text] individually influence the enhancement or suppression of entanglement in the associated quasi-Bell states.
We present the truncated (or [Formula: see text]-deformed) para-Bose oscillator algebra of order [Formula: see text], with [Formula: see text] being a half-integer, along with its [Formula: see text]-dimensional Fock representation. The model reduces to the truncated simple harmonic oscillator and the conventional para-Bose oscillator algebras in the limiting cases where the parameters [Formula: see text] and [Formula: see text] approach zero and infinity, respectively. A Fock–Bargmann realization is constructed in such a way that the creation operator is expressed as a function of both deformation parameters [Formula: see text] and [Formula: see text]. Two-component orthogonal cat states are formulated through suitable superpositions of even and odd parity states within the Fock representation space. The corresponding positive-definite measures over the entire complex plane are derived in terms of Meijer’s [Formula: see text]-functions parameterized by [Formula: see text] and [Formula: see text]. In addition, the nonclassical properties of the even and odd cat states are analyzed, including the manifestation of sub-Poissonian statistics, photon antibunching effect, and quadrature squeezing. We further investigate how the parameters [Formula: see text] and [Formula: see text] individually influence the enhancement or suppression of entanglement in the associated quasi-Bell states.
The normalized even and odd [Formula: see text]-cat states corresponding to Arik–Coon [Formula: see text]-oscillator on the noncommutative complex plane [Formula: see text] are constructed as the eigenstates of the lowering operator of a [Formula: see text]-deformed [Formula: see text] algebra with the left eigenvalues. We present the appropriate noncommutative measures in order to realize the resolution of the identity condition by the even and odd [Formula: see text]-cat states. Then, we obtain the [Formula: see text]-Bargmann–Fock realizations of the Fock representation of the [Formula: see text]-deformed [Formula: see text] algebra as well as the inner products of standard states in the [Formula: see text]-Bargmann representations of the even and odd subspaces. Also, the Euler’s formula of the [Formula: see text]-factorial and the Gaussian integrals based on the noncommutative [Formula: see text]-integration are obtained. Violation of the uncertainty relation, photon antibunching effect and sub-Poissonian photon statistics by the even and odd [Formula: see text]-cat states are considered in the cases [Formula: see text] and [Formula: see text].
This paper has been motivated by a recent paper by Dey [Phys. Rev. D 91, 044024 (2015)] on the known Arik-Coon q oscillator. We construct q coherent, even and odd q-cat states in Fock representation for the Biedenharn-Macfarlane q oscillator with q>1 and study their nonclassical properties. The q-coherent states minimize the Heisenberg uncertainty relation between the generalized position and momentum operators as well as the x and y components of a q-deformed su(1,1) algebra in the Schwinger boson representation. The latter is also minimized by the even and odd q-cat states. We show that, contrary to the undeformed harmonic oscillator, the squeezing effect in both position and momentum operators can be exhibited by odd q-cat states. It is also violated by even q-cat states. Furthermore, it is shown that the antibunching effect and sub-Poissonian or super-Poissonian statistics can simultaneously appear by each of the even or odd q-cat states. Finally, a unitary Fock representation of the q-deformed su(1,1) algebra is obtained by the q-deformed Bargmann-Fock realization.
In this paper, we introduce two classes of superposed states generated by a superposition of two single-mode para-Bose coherent states (CS) with arbitrary relative phase factors. The first class is superposition of two opposite para-Bose CS and second class consists of two para-Bose CS, [Formula: see text] out of phase with each other. These states are reduced to the well-known superposed single-mode CS of the simple harmonic oscillator when the deformation parameter tends to one. We study the nonclassical properties of the introduced states by evaluating their para-Bose Fock state distribution, second-order squeezing, Klyshko’s and Mandel’s parameters. We investigate the essential role of coherent and deformation parameters on their nonclassicality. We show that some nonclassical properties of these states are different from those of the even and odd coherent states. Finally, we present a simple scheme for the physical generation of the introduced states.
The optical charge pair coherent states for a two-mode electromagnetic field corresponding to [Formula: see text]- and [Formula: see text]-deformed oscillator algebras that are both of the Arik–Coon or Biedenharn–Macfarlane type are constructed. Next, their associated even and odd cat states are formulated in terms of the charge, deformation parameters [Formula: see text] and [Formula: see text], and coherent field, in a linear combination form of two-mode number states of the deformed oscillators. The two-mode higher-order anti-bunching, squeezing, and entanglement traits of the even and odd charge cat states corresponding to the oscillators with the same deformation parameters are considered in terms of the charge and the coherent field as well as different values for deformation parameter itself. We compare the difference of these non-classical behaviors not only between the odd and even states of each two-mode oscillator but also between two-mode Arik–Coon and Biedenharn–Macfarlane oscillators. For example, we answer whether the entanglement of the two-mode cat states increases or decreases with the increase of the charge.
By introducing a generalization of the (p, q)-deformed boson oscillator algebra, we establish a two-parameter deformed oscillator algebra in an infinite-dimensional subspace of the Hilbert space of a harmonic oscillator without first finite Fock states. We construct the associated coherent states, which can be interpreted as photon-added deformed states. In addition to the mathematical characteristics, the quantum statistical properties of these states are discussed in detail analytically and numerically in the context of conventional as well as deformed quantum optics. Particularly, we find that for conventional (nondeformed) photons the states may be quadrature squeezed in both cases Q = pq < 1, Q = pq > 1 and their photon number statistics exhibits a transition from sub-Poissonian to super-Poissonian for Q < 1 whereas for Q > 1 they are always sub-Poissonian. On the other hand, for deformed photons, the states are sub-Poissonian for Q > 1 and no quadrature squeezing occurs while for Q < 1 they show super-Poissonian behavior and there is a simultaneous squeezing in both field quadratures.PACS Nos.: 42.50.Ar, 03.65.w
Abstract In this paper, we introduce some distinct classes of entangled cat states associated to generalized displaced Fock states. For this purpose, we use the formalism of nonlinear coherent states corresponding to nonlinear oscillator algebra which yields various kinds of f-deformed entangled states. We also take a particular class of Gilmore-Perelomov-type of SU(1, 1) and a class of SU(2) coherent states. We then obtain the amount of entanglement between subsystems of the quantum states of interest by applying the measure of concurrence. Furthermore, examining some of the most important criteria, such as Mandels Q parameter, quadrature squeezing and Vogels characteristic function, we study the nonclassicality of the introduced quantum states. The numerical results show remarkable values of entanglement, sub-Poissonian statistics of the field, and squeezing indicating that the introduced states can be regarded as possible candidates for nonclassical entangled states. Afterwards, we see that the Vogel function for quantum states of interests goes beyond the value of characteristic function of the ground state, which shows the nonclassicality of the introduced states.