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Optics Letters

Phase space nonclassicality and sub-Poissonianity of deformed photon-added nonlinear cat states: algebraic and group theoretical approach

Sogand Torkzadeh-Tabrizi, Mohammad Javad Faghihi, Gholamreza Honarasa

Published Jan 3, 2023• 4 citations
Publisher

Abstract

In this Letter, we introduce four distinct classes of f-deformed photon-added nonlinear cat state. This would be achieved by recalling a nonlinear coherent states approach, as well as a particular class of Gilmore-Perelomov-type of SU(1,1) coherent state and a class of SU(2) coherent state. We then examine the role of photon addition and nonlinearity functions in the phase space structure and sub-Poissonianity of even, odd, and Yurke-Stoler nonlinear cat states. The effect of photon addition, which results in a π phase shift at the origin of the Wigner function toward negativity, interestingly enhances the nonclassicality by means of the Wigner function and Mandel parameter. Furthermore, owing to photon addition, we can observe a deformation in the Gaussian shape of the Wigner function, which may be found to be potentially useful in quantum noise reduction. Moreover, the deformation function shows a remarkable role in revealing the nonclassical behavior and can increase the depth and the domain of nonclassicality.

DOI
10.1364/ol.481568

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In this Letter, we introduce four distinct classes of f-deformed photon-added nonlinear cat state. This would be achieved by recalling a nonlinear coherent states approach, as well as a particular class of Gilmore-Perelomov-type of SU(1,1) coherent state and a class of SU(2) coherent state. We then examine the role of photon addition and nonlinearity functions in the phase space structure and sub-Poissonianity of even, odd, and Yurke-Stoler nonlinear cat states. The effect of photon addition, which results in a π phase shift at the origin of the Wigner function toward negativity, interestingly enhances the nonclassicality by means of the Wigner function and Mandel parameter. Furthermore, owing to photon addition, we can observe a deformation in the Gaussian shape of the Wigner function, which may be found to be potentially useful in quantum noise reduction. Moreover, the deformation function shows a remarkable role in revealing the nonclassical behavior and can increase the depth and the domain of nonclassicality.
The phase space structure and statistics of the photon added cat state are studied in the state’s general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke–Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.
Multi-photon-added cat states are constructed by repeatedly applying the creation operator to a cat state. We study in detail their photon-number distribution, QQQ parameter, squeezing properties, and Wigner function. We show that photon addition induces a πππ phase shift in the original parity configuration whenever an odd number of photons is added, reflected as swapped vanishing probabilities and phase space displacements at the origin. Remarkably, the same process drives these states into a sub-Poissonian regime regardless of the relative phase between their coherent state components, making them valuable resources for quantum imaging, at the cost of losing quadrature squeezing, but gaining amplitude-squared one. We also discuss how these states can be generated using existing hardware.
In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.
Recently, nonlinear displaced number states (NDNSs) have been manually introduced, in which the deformation function f ( n ) has been artificially added to the previously well-known displaced number states (DNSs). Indeed, just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs. In the present paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore–Perelomov-type of SU (1, 1) and a class of SU (2) coherent states, the NDNSs are introduced via group-theoretical approach. Then, in order to examine the nonclassical behavior of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.
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.
We have introduced the notion of ‘four-photon nonlinear coherent states’ (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator A4. It has been shown that there are four possible sets of such states which all can be expressed as the deformed Schrödinger cat type states derived from the superposition of four nonlinear coherent states (NCSs) which are π/2 out of phase. The nonclassical properties of the FPNCSs would be studied for two well-known quantum systems, a Kerr-like medium and a trapped laser-driven ion far from the Lamb-Dicke regime. We have found that the depth or the domain of the nonclassical features of FPNCSs in terms of sub-Poissonian photon statistics, higher order squeezing as well as amplitude-squared squeezing are higher than the corresponding standard states. Specifically, the proposed states in this paper exhibit sub-Poissonian statistics over an extensive range of real amplitudes which is in contrast with the lower level of sub-Poissonian characteristics of four-photon standard coherent states. Also the depth or domain of the nonclassical features of the FPNCSs can be modified by changing the magnitude of the nonlinearity parameters. Analysis of the quasi-probability distributions like Glauber–Sudarshan P-function, Husimi Q-function and Wigner distribution function verifies the nonclassical nature of the presented states. Studying the cavity field evolution in the interaction of a single two-level atom with an even NCS in the framework of f-deformed Jaynes-Cummings model shows that such a system can potentially be considered as a possible source for generating the proposed states.