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arXiv:2406.10049

Nonclassical features of the pointer states in the $q$-deformed post-selected weak measurement

Seyyede Elham Mousavigharalari, Azmi Ali Altıntaṣ, Fatih Özaydin

Published Jun 14, 2024• 0 citations
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Abstract

We study $q$-deformed coherent states of the Arik-Coon harmonic oscillator as the quantum resource in the post-selected weak measurement. First, we show how the precision of weak measurement is improved significantly due to $q$-deformation. Next, we focus on the role of the interplay between the deformation parameter and the interaction strength on the nonclassical nature of light. In particular, we show that sub-Poissonian photon distribution as characterized by Mandel parameter, photon antibunching effect, and quadrature squeezing are greatly enhanced by $q$-deformation. Our results not only advance the understanding of the fundamentals of $q$-deformed quantum mechanics, but also raise the potential to contribute to quantum technologies.

DOI
10.48550/arxiv.2406.10049

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Nonclassical features of the pointer states in the qqq-deformed post-selected weak measurement
We study qqq-deformed coherent states of the Arik-Coon harmonic oscillator as the quantum resource in the post-selected weak measurement. First, we show how the precision of weak measurement is improved significantly due to qqq-deformation. Next, we focus on the role of the interplay between the deformation parameter and the interaction strength on the nonclassical nature of light. In particular, we show that sub-Poissonian photon distribution as characterized by Mandel parameter, photon antibunching effect, and quadrature squeezing are greatly enhanced by qqq-deformation. Our results not only advance the understanding of the fundamentals of qqq-deformed quantum mechanics, but also raise the potential to contribute to quantum technologies.
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.
We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a qqq-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.
This paper has been motivated by a recent paper by Dey [Phys. Rev. D 91, 044024 (2015)] on the known Arik-Coon qqq oscillator. We construct qqq coherent, even and odd qqq-cat states in Fock representation for the Biedenharn-Macfarlane qqq oscillator with q>1q>1q>1 and study their nonclassical properties. The qqq-coherent states minimize the Heisenberg uncertainty relation between the generalized position and momentum operators as well as the xxx and yyy components of a qqq-deformed su(1,1)\text{su}(1,1)su(1,1) algebra in the Schwinger boson representation. The latter is also minimized by the even and odd qqq-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 qqq-cat states. It is also violated by even qqq-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 qqq-cat states. Finally, a unitary Fock representation of the qqq-deformed su(1,1)\text{su}(1,1)su(1,1) algebra is obtained by the qqq-deformed Bargmann-Fock realization.
We study several classical-like properties of qqq-deformed nonlinear coherent states as well as nonclassical behaviors of qqq-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in qqq-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the qqq-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.
We investigate how post-selected von Neumann measurements modify the nonclassical properties of two-mode entangled coherent states (ECSs). From the conditional pointer state, we characterize squeezing, photon statistics, intermode correlations, entanglement, fidelity, and post-selection probability. Anomalous weak values with moderate coupling enhance squeezing, antibunching, sub-Poissonian statistics, intermode correlations, and bipartite entanglement, while fidelity captures the crossover from weak perturbation to strong distinguishability. These results demonstrate post-selection as a tunable approach to engineering ECSs.
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