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International Journal of Scientific Research in Physics and Applied Sciences

Nonclassical properties of non-Gaussian two-mode quantum vortex state

Vikram Singh, Devendra Kumar Mishra

Published Aug 31, 2018• 0 citations
Publisher

Abstract

Nonclassicality of optical fields are the key resources in quantum information processing.Recently, Agarwal [New J. Phys., 13, 073008(2011)] proposed a method for engineering of a two-mode vortex state, a non-Gaussian state, by subtracting a photon from a two-mode squeezed state produced by down-converter from idler mode via a beam splitter with low reflectivity and detection of one photon by the avalanche photo diode (APD), or even better by a single-photon detector.We study the nonclassicalities of this state in terms of squeezing, antibunching, photon number correlation and distribution of photon number.In addition, we study higher-order nonclassical properties, viz., sum squeezing.We find that the non-Gaussian state shows strong nonclassical effects.

DOI
10.26438/ijsrpas/v6i4.15

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Abstract Recently, experimental demonstrations of the pair coherent state of microwave photons in superconducting cavities (PRX QUANTUM 4, 020319, 2023) and experimental results of photon addition and subtraction in multimode entangled optical fields (Physical Review Research 6, 013065, 2024) were reported. Motivated by these results, we study the nonclassical properties of non-Gaussian photon-added and subtracted pair coherent states. More specifically, we explore quantum polarization, quadrature squeezing, sum and difference squeezing, Shchukin-Vogel Entanglement, EPR entanglement correlation, two-mode higher-order antibunching, and quasiprobability distribution function (Q function). The effect of photon addition and subtraction is visible in this study with different parameters, as we compared our results with the original pair coherent state (PCS). This study provides a deeper understanding of the quantum behavior of modified pair coherent states, with potential implications for advancements in quantum optics and information processing.
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Abstract Recently, photon subtraction from the single-mode squeezed vacuum state (SVS) has been explored as a technique to enhance its squeezing strength (SS). Notably, the enhancement is observed only when an even number of photons is subtracted, and this effect is limited to a specific range of the squeezing parameter r. In this paper, we introduce a novel class of single-mode nonclassical states, termed as qubit superposed SVSs (qSSVSs), via the coherent superposition of a SVS and a single-photon-subtracted SVS. The primary objective of this work is to enhance the SS for any r > 0 through the creation of these superposed states. Our analysis reveals that the qSSVSs not only improve the SS but also exhibit enhanced nonclassical features such as the negativity of Wigner function, single-mode antibunching effect, photon-number distribution, and sub-Poissonian photon statistics. Furthermore, we demonstrate that the qSSVSs provide superior phase sensitivity in a quantum Mach–Zehnder interferometer compared to the original SVS. Importantly, the generation of qSSVSs is feasible using readily available optical devices, including a beam splitter, a photodetector, and an amplitude displacement. These states hold significant potential for practical applications in quantum information science, particularly for tasks such as information encoding and processing in quantum computing systems.
Gaussian states with nonclassical properties such as squeezing and entanglement serve as crucial resources for quantum information processing. Accurately quantifying these properties within multimode Gaussian states has posed some challenges. To address this, we introduce a unified quantification: the "classical-nonclassical polarity," represented by P. For a single mode, a positive value of P captures the reduced minimum quadrature uncertainty below the vacuum noise, while a negative value represents an enlarged uncertainty due to classical mixtures. For multimode systems, a positive P indicates bipartite quantum entanglement. We show that the sum of the total classical-nonclassical polarity is conserved under arbitrary linear optical transformations for any two-mode and three-mode Gaussian states. For any pure multimode Gaussian state, the total classical-nonclassical polarity equals the sum of the mean photon number from single-mode squeezing and two-mode squeezing. Our results provide a new perspective on the quantitative relation between single-mode nonclassicality and entanglement, which may find applications in a unified resource theory of nonclassical features.
Photon addition and subtraction are well-known to render Gaussian states non Gaussian. We evaluate how their optical nonclassicality is affected by the photon addition/subtraction process. It is known that photon addition always transforms a Gaussian state into a nonclassical state. We show that photon subtraction transforms classical states into classical ones and nonclassical ones into nonclassical ones. For a quantitative analysis of the resulting nonclassicality, we use a recently introduced nonclassicality witness, the quadrature coherence scale, and compute the relative nonclassicality gain of the single-photon added/subtracted Gaussian states with respect to the original Gaussian states. For arbitrary single-mode Gaussian states, we show that this relative gain can be substantial in both cases. Whereas the gain is always higher for photon-added states, it is only slightly so for a large parameter range and in particular in the limit of high squeezing, where both gains are identical. We also analyze the Wigner negative volume of the photon-added/subtracted states. Whereas photon-added Gaussian states are never Wigner positive, we show that single-mode photon-subtracted states are Wigner positive if and only if they are weakly nonclassical or classical. Our analysis relies on explicit and general expressions for the characteristic and Wigner functions of photon added/subtracted multi-mode Gaussian states that we obtain simply.
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.