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East European Journal of Physics

Nonclassicalities of the Superposition State of Coherent and Photon-Added-Coherent State

Sandip Kumar Giri

Published Mar 5, 2024• 3 citations
Publisher

Abstract

The nonclassical properties of the hybrid coherent state (HCS), which is the superposition state of the coherent state and photon-added coherent (PAC) state, is investigated analytically. We evaluated the photon number statistics, the Wigner-Yanase skew information, the Mandel Q factor and the quadrature squeezing of the HCS to quantify its nonclassicality. This superposition state exhibits more nonclassical properties than the PAC state and even the superposition state of coherent state and single-photon-added coherent (SPAC) state. We reported that the addition of more photons to the PAC state part of the HCS generally quantifies more nonclassicalities. The nonclassical properties of the HCS also depend on the amplitudes of coherent state and the PAC state in the HCS.

DOI
10.26565/2312-4334-2024-1-12

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The nonclassical properties of the hybrid coherent state (HCS), which is the superposition state of the coherent state and photon-added coherent (PAC) state, is investigated analytically. We evaluated the photon number statistics, the Wigner-Yanase skew information, the Mandel Q factor and the quadrature squeezing of the HCS to quantify its nonclassicality. This superposition state exhibits more nonclassical properties than the PAC state and even the superposition state of coherent state and single-photon-added coherent (SPAC) state. We reported that the addition of more photons to the PAC state part of the HCS generally quantifies more nonclassicalities. The nonclassical properties of the HCS also depend on the amplitudes of coherent state and the PAC state in the HCS.
One of the most promising nonclassical states in the context of quantum optics are hybrid coherent states, which include a combination of coherent states and single-photon-added coherent states. Although hybrid coherent states have been proposed and experimentally generated in various forms, the realization of two-mode hybrid coherent states is still lacking. Here, two-mode hybrid coherent states are introduced by employing two nonlinear optical Kerr media. The two-mode hybrid coherent states can be applied in quantum information and communication applications. In this paper, we investigate the key nonclassical properties of hybrid coherent states, such as photon statistics, the Mandel factor, and Wigner function negativity.
Abstract Pair coherent states (PCSs) as a kind of two-mode non-Gaussian and nonclassical states were introduced and studied. Some nonclassical characteristics of them such as two-mode sum-squeezing, two-mode antibunching, and entanglement have been well investigated. In this paper, we focus on studying the superposition of photon addition and subtraction to the PCSs called superposition of photon-added and photon-subtracted pair coherent states (SPAPSPCSs). Our main purpose is to show that the non-Gaussian feature and all the above-mentioned nonclassical properties of the SPAPSPCSs can be enhanced compared with the photon-added-and-subtracted two modes pair coherent states (PAASTMPCSs) and the original PCSs. In general, we demonstrate that the SPAPSPCSs have more enhanced non-Gaussian character and nonclassical properties than the PCSs and the PAASTMPCSs by examining the negativity of the Wigner function. Specifically, we indicate that both the SPAPSPCSs and the PAASTMPCSs can exist in two-mode sum-squeezing while the original PCSs (without photon-addition and photon-subtraction) cannot, and the degree of squeezing is stronger in the SPAPSPCSs than in the PAASTMPCSs. The obtained results also indicate that the superposition of photon addition and subtraction of the SPAPSPCSs plays a vital role in enhancing the two-mode antibunching property and the entanglement degree compared with the PCSs and the PAASTMPCSs.
The addition of a photon into the same mode as a coherent state produces a nonclassical state that has interesting features, including quadrature squeezing and a sub-Poissonian photon-number distribution. The squeezed nature of photon-added coherent (PAC) states potentially offers an advantage in quantum sensing applications. Previous theoretical works have employed a single-mode treatment of PAC states. Here, we use a continuous-mode approach that allows us to model PAC state pulses. We study the properties of a single-photon and coherent-state wave packet superimposed with variable temporal and spectral overlap. We show that, even without perfect overlap, the state exhibits a sub-Poissonian number distribution, second-order quantum correlations, and quadrature squeezing for a weak coherent state. We also include propagation loss in waveguides and study how the fidelity and other properties of PAC state pulses are affected.
Abstract We present a theoretical study on the generation and nonclassical properties of hybrid squeezed states (HSS), a class of engineered quantum states with enhanced quantum features. Using a modified beam splitter-Kerr medium scheme, we construct superpositions of squeezed vacuum and two-photon-added squeezed states, providing a flexible framework to generate and control hybrid quantum states. Nonclassicality is analysed via Mandel's QQQ parameter, photon number distributions, probability distribution functions, and Wigner functions, revealing sub-Poissonian statistics, oscillatory photon distributions, and significant Wigner negativity. Phase-sensitivity analysis within a Mach-Zehnder interferometric framework demonstrates that HSS outperform conventional squeezed and photon-added squeezed states, achieving measurement precisions that exceed the standard quantum limit and approach the Heisenberg limit under optimal parameters. These results establish hybrid squeezed states as a powerful resource for quantum metrology, communication, and optical interferometry.
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.