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Results in Physics

Nonclassicalities of two-mode photon‑added coherent states

Hassan Sobhani, Hoda Lotfipoor, Mohamad Taghi Dejpasand

Published Nov 1, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2025.108507

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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.
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.
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 a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.
Abstract We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations .
Abstract The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.