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Physica Scripta

Non-classical properties and entanglement of two-mode nonlinear semi-coherent states

Azam Anbaraki, Davood Afshar

Published May 23, 2025• 3 citations
Publisher

Abstract

Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.

DOI
10.1088/1402-4896/addca5

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Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.
Quasi Bell states are introduced as a result of superposition of two-mode separable nonlinear coherent states. In this paper, we consider the nonlinearity function related to the harmonious states. To evaluate the effectiveness of these states in quantum information theory, nonclassical properties such as photon statistics, squeezing, and entanglement are studied. The entanglement of these states is examined by calculating the concurrence. According to our calculations, three of the introduced states are maximally entangled states. In addition, the cross-correlation function of the three maximally entangled states is less than 1 for all values of |α|2.
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Nonclassical features of entangled coherent states (two-mode superposition coherent states) based on two coherent states shifted in phase by π/2 are discussed. Analysis of Cauchy–Schwartz inequality, two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. Furthermore, it is also observed that special states have remarkably strong nonclassical properties than the entangled coherent states based on famous even–odd coherent states.
Coherent states are the quantum states, which give the closest description to classical states. Since their superpositions show quantum properties, research on these states has been of great interest. In addition, having nonclassical properties is necessary for quantum correlations. In this paper, we focus on two-mode entangled coherent states which are out of phase, and study the nonclassical properties such as squeezing of quadrature operators, antibunching and oscillatory photon statistics. Then we discuss about their entanglement, which is a quantum correlation in different conditions and compare the results.