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Influence of a Non-Linear Interaction and Kerr Medium on the Emission Spectrum and Entropy Squeezing of Su(1,1) Algebra with Single Qubit

Maged Faihan Alotibi

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.2139/ssrn.4113671

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Influence of a non-linear interaction and Kerr medium on the emission spectrum and entropy squeezing of Su(1,1) algebra with single qubit

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The interaction of a quantum algebraic system su(1,1) interacting with a qubit is studied. A nonlinear function has been added to interaction with the presence of Kerr medium (KM). The general solution is obtained using the constants of motion and Heisenberg equation for the time-evolution operator. The effects of the nonlinear function and KM on the emission spectrum and entropy squeezing are calculated. The results showed that the emission spectrum is affected by the nonlinear function. Symmetric peaks are generated around the vertical axis with increasing influence of the nonlinear function. By activating the role of the KM, the emission spectrum loses symmetry around the vertical axis and the maximum values decrease. Moreover, the KM reduces the squeezing intervals, while the squeezing intervals are improved by increasing the effect of the nonlinear function.

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Nonlinear squeezed states for SU(1,1) Lie algebra

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The European Physical Journal D•Aug 31, 2006•6 citations
The interaction of a quantum algebraic system su(1,1) interacting with a qubit is studied. A nonlinear function has been added to interaction with the presence of Kerr medium (KM). The general solution is obtained using the constants of motion and Heisenberg equation for the time-evolution operator. The effects of the nonlinear function and KM on the emission spectrum and entropy squeezing are calculated. The results showed that the emission spectrum is affected by the nonlinear function. Symmetric peaks are generated around the vertical axis with increasing influence of the nonlinear function. By activating the role of the KM, the emission spectrum loses symmetry around the vertical axis and the maximum values decrease. Moreover, the KM reduces the squeezing intervals, while the squeezing intervals are improved by increasing the effect of the nonlinear function.
In the present communication, we consider the problem of two quantum systems with the Kerr-like medium nonlinearity. The system is cast form of an interaction between two operators of the form su(1,1) Lie algebra and su(2) Lie algebra. We obtain the wave function via the evolution operator where we use the Heisenberg equations of motion to derive the constants of motion. We discuss the atomic inversion. It is found that the Kerr-like medium decreases the amplitude and increases the fluctuations. Also we consider different types of squeezing, it is shown that the entropy squeezing is pronounced in the second quadrature, but it shows a small amount in the first quadrature. For the variance squeezing, a small amount occurs in the presence of the Kerr-like medium. However, the normal squeezing occurs in the first quadrature where the squeezing is sensitive to both the Kerr-like medium parameter and the initial state. Furthermore, the degree of entanglement is examined through the linear entropy. It is shown that the function decreases besides rapid fluctuations. The correlation function displays nonclassical behavior in addition to an increase in the amplitude of the fluctuations.
In the language of quantum information theory we study the entropy squeezing of a two-level atom in a Kerr-like medium. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining the entropy squeezing of a two-level atom with a Kerr-like medium. The influence of the non-linear interaction of the Kerr medium, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables is examined.