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Chinese Physics Letters

A Lower Bound on the Entanglement in the Jaynes-Cummings Model

蔡金芳, 邹健

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.

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The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.
The entanglement between an atom and field is investigated by using the Jaynes–Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r .
In this paper, by using the notion of negativity, we study the degree of entanglement of a two-level atom interacting with a quantized radiation field, described by the Jaynes–Cummings model (JCM). We suppose that initially the field is in a pure state and the atom is in a general mixed state. In this case the negativity fully captures the entanglement of the JCM. We investigate the case that the initial state of the field is a coherent state. The influences of the detuning on the degree of entanglement are also examined.
We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an arbitrarily high temperature. We find the time and temperature variation of a lower bound on the amount of entanglement produced and study the classical correlations quantified by the mutual information.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.
The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.