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Journal of Physics A Mathematical and General

Coherent Jaynes-Cummings dynamics modified by a quasi-instantaneous perturbation of the two-level system

Istok P. Mendaš

Published Oct 31, 2001• 3 citations
Publisher

Abstract

The coherent Jaynes-Cummings (JC) dynamics modified by a quasi-instantaneous perturbation of the two-level system is discussed, and the corresponding evolution operator is determined with the help of the anticommutator analogue of the Baker-Hausdorff lemma. The evolution operator leads to a coherent superposition of two JC evolutions, one with the original values of the coupling constant and detuning, and the other with the modified, effective values of these parameters followed (in the resonant case) by a phase pulse. This leads to various possibilities for controlling and modifying the final state of the harmonic oscillator depending on the choice of the initial state and the perturbing phase and on the instant the perturbation acts.

DOI
10.1088/0305-4470/34/44/103

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The coherent Jaynes-Cummings (JC) dynamics modified by a quasi-instantaneous perturbation of the two-level system is discussed, and the corresponding evolution operator is determined with the help of the anticommutator analogue of the Baker-Hausdorff lemma. The evolution operator leads to a coherent superposition of two JC evolutions, one with the original values of the coupling constant and detuning, and the other with the modified, effective values of these parameters followed (in the resonant case) by a phase pulse. This leads to various possibilities for controlling and modifying the final state of the harmonic oscillator depending on the choice of the initial state and the perturbing phase and on the instant the perturbation acts.
Reversing the JaynesndashndashndashCummings dynamics to measure decoherence
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
The exactly analytic solution of the coherent sbate Jaynes-Cummings (JC) model is derived for the detunings using the interaction picture. The atomic level occupation probabilities are investig-ated numerically as function of time and detuning parameter and initial mean photon number. For detuning parameter, the quantum collapse and revival phenomenon of the atomic level occupation probabilities is found. Interference between revival signals is discussed. The time evolution of the coherent states of field is studied numerically. It is discovered that the evolution of the state of field appears to be quasi-reversible for a short period of time. This is an interesting and important new phenomenon of JC model. Detailed discussion is presented.
Jaynes–Cummings (JC) models are by far the most widely used to study the dynamics of two-level systems, such as atoms or molecules under suitable conditions, coupled to quantized electromagnetic fields. Nowadays, analytical solutions of JC models are more useful than ever for understanding and controlling radiation-matter interactions relevant to quantum information processing, quantum computing, and other quantum technologies. This study presents the analysis and generalization of a method for the solution of the dynamical problem in the time-independent JC model (Carbonaro et al., 1979) that enables an exact description of the atom-field dynamics in the resonant time-dependent JC model and in a nontrivial class of off-resonance time-dependent JC models. Our analysis produces the ready-to-use forms of the evolution operator in the resonant and non-resonant cases, which are then used to derive the evolution of the atomic population inversion for some types of atom-field coupling. The central idea behind the proposed approach offers opportunities for its extension to other time-dependent cases and its generalization to JC-related models.
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.