Resonant retuning of Rabi oscillations in a two-level system

Abstract

UDC 535.14 The evolution of a two-level system in a single-mode quantum field is considered beyond the rotating wave approximation. The existence of quasi-degenerate energy levels is shown to influence the essential charac- teristics of temporal and amplitude Rabi oscillations of the system in a resonant manner. Introduction. The Jaynes-Cummings model (JCM) is currently undergoing a second birth due to its use to describe the interaction of the elementary quantum cell (two-level atom) with a quantum electromagnetic field in a cavity (2). The actual physical manifestation of such a structure can be varied (resonant transitions in atoms, quantum dots, impurity centers, etc.). However, the use of the JCM in any instance enables its qualitative features to be de- scribed. The applied significance of the JCM in spectroscopy and quantum optics is due to the ability to describe based on it the population change dynamics of quantum system states upon the reception, retention, and transfer of information (3, 4). The most common approaches to a theoretical study of the evolution of the JCM are based on the rotating wave approximation (RWA) and Bloch equations in which the quantum field is replaced by a classical one. A char- acteristic system property in this instance is the so-called Rabi oscillations, periodic changes with time of the popula- tion of atomic states (5). Analogous oscillations were recently observed also for the population as a function of the field amplitude, Rabi amplitude oscillations (RAO). This has applied significance for controlling the quantum system (6 and references therein). It was recently shown (7) that consideration of the non-Markovian nature of the evolution of the two-level atom in an external periodic field leads to damping of RAO. The energy dissipation process in the cavity as an open system was viewed as the physical reason for the change of RAO. Herein it is demonstrated that population amplitude oscillations can behave analogously due to another physical effect that is essentially quantum in nature. It is due to quasi-interchange of JCM energy levels that arise on exceeding the limits of the RWA (8, 9) and is resonant in nature with respect to the amplitude field. An analysis of the relationship between these effects under actual experimental conditions is important for understanding the role of anti-rotational terms in the JCM Hamiltonian and a correct de- scription of the system evolution. Quasi-Interchange of JCM Energy Levels. Let us examine the JCM Hamiltonian