We have found an analytical expression describing the evolution of a two-level system in a strong resonant quantum field beyond the rotating wave approximation. The solution obtained has allowed us for the first time to identify the qualitative features of the behavior of the system in this case: suppression of the "collapse-revival" effect, and a change in the spectrum and shape of Rabi oscillations for an inverted population. The results are of interest for applied spectroscopy, quantum optics, and nanomechanics.Introduction. At the present time, considerable attention is focused on experimental study of the interaction between various quantum objects (atoms, quantum dots, impurity centers, etc.) and resonant external fields, making it possible to control the characteristics of these systems [1][2][3]. Such studies are of considerable importance for spectroscopy [4], quantum optics [5, 6], nanomechanics [7], and other applications. The dimensionless coupling constant f between the system and the field as well as the average number of photons n 0 in the resonant mode vary over a very broad range [8][9][10]. In particular, even for relatively small f but in strong fields, the parameter defining the ratio of the Rabi frequency Ω to the field frequency ω, ξ = Ω ⁄ ω ≈ 2f√ ⎯⎯ n 0 , can be rather large [11] and, as has been shown in many papers, for quantitative analysis of experiments in this area, we need to go beyond the rotating wave approximation (see, for example, [12][13][14]). In the case n 0 >> 1, the field is usually considered as classical, but the influence of quantum effects and the possibility of using the rotating wave approximation when describing the evolution in such a limit have not been sufficiently completely studied. Therefore a number of experimental results in this area have still not been theoretically explained [11].Accordingly, development of methods for numerical and analytical description of the evolution of a two-level system in a resonant quantum field, applicable over the entire range of variation in its parameters, remains a timely problem. A uniformly valid method for calculation of stationary states for such a system is proposed in [15,16]. In this paper, a similar approach is generalized for calculation of the exact quantum operator for evolution of the system. Numerical modeling and analytical study of the time variation of the population of states of the system in a strong quantum field were done beyond the rotating wave approximation. This allowed us to give a theoretical description of new effects in evolution of a two-level system for ξ >> 1: suppression of "collapse-revival" processes, and a qualitative change in the shape and spectrum of the oscillations in the population compared with Rabi oscillations. The considered effects are consistent with the experimental results presented in [11].Uniformly Valid Approximation for Stationary States in the Rabi Model. The Hamiltonian for a two-level system in a single-mode quantum field (the Rabi model) is well known [17]: