Revivals for a two-level atom in a free space under bichromatic excitation

Abstract

A two level atom in a free space excited by a bichromatic symmetrical field is shown to display the property of revivals for relatively small frequency detunings and a large driving field amplitude. The property of revivals is a bright physical phenomenon which is usually associated with the quantum properties of an atom-field interactions in the framework of the Jaynes-Cummings model [1]. In fact this phenomenon predicted in [2] has been observed by Herbert Walther with coworkers in 1987 [3] for a single two-level atom interacting with a quantized field mode in a high-Q cavity. Mathematically the revivals arise as a result of the quasi-equidistant spectrum of the Jaynes-Cummings Hamiltonian for a large number of photons in the mode and the peak-like form of the Fourier spectrum of atomic and field variables at the initial coherent state for the field mode. But it is obvious that there are other physical systems with the same spectral properties, and therefore they can exhibit revivals too. As we show in this Letter one of such systems is a bichromatically driven two-level atom in a free space, and what's more, the driving field is classical.The problem of bichromatically driven two-level atom dynamics and spectra has received considerable attention since the 70's. Initial and subsequent works in this area indicate that the system presents qualitatively new types of spectral [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and dynamical [22][23][24][25][26][27] behavior compared with the monochromatic excitation. The main activity has been concentrated on spectral peculiarities connected with subharmonic resonances [8]. Dynamical properties of the system have received much less attention. For example, it has been predicted [22,23] and observed [27] that bichromatically driven atoms exhibit dynamical behavior that's strongly dependent on the relative phase of the excitation field components.In this Letter, we report a new type of dynamical behavior of a bichromatically driven two-level atom which can be observed for the special case wherein the field components have very small frequency detunings from atomic resonance and the intensities of both components are strong enough. For this case many spectral components of the atomic variables are exited with a definite phase relations between them. As a result, synchronization (in other terminology, constructive interference) between the components occurs at definite moments, giving the revivals in the temporal behavior of the atomic variables.Let a two-level atom driven by a bichromatic coherent field with amplitudeinteract with a continuum of electromagnetic free field modes which are in the vacuum state. The atom also interacts with a relaxation bath that leads to an additional dephasing of the atomic polarization. We restrict ourselves to the simplest case of bichromatic excitation -with equal amplitudes of the field components (E 1 = E 2 = E 0 ) and symmetrically located field frequencies ω 1 − ω 21 = ω 21 − ω 2 = , where ω 21 is the ato...