Theory of coherent one- and two-photon interaction in a three-level system

S. Boublil, A. D. Wilson‐Gordon, Harry Friedmann

We study the correlation between level populations, absorption and two-photon coherence in closed Λ- and V-shaped three-level systems interacting with two lasers of arbitrary intensity. Whereas it is well known that maximum two-photon coherence leads to population trapping in Λ-shaped three-level systems interacting with two equally detuned lasers, we demonstrate that minimum two-photon coherence, under saturation conditions, can lead to equal populations in all the levels of a Λ- or V-shaped system when the lasers are symmetrically detuned. Moreover we show that steady-state population inversion between one of the upper levels of a V-shaped system and the ground state can occur when either the detunings are asymmetrical or the upper states decay at different rates. It is shown that this population inversion does not lead to stimulated emission into the lasing modes. These effects are also correlated with two-photon coherence and are explained physically by a cross three-photon scattering process involving two laser photons of different frequencies.

Nikolay N. Bogolubov, Fam Le Kien, A.S. Shumovsky

Sophia E. Economou, Ren‐Bao Liu, Lu Jeu Sham +1 more

In a $\ensuremath{\Lambda}$ system with two nearly degenerate ground states and one excited state in an atom or quantum dot, spontaneous radiative decay can lead to a range of phenomena, including electron-photon entanglement, spontaneously generated coherence, and two-pathway decay. We show that a treatment of the radiative decay as a quantum evolution of a single physical system composed of a three-level electron subsystem and photons leads to a range of consequences depending on the electron-photon interaction and the measurement. Different treatments of the emitted photon channel the electron-photon system into a variety of final states. The theory is not restricted to the three-level system.

Leonid A Bol'shov, Anatoly P. Napartovich

Tak‐San Ho, Shih‐I Chu

The SU(3) dynamical evolution of three-level systems at two-photon resonance induced by two strong linearly polarized monochromatic fields is studied exactly by means of the semiclassical many-mode Floquet theory (MMFT) recently developed by the authors. Within the rotating-wave approximation (RWA), Hioe and Eberly have recently shown that the eight-dimensional SU(3) coherent vector S\ensuremath{\rightarrow} characterizing the time evolution of three-level systems can be factored into three independent vectors of dimensions three, four, and one, at appropriate two-photon resonance conditions. In practice, however, if the laser-atom interactions occur away from the two-photon resonance, or if the RWA is not valid, etc., this Gell-Mann--type SU(3) dynamical symmetry will be broken. It is shown in this paper that instead of solving the time-dependent generalized Bloch equations, the SU(3) dynamical evolution of the coherent vector S\ensuremath{\rightarrow} as well as various symmetry-breaking effects can be expediently studied by the use of the MMFT and expressed in terms of a few time-independent quasienergy eigenvalues and eigenvectors. Furthermore, we have extended the generalized Van Vleck (GVV) nearly degenerate perturbation theory to an analytical treatment of the two-mode Floquet Hamiltonian. This reduces the infinite-dimensional time-independent Floquet Hamiltonian into a 3\ifmmode\times\else\texttimes\fi{}3 effective Hamiltonian, from which useful analytical properties of the SU(3) coherent vector can be easily obtained. The combination of the MMFT and the GVV method thus greatly facilitates the study of the dynamical evolution. Pictorial comparison of the exact and the RWA results of the time evolution of the eight-dimensional coherent vector under several different physical conditions is presented and discussed at length.