Exact solution for the dynamics of two- and three-level systems (A)

W. Zwerger

Christopher C. Gerry

The population of a three-level system in the lambda configuration interacting with three classical fields is studied. The system is essentially a Raman coupled system with pump, Stokes and anti-Stokes fields. One channel between the two ground states involves the pump and Stokes field while the other involves the pump and anti-Stokes field. Since exact solutions are not generally available the author studies the dynamics numerically. But when the excited state is highly detuned, it may be adiabatically removed so that the system becomes effectively a two-level system but with an effective Rabi frequency that depends on the relative phases of the driving fields. For some choices of the phases this frequency can be made to vanish, an effect of the interference between the two channels. For the special case of equal and opposite detunings, an exact solution of the full three-level equations is presented. The effects of ionization of the excited state are also briefly considered.

W. Zwerger

Xiaoyun Wang, Bang-Fu Ding, Jinfeng Liu +2 more

The reduced dynamics of a V-type three-level atom in a structure reservoir is presented, which has the exact solution in certain special condition. The Markovian and non-Markovian master equations for this composite system are solved and compared with the exact solution. The solving approach can be directly generalized to the solution of a V-type multilevel system dynamics interacting with a reservoir. The results further testify that these two kinds of master equations are exploited in different coupling regime, providing guidance for further application of these variants master equations to solve multilevel system dynamics without the exact solution.

M. B. Kenmoe, S. E. Mkam Tchouobiap, C. Kenfack-Sadem +2 more

We investigate the Landau–Zener (LZ) like dynamics of decaying two- and three-level systems with decay rates Γ 1 and Γ 2 for levels with minimum and maximum spin projection. Non-adiabatic and adiabatic transition probabilities are calculated from diabatic and adiabatic bases for two- and three-level systems. We extend the familiar two-level model of atoms with decay from the excited state out of the system into the hierarchy of three-level models which can be solved analytically or computationally in a non-perturbative manner. Exact analytical solutions are obtained within the framework of an extended form of the proposed procedure which enables to take into account all possible initial moments rather than large negative time t 0 = − ∞ as in standard LZ problems. We elucidate the applications of our results from a unified theoretical basis that numerically analyzes the dynamics of a system as probed by experiments.

K. Lendi