Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

Abstract

Abstract. This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66 Ga.

Gaussian and sinc-shaped few-cycle-pulse-driven ultrafast coherent population transfer inΛ-like atomic systems

“…Hence the model proposed by us may be tested experimentally in atomic systems such as indium, thallium, and gallium. In passing, it may be noted that indium, thallium and gallium have been studied extensively both theoretically and experimentally in the context of laser cooling of atoms [43][44][45][46].…”

Radiation pressure on single atoms: generalization of an exact analytical approach to multilevel atoms

“…For N = 2 and ω 1 ≠ ω 2 , the system can be tackled in a continued fraction approach as in the two-level atom case [9], though with a matrix formalism. The Fourier components x (n) ξ that obey the infinite system (19) of equations subdivide in two decoupled groups: a first group of components of indices n = kn s (k ∈ Z) and the group of all remaining components (n ≠ kn s ), where n s = n 1 + n 2 , with n 1 and n 2 two positive coprime integers such that n 2 κ 1 = n 1 κ 2 . The components of the first group get coupled between each other through the system…”

“…In practice, purely numerical approaches are enforced in this case (see, e.g., Refs. [16][17][18][19][20][21][22]).…”