Transition width between two metastable states

Landau-Zener problem with decay and dephasing

“…This kind of plot was first suggested in Ref. [5]. The figure clearly shows that e βT P (T ; λ, β, β) is independent of β.…”

“…The factor −i(β 1 + β 2 ) appears in both eigenvalues and affects the decay dynamics by introducing exponential decay of the time-dependent wave function [5]. When |β 1 − β 2 | ≥ 4λ the eigenvalues cross.…”

“…First, we focus on the case where one or both of the energy levels decay. The motivation for studying the effects of level decay on the LZ probability is that decay occurs in many physical processes, including light-induced transitions between metastable states [5], collision-induced losses of laser-cooled atoms in magneto-optical traps [6,7], photoassociative ionization collisions in a magneto-optical traps [8], and adiabatic fast passage in nuclear magnetic resonance population inversion processes in the presence of radio-frequency magnetic fields [9], to mention a few. Level decay can be modeled by letting the diagonal elements of the Hamiltonian acquire a time-independent negative imaginary part, Im[H ii ] = −Γ i /2, where Γ i / is the decay rate of level i, (i = 1, 2).…”

“…Transitions between decaying states were analyzed both using a master equation approach and by adding a decay term to the Hamiltonian in Ref. [5].…”

“…Work on related problems has been reported in Refs. [5,7,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], Refs. [27][28][29] consider a LZ transition for two states coupled to a bath of harmonic oscillators, and Refs.…”