Phonon-induced relaxation of a two-state system in solids

We study phonon-induced relaxation of quantum states of a particle (e.g., electron or proton) in a rigid double-well potential in a solid. The relaxation rate due to Raman two-phonon processes has been computed. We show that in the two-state limit symmetry arguments allow one to express these rates in terms of independently measurable parameters. In general, the two-phonon processes dominate relaxation at higher temperature. Due to parity effects in a biased two-state system, their rate can be controlled by the bias.

Figure 1

Raman process on tunnel-split levels in a double-well potential, including virtual transitions to higher levels $E_{\xi }$ [the first term in Eq. (24) shown].