The magnitude of tunneling splitting, $3\Gamma$, that governs decoherence in quantum systems under symmetric potentials, is frequently unknown. Using first-principles calculations, we have obtained $3\Gamma$ for a number of $E\otimes e$ Jahn-Teller impurities in solids. Calculated values span 6 orders of magnitude on passing from $\mathrm{KCl}:{\mathrm{Ag}}^{2+}$ to $\mathrm{MgO}:{\mathrm{Cu}}^{2+}$. Values associated with ${\mathrm{Cu}}^{2+}$- and ${\mathrm{Ag}}^{2+}$-doped MgO are 2 orders of magnitude larger than those previously assumed and consistent with the existence of a dynamic Jahn-Teller effect. The origin and enhancement with pressure of these high $3\Gamma$ values is discussed in detail.

• Received 31 July 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.035901