Dynamics of a dissipative two level system. Pt. 2

The problem of quantum coherence in a symmetric double well potential with a dimensionless damping coefficient α for classical motion is studied within a spin 1/2-boson model. The experimentally measured probability p(t) of refinding a definite initial state after time t is approximately expressed by the transverse spin relaxation function phi(t), which is determined from a three-pole approximation, that incorporates both the correct long and short time behaviour. For a bare tunnelsplitting Δ small compared to the heat bath cutoff ωsub(c) we find, that the oscillating component of phi(t) is negligible compared to the relaxational one unless α is of order Δ/ωsub(c). Thus p(t)approx.=(1+exp(-νt))/2 with a mean tunneling rate ν proportional to Δ=Δ(Δωsub(c))a/2-a for α<2 and T<<Δ and proportional to Δ2/ωsub(c)x(T/ωsub(c))sup(α-1) otherwise. The results apply directly to recent measurements of the dynamics of flux states in a SQUID. (orig.)