finite energy spread to the Pauling manifold [@Vedmedenko] (here of order $\sim$0.1 K [@Melko]). The mechanism of the hop is believed to be quantum tunnelling and several key signatures of this have been observed in the high temperature regime between 2 K and 10 K [@Ehlers; @Snyder; @JaubertHoldsworth; @Bovo; @Tomasello].

At lower temperatures ($T < 0.6$ K), spin ice starts to freeze [@Snyder]. This is due in part to the rarefaction of the monopole gas whose density $n(T)$ varies as $\sim e^{-|\mu|/T}$ where the chemical potential $|\mu| = 4.35 $ and 5.7 K for [Dy$_{2}$Ti$_{2}$O$_{7}$]{} and [Ho$_{2}$Ti$_{2}$O$_{7}$]{} respectively [@CMS], and also in part to geometrical constraints that create noncontractable, monopole-antimonopole pairs that cannot easily annihilate [@noncontractable]. These factors, which are independent of the monopole hopping mechanism, suggest that the relaxation rate $\nu(T) \propto n(T)$ will fall to exponentially small values at low temperature ($T~<~ 0.35$ K).

Previous thermal quenching experiments have demonstrated monopole populations well below the nominal freezing temperature that are both long lived and able to mediate magnetic relaxation [@PaulsenAQP]. This paradoxical frozen but dynamical character of the system suggests the relevance of resonant magnetic tunnelling, where magnetisation reversal can only occur when the longitudinal field is smaller 