In the quest for signatures of coherent energy transfer we consider the trapping of excitations in frozen Rydberg gases within the continuous-time quantum walk (CTQW) framework. The dynamics takes place on a discrete network of N sites. Out of the N sites we assume M<N sites to be traps and incorporate those phenomenologically into the CTQW formalism by a trapping operator, which leads to a new, non-hermitian Hamiltonian The average CTQW survival probability for an excitation not to be trapped after some time t follows from the transition probabilities to go from site j to site k. For small M/N we show that the survival probability displays different decay domains, related to distinct regions of the (imaginary part of the) spectrum of the Hamiltonian. In the asymptotic limit, where t becomes large, this leads in most cases to a simple exponential decay. However, this is not the case at intermediate, experimentally relevant times. We examplify our analysis with a discrete linear system of N sites with traps at each end (sites 1 and N, M=2). In this case the decay at intermediate times obeys a power-law, which strongly differs from the corresponding classical exponential decay found in incoherent continuous-time random walk (CTRW) situations. Moreover, we show that in this time domain the survival probability scales with N and is basically independent of the coupling strength between traps and non-trap sites. In order to investigate the intermediate time domain and to differentiate between the CTQW and CTRW mechanisms, we present an experimental protocol based on a frozen Rydberg gas structured by optical dipole traps.

Refs:

arXiv:0705.3700