Survival Probabilities in Coherent Exciton Transfer with Trapping

In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the Hamiltonian. For linear systems and at intermediate times the decay obeys a power law, in contrast with the corresponding exponential decay found in incoherent continuous-time random walk situations. To differentiate between the coherent and incoherent mechanisms, we present an experimental protocol based on a frozen Rydberg gas structured by optical dipole traps.

Figure 1

Imaginary parts ${\gamma }_l$ (dots) in ascending order for $N=100$ and $\Gamma =1$. Note the shortened $y$ axis. The inset shows ${\gamma }_l$ in log-log scale for $l=10,\dots ,90$.

Figure 2

Temporal decay of ${\Pi }_M(t)$ (solid black lines) and $P_M(t)$ (short dashed green lines) for $N=100$ and $\Gamma =1$ in double logarithmic scales (upper three curves) and in logarithmic scales (lower three curves). Indicated are the fits to ${\Pi }_M(t)$ (long dashed lines) in the intermediate (upper, red curve) and the long (lower, blue curve) time regime.

Figure 3

$N$ dependence of ${\Pi }_M(t)$ for $\Gamma =1$; $N$ increases in steps of 10 from 20 (blue line) to 100 (green line). The inset shows ${\Pi }_M(t)$ versus the rescaled time $t/N^{3-\mu }$.

Figure 4

$\Gamma$ dependence of ${\Pi }_M(t)$ for intermediate $t$ and $N=50$.