Quantum Stochastic Synchronization

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength $\alpha >1$) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes.

Figure 1

(a)–(c) Stochastic frequency of quantum tunneling jumps ${\overline{\Omega }}_{\mathrm{ph}}$, phase-diffusion coefficient ${\overline{D}}_{\mathrm{ph}}$, and the synchronization quality factor $R$ vs the scaled temperature $\kappa =k_{B}T/\hslash {\omega }_c$ for two values of the angular driving frequency $\Omega$. (d) Quality factor $R$ vs driving frequency $\Omega$ at the fixed temperature $\kappa =0.3$ and for four driving strengths ${ϵ}_0=1$, 2, 3, and 5. The arrows indicate the resonant driving frequencies which are expected from matching the inverse tunneling rate $1/W_{+}({ϵ}_0)$ with the driving half-period, i.e., $\pi W_{+}={\Omega }_{\mathrm{SR}}$. The used parameter values are $\alpha =10$, $\Delta =4\times {10}^{-4}$, and ${ϵ}_0=5$ (a)–(c). The frequencies are scaled with ${\omega }_c$ and the energies with $\hslash {\omega }_c$. For $\hslash {\omega }_c=12.5\mathrm{meV}$, ${\omega }_c\approx 1.9\times {10}^{13}1/\sec $, and $r=14.9\AA$ (chosen to match the charge transfer in molecules from Ref. 19), one obtains a field strength of ${\mathcal{E}}_0\approx 4.19\times {10}^4\mathrm{V}/\mathrm{cm}$. The value $\kappa =1$ corresponds to $145\mathrm{K}$.