Non-Markovian effects in stochastic resonance in a two level system

Stochastic resonance is a phenomenon where the response signal to external driving is enhanced by environment noise. In quantum regime, the effect of environment is often intrinsically non-Markovian. Due to the combination of such non-Markovian quantum noise and external driving force, it is difficult to evaluate the correlation function and hence the power spectrum. Nevertheless, a recently developed algorithm, which is called time-evolving matrix product operators (TEMPO), and its extensions provide an efficient and numerically exact approach for this task. Using TEMPO we investigate non-Markovian effects in quantum stochastic resonance in a two level system. The periodic signal and the time-averaged asymptotic correlation function, along with the power spectrum, are calculated. From the power spectrum the signal-to-noise ratio is evaluated. It is shown that both signal strength and signal-to-noise ratio are enhanced by non-Markovian effects, which indicates the importance of non-Markovian effects in quantum stochastic resonance. In addition, we show that the non-Markovian effects can shift the peak position of the background noise power spectrum.