Dissipative tunneling with periodic polychromatic driving: Exact results and tractable approximations Original Research Article

We investigate the long-time dynamics in dissipative two-level-systems (TLS) when driven by — monochromatic or pulse-shaped — periodic fields. The environmental influence is investigated within the noninteracting-blip approximation (NIBA), while no restrictions are assumed on the driving force. With the focus being on electron-transfer (ET) reactions in condensed media, we consider a continuous Ohmic spectrum for the bath modes. The asymptotic dynamics exhibits always the periodicity of the external force. The induced oscillations show a smooth periodic behavior which becomes richer, if, for example, multiphoton resonances occur. For monochromatic driving, the oscillatory multiresonance pattern becomes gradually smoothed out when the temperature, and/or the Ohmic strength are sufficiently high. It may persist, however, for pulse-shaped driving. Exact NIBA analytical and/or numerical solutions, for both the Ohmic transfer rate and for the driven dynamics, are used to determine the validity range of the short-time approximation for the bath correlation functions. The latter is frequently employed to investigate the ET dynamics. Our analysis shows that the short-time approximation may give qualitative incorrect results at low temperatures.