Effective tunneling coefficient of a coupled double-well system modulated by anharmonic periodic potentials

Abstract

We numerically study coherent tunneling oscillations of the particles between two levels in a double-well potential in the presence of anharmonic periodic potentials. Extremely short driving pulses modify the tunneling coefficient to ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}A$, where $\ensuremath{\kappa}$ is the bare tunneling coefficient without the driving field and $A$ is the pulse area of the driving wave form. The modulation amplitude of the ${\ensuremath{\kappa}}_{\mathit{eff}}$ gradually decreases as the driving wave form becomes broad and is given by ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}{J}_{0}(A)$ for the sinusoidal modulation, where ${J}_{0}(x)$ denotes the ordinary Bessel function of order zero. Theoretical derivation of the effective tunneling coefficient ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}A$ is also shown for a periodic $\ensuremath{\delta}$ kick with alternating sign by means of the transfer matrix formula.