Gaussian wavepacket dynamics and quantum tunneling in asymmetric double-well systems

Abstract

We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schr\"{o}dinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. Time dependences of wavefunction, averages of position and momentum, the auto-correlation function, an uncertainty product and the tunneling probability have been calculated. Our calculations have shown that (i) the tunneling probability is considerably reduced by a potential asymmetry $\Delta U$, (ii) a resonant tunneling with $|\Delta U| \simeq \kappa \:\hbar \omega$ is realized for motion starting from upper minimum of asymmetric potential wells, but not for motion from lower minimum, ($\kappa=0,1,2,...$; $\omega$: oscillator frequency at minima), (iii) the reduction of the tunneling probability by an asymmetry is less significant for the Gaussian wavepacket with narrower width, and (iv) the uncertainty product $<\delta x^2> <\delta p^2>$ in the resonant tunneling state is larger than that in the non-resonant tunneling state. The item (ii) is in contrast with the earlier study [Mugnai {\it et al.}, Phys. Rev. A {\bf 38} (1987) 2182] which showed the symmetric result for motion starting from upper and lower minima.