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 Schrödinger 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 $ΔU$, (ii) a resonant tunneling with $|ΔU| \simeq κ\:\hbar ω$ is realized for motion starting from upper minimum of asymmetric potential wells, but not for motion from lower minimum, ($κ=0,1,2,...$; $ω$: 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 $<δx^2> <δp^2>$ 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.