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WORLD SCIENTIFIC eBooks

Tunneling in Confining Symmetric and Asymmetric Double-Wells

Published Jan 1, 2003• 0 citations
Publisher
DOI
10.1142/9789812564887_0007

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We investigate the coherent control of a single particle held in a quartic double well with a symmetric or asymmetric driving and exhibit time evolutions of relative probability of the particle in one of the double-well wells. It is shown analytically and numerically that the coherent destruction of tunneling could occur only for the symmetric intense driving, and application of the asymmetric sawtooth driving leads to an increase in the tunneling rate. The results agree with the recent experimental data reported by Kierig et al. [Phys. Rev. Lett. 100, 190405 (2008)]. We also exhibit the effect of multiple photon resonances on the tunneling through a dc field. Finally, we demonstrate a connection between the classically chaotic barrier crossing and quantum tunneling numerically.
The motion of the center of a wave packet localized in one of the wells of an asymmetric double-well potential is studied. The asymmetric potential is obtained from a solvable symmetric potential using the Gel'fand–Levitan formalism, by keeping the energy eigenvalues unchanged, but changing the normalization of the ground-state wave function. While in a symmetric double well the wave packet tunnels back and forth between the two wells, for an asymmetric well, in general, tunneling does not take place. This is independent of the initial location of the wave packet, i.e., whether it is centered at the minimum of the shallower or of the deeper well. However, when such a system is coupled to a dissipative force, then the tunneling becomes possible. For instance it is shown that if, as a model of dissipative coupling, one chooses Gisin's nonlinear evolution equation, then the center of the wave packet ends up in the deeper well (decay of false vacuum). This result depends on the particular model of dissipation, for instance, an optical potential model yields a different result.