From periodically driven double wells to volcano potentials: Quantum dynamics

Abstract

We consider the dynamics of a particle confined in a double well potential which is subjected to a periodic drive. In the case of deep and well separated wells, we find that by adjusting the parameters of the drive we can generate, to a very good approximation, a volcano potential. The quantum dynamics in this volcano potential is studied by a variation of what can be called a generalized Ehrenfest's theorem. We find that the coupling of the mean position and the width of the wave packet in this dynamics causes the particle to escape from the central well in accordance with the fact that the volcano potential only supports resonance states.

Fast driven quantum systems: interaction picture and boundary conditions

“…with boundary conditions (38), and with an upward convex potential V(x) inside this box, can be approximately considered as a particle in a double well. For example, a double well potential may be given by U(x) = − m ω 2 x 2 /2 + λ mx 4 /4 [30]. The authors considered the dynamics of a particle cofined in such a double well potential which is subjected to a periodic drive, so that the Hamiltonian is given by H = p 2 /2m + (1 + ò f (t))U(x).…”

“…ò ω 2 . Then, by adjusting the parameters of the drive, an effective volcano potential can be generated [30], as in our example.…”