Tunneling between two inequivalent potential wells

George N. Gibson, Gerald V. Dunne, K. J. Bergquist

Boris I. Ivlev

Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. A periodic structure of the wave function is formed in the direction joining the wells. The resulting motion can be coherent like motion in a conventional narrow band periodic structure. A particle penetrates the barrier over a long distance which strongly contrasts to WKB-like tunneling. The whole problem is stationary. The coherent process can be influenced by dissipation.

Marlin D. Harmony

重貴 松本

Ming-Jer Lee, Thomas M. Antonsen, Edward Ott +1 more

Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.

S.K. Dutta, Boon-Keng Kevin Teo, Georg A. Raithel

Summary form only given. It has been predicted that topological potentials play a significant role in gray optical lattices. However, so far there has been no direct experimental demonstration of their existence. Unlike light-shift potentials, which, in the case of low saturation, scale as the laser intensity, topological (or gauge) potentials are intensity independent and solely depend on the topology of the lattice, which is determined by the detuning, beam geometry and magnetic fields. In our experiment, /sup 87/Rb atoms are collected in a standard magneto-optic trap and loaded into a 1D optical lattice. The lattice is formed by counterpropagating, orthogonally polarized laser beams. The minima of the trapping potential form at the antinodes of the standing waves and, as a result of optical pumping, the wells are alternately occupied. When an atom tunnels from one type of well to another, it must then flip its magnetic spin state. The gauge potential is associated with the energy needed for this change. In this gray lattice, the potential wells are shallow due to the weak interaction with the light field. Shallow potentials are necessary for tunneling. We use two schemes to observe tunneling. In the first, we use an auxiliary weak laser pulse to selectively depopulate one of the two types of wells. We observe tunneling by measuring the population in each type of well as a function of time. The second way we study tunneling is to create atomic wave-packets within the wells and to observe their motion as they oscillate. The wave-packets are created by diabatically displacing the trapped atoms in either position or momentum space. Tunneling occurs when the wave-packets run against barriers provided by the maxima of the trapping potential.