Switching of Geometric Phase in Degenerate Systems

The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the system possesses degenerate levels, the geometric phase becomes anomalous, undergoing a sign switch. A physical system to which the results apply is a molecular dimer with two interacting electrons. Additionally, the sudden switching of the geometric phase promises to be an efficient control in two-qubit quantum computing.Comment: 15 pages, 4 figures,accepted by Physics Letters A (2000

Generalized "Quasi-classical" Ground State for an Interacting Two Level System

We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the lowest pair of electronic states, approximate "vibronic" (vibration-electronic) ground state wave functions are constructed having the form of simple, closed expressions. The basis of the method is to regard electronic density operators as classical variables. It extends an earlier "guessed solution", devised for the dynamical Jahn-Teller effect in cubic symmetry, to situations having lower (e.g., dihedral) symmetry or without any symmetry at all. While the proposed solution is expected to be quite close to the exact one, its formal simplicity allows straightforward calculations of several interesting quantities, like energies and vibronic reduction (or Ham) factors. We calculate for dihedral symmetry two different $q$-factors ("$q_z$" and "$q_x$") and a $p$-factor. In simplified situations we obtain $p=q_z +q_x -1$. The formalism enables quantitative estimates to be made for the dynamical narrowing of hyperfine lines in the observed ESR spectrum of the dihedral cyclobutane radical cation.Comment: 28 pages, 4 figure

Discrimination between evolution operators

Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is demonstrated for every scenario but a special one. This discrimination between evolutions is experimentally much simpler than procedures proposed earlier based on either sequential or parallel application of the unknown unitaries. A lower bound for the orthogonalization time is proposed in terms of the properties of the two Hamiltonians.Comment: 7 pages, 2 figures, REVTe