Double-well potentials have extensive applications in many branches of physics and have resulted in devices that are useful for precision sensing as well as quantum information processing. Here, we present a theoretical analysis of the transverse phonon coupling between a pair of trapped ions as described by a double-well system. Typically the phonons in trapped ions are used as an intermediary in quantum information processing, but here we focus on the dynamics of the phonons themselves. The double-well system is a special case of the more generalized Bose-Hubbard Model, with exactly two sites available to store particles. We draw an analogy to another double-well system in solid state physics: a Josephson junction containing a thin insulating barrier between two superconductors. Applications of the Josephson junction include superconducting quantum interference devices (SQUIDs), which have emerged as sensitive magnetometers and also as qubits for quantum computation. Another analogy is the recent demonstrations of matter-wave interference with Bose-Einstein condensates in double-well traps, which have also shown great promise for applications in precise inertial and gravitational field sensing. We will also discuss experimental techniques that can be applied to control and manipulate this double-well system.
Patricia J. Lee, Patricia J. Lee,
"Phonons in a double-well: transverse vibrations in a pair of trapped ions", Proc. SPIE 8400, Quantum Information and Computation X, 840007 (8 May 2012); doi: 10.1117/12.918940; https://doi.org/10.1117/12.918940