A family of exact eigenstates for a single trapped ion interacting with a laser field

Abstract

We show that, under certain combinations of the parameters governing the interaction of a harmonically trapped ion with a laser beam, it is possible to find one or more exact eigenstates of the Hamiltonian, with no approximations except the optical rotating-wave approximation. These are related via a unitary equivalence to exact eigenstates of the full Jaynes-Cummings model (including counter-rotating terms) supplemented by a static driving term.

Fidelity and concurrence of entangled qudits between a trapped ion and two laser beams

“…Two studies on ion-laser interaction help us understand photon dynamics [35,38]. The Hamiltonian of our model system is…”

Several Ways to Solve the Jaynes-Cummings Model

“…and it is straightforward to calculate then the evolution operator (16) via Taylor series. The evolution operator then may be written as…”

“…The fact that some other problems, such as the ion-laser interaction [16] are similar to the atom-field interaction, has made possible to produce JC-type interaction in these systems [17][18][19][20][21], such as multiphonon and anti-JC interactions [22]. This has allowed the reconstruction of quasiprobability distributions also in such systems [23].…”

Dynamical Invariants for Generalized Coherent States via Complex Quantum Hydrodynamics

“…The invariant is present in several different technological applications [8]: "The extensions from single harmonic oscillators to coupled time dependent harmonic oscillators may be found in ion-laser interactions [9][10][11], quantized fields propagating through dielectric media [12], shortcuts to adiabaticity [13], the Casimir effect [14] to name some". For further details on the historical development of the Ermakov invariant, see [15] and the literature quoted therein.…”