We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a travelling laser field, in the Lamb–Dicke regime. Unlike the customary approach, based on the interaction picture and the rotating wave approximation, we reduce the original Hamiltonian to a time-independent model, unitarily equivalent to a spin-boson model, which features a form well suited to apply the perturbation theory. We determine the first- and second-order corrections of eigenstates and eigenvalues. By varying the interaction parameters we identify four regimes characterized by different eigenvalue distributions (possibly including level doublets) and suggest the presence of an intermediate regime where the spectrum undergoes macroscopic changes. In this regime, where the perturbation approach does not hold, our reduced Hamiltonian is shown to reproduce the Jaynes–Cummings model.

Perturbative approach to the dynamics of a trapped ion interacting with a light field / Penna, Vittorio; Raffa, Francesco Antonino. - In: JOURNAL OF PHYSICS. B, ATOMIC MOLECULAR AND OPTICAL PHYSICS. - ISSN 0953-4075. - 47:(2014), pp. 075501-1-075501-8. [10.1088/0953-4075/47/7/075501]

Perturbative approach to the dynamics of a trapped ion interacting with a light field

PENNA, Vittorio;RAFFA, Francesco Antonino
2014

Abstract

We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a travelling laser field, in the Lamb–Dicke regime. Unlike the customary approach, based on the interaction picture and the rotating wave approximation, we reduce the original Hamiltonian to a time-independent model, unitarily equivalent to a spin-boson model, which features a form well suited to apply the perturbation theory. We determine the first- and second-order corrections of eigenstates and eigenvalues. By varying the interaction parameters we identify four regimes characterized by different eigenvalue distributions (possibly including level doublets) and suggest the presence of an intermediate regime where the spectrum undergoes macroscopic changes. In this regime, where the perturbation approach does not hold, our reduced Hamiltonian is shown to reproduce the Jaynes–Cummings model.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2536093
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