A Single Trapped Ion as a Time-Dependent Harmonic Oscillator

Abstract

We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al. [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.

5 pages (two-column format), no figures, added introductory material, other minor content revisions

References in corpus (3)

• Semiclassicality and Decoherence of Cosmological Perturbations
• Quantum dynamics of cold trapped ions, with application to quantum computation
• The Coherence of Primordial Fluctuations Produced During Inflation

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• Investigations on Dynamical Stability in 3D Quadrupole Ion Traps
• Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method
• Quasienergy operators and generalized squeezed states for systems of trapped ions
• Optical realization of the dissipative quantum oscillator
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method
• Contributions to the study of time dependent oscillators in Paul traps. Semiclassical approach
• Discrete-time reservoir engineering with entangled bath and stabilizing squeezed states