# A Single Trapped Ion as a Time-Dependent Harmonic Oscillator

## TL;DR

This paper demonstrates how a single trapped ion can serve as a versatile platform for simulating time-dependent harmonic oscillators, enabling tests of fundamental physical models and correcting previous theoretical proposals.

## Contribution

It provides a general solution for using a trapped ion as a time-dependent harmonic oscillator and corrects prior theoretical models related to Gibbons-Hawking radiation simulation.

## Key findings

- Corrected the Hamiltonian used in previous proposals
- Showed the ion's spectrum differs from Gibbons-Hawking radiation but shares key signatures
- Validated the ion's use as a motional detector in various models

## 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.