Abstract
We propose a method to simulate the dynamics of spin-boson models with small
crystals of trapped ions where the electronic degree of freedom of one ion is
used to encode the spin while the collective vibrational degrees of freedom are
employed to form an effective harmonic environment. The key idea of our
approach is that a single damped mode can be used to provide a harmonic
environment with Lorentzian spectral density. More complex spectral functions
can be tailored by combining several individually damped modes. We propose to
work with mixed-species crystals such that one species serves to encode the
spin while the other species is used to cool the vibrational degrees of freedom
to engineer the environment. The strength of the dissipation on the spin can be
controlled by tuning the coupling between spin and vibrational degrees of
freedom. In this way the dynamics of spin-boson models with macroscopic and
non-Markovian environments can be simulated using only a few ions. We
illustrate the approach by simulating an experiment with realistic parameters
and show by computing quantitative measures that the dynamics is genuinely
non-Markovian.
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