Phonon effects on analog quantum simulators with ultracold trapped ions

Details Phonon effects on analog quantum simulators with ultracold trapped ions Phonon effects on analog quantum simulators with ultracold trapped ions

2011-12-12

arxiv.org/abs/1112.2715v2

Physics

Condensed Matter

Quantum Gases

21 pages, 12 figures

Scientific paper

Linear Paul traps have been used to simulate the transverse field Ising model with long-range spin-spin couplings. We study the effects of phonon creation on the spin-state probability and spin entanglement for such quantum spin simulators. We use a many-body factorization of the quantum time-evolution operator of the system to determine the different roles spins and phonons have in affecting how well the coupled spin-phonon system can be approximated by a simple static Ising model in a time-varying transverse magnetic field. We also examine the problem using adiabatic perturbation theory and exact numerical integration of the Schr\"odinger equation in a truncated spin-phonon Hilbert space. One of our main results is that generically, small amounts of phonon creation help the probabilities of different spin states look more like that of the pure spin model, but at the cost of reducing the spin entanglement in the spin eigenfunction (determined by tracing out the phonons). We also evaluate the feasibility of generating novel spin "kink" phases based on either tuning the beatnote of the lasers in between different transverse phonon modes (where phonon effects are stronger) or quenching the transverse magnetic field. We describe practical means to suppress deleterious phonon effects in experiments. In general, there is a compromise in optimizing adiabatic spin dynamics and suppressing phonon creation during the simulation.

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