Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

TL;DR

This paper investigates how intrinsic phonon creation affects the accuracy of quantum simulations of spin models using ultracold trapped ions, revealing significant impacts on spin probabilities and entanglement, especially with added transverse fields.

Contribution

It provides a detailed analysis of phonon effects on spin dynamics in ion trap quantum simulators, highlighting conditions where phonons influence simulation fidelity.

Findings

Moderate phonon creation alters spin state probabilities.

Phonon effects can reduce spin entanglement.

Phonon creation impedes observing kink transitions in frustrated systems.

Abstract

Linear Paul traps have been used recently to simulate the transverse field Ising model with long-range spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbation theory and exact numerical integration of the Schr\"odinger equation in a truncated spin-phonon Hilbert space followed by a tracing out of the phonon degrees of freedom to study this problem. We find that moderate phonon creation often makes the probabilities of different spin states behave differently from the static spin Hamiltonian. In circumstances in which phonon creation is minor, the spin dynamics state probabilities converge to the static spin Hamiltonian prediction at the cost of reducing the spin entanglement. We show how phonon creation can severely impede the observation of kink transitions in frustrated spin systems when the number of ions increases. Many of our results also have implications for quantum simulation in a Penning trap.