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arXiv · 1512.05316

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap based quantum simulator

Bryce T. Yoshimura·J. K. Freericks
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Abstract

Recent work proposed a variant on Ramsey interferometry for coupled spin-$1/2$ systems that directly measures the retarded spin-spin Green's function. We expand on that work by investigating nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excited higher-energy states via a temporally ramped transverse magnetic field. We then apply the Ramsey spectroscopy protocol to the final Hamiltonian, which has a constant transverse field. The short-time behavior directly relates to Lieb-Robinson bounds for the transport of many-body correlations, while the long-time behavior relates to the excitation spectra of the Hamiltonian. Compressive sensing is employed in the data analysis to efficiently extract that spectra.

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Bryce T. Yoshimura, J. K. Freericks. 2015-12-16. Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap based quantum simulator. https://doi.org/10.1103/physreva.93.052314

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