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

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.arXiv:1512.05316v1 [quant-ph]

Dynamical structure factors of dynamical quantum simulators

“…In this section, we will assume, for the sake of simplicity, that the quantum simulator will be initialized in the unique ground-state vector of , which we refer to as , though in principle, the protocol we employ can be used with any initial state, be it in equilibrium or not, as exemplified in ref. 34 with the Ramsey spectroscopy technique.…”

“… 33 [see also ref. 34 for a detailed study of the idea] has been that the operator at initial time can be obtained as part of a unitary operation, the pulse of Ramsey interferometry .…”

Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation

“…x,x,i,j components of the Green's function because they can be measured experimentally with Ramsey spectroscopy [16][17][18].…”

“…For transverse field strengths on the order of 10J 0 and times on the order of 1 J0 , however, deviations of this Green's function from a time translation invariant one are negligible, so we ignore them. We choose to compare the G R x,x,i,j components of the Green's function because they can be measured experimentally with Ramsey spectroscopy [16][17][18].…”

Probing unitary two-time correlations in a neutral atom quantum simulator

“…One possible way out is to devise schemes that give access to quantities encoding the two-time correlation function (1), but that do not require any measurement at t 1 . * kastner@sun.ac.za An example is linear response theory, which can give access to the imaginary part of C, but other, more specific schemes have been proposed as well [8][9][10]. The shortcoming of these schemes is that they work only in specific settings, for specific initial states, and/or give access only to certain specific correlation functions.…”