title: Probing real-space and time-resolved correlation functions with many-body Ramsey interferometry.
abstract: We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Knap
authors.forename: Adrian
authors.initials: A
authors.lastname: Kantian
authors.forename: Thierry
authors.initials: T
authors.lastname: Giamarchi
authors.forename: Immanuel
authors.initials: I
authors.lastname: Bloch
authors.forename: Mikhail D
authors.initials: MD
authors.lastname: Lukin
authors.forename: Eugene
authors.initials: E
authors.lastname: Demler