The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-1/2 models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.
Time domain interferometry is a promising method to characterizes spatial and temporal correlations at x-ray energies, via the so-called intermediate scattering function and the related dynamical couple correlations. However, so far, it has only been analyzed for classical target systems. Here, we provide a quantum analysis, and suggest a scheme which allows to access quantum dynamical correlations. We further show how TDI can be used to exclude classical models for the target dynamics, and illustrate our results using a single particle in a double well potential.
Time-domain interferometry (TDI) is a method to probe space-time correlations among particles in condensed matter systems. Applying TDI to quantum systems raises the general question of whether two-time correlations can be reliably measured without an adverse impact of the measurement backaction on the dynamics of the system. Here, we show that a recently developed quantum version of TDI (QTDI) indeed can access the full quantum-mechanical two-time correlations without backaction. We further generalize QTDI to weak classical continuous-mode coherent input states, alleviating the need for single-photon input fields. Finally, we interpret our results by splitting the space-time correlations into two parts. While the first one is associated with projective measurements and thus insensitive to backaction, we identify the second contribution as arising from the coherence properties of the state of the probed target system, such that it is perturbed or even destroyed by measurements on the system.
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