Probing Quantum Dynamical Couple Correlations with Time-Domain Interferometry

Abstract

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.

Backaction-free measurement of quantum correlations via quantum time-domain interferometry

“…The final state thus contains a single-photon spherical wave packet that carries information about the target at two different times, even though the radiation interacted only once with the target, as is apparent from the first-order perturbative treatment. Therefore, even though the initial state is a classical-like state, due to the single-scattering approximation a similar final state is encountered as in our previous work [8] in which we assumed an incoming single-photon state. As a result, we will again see in the following that by making the two pathways indistinguishable, the full ISF can be retrieved via the detection of the scattered photon.…”

“…Time-domain interferometry (TDI) is an experimental technique to probe space-time correlations among particles in condensed matter systems [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such correlations are quantified by a generalization of the static pair distribution function [14], called the dynamical couple correlation function (DCF), which is given by…”

“…In particular, the presence of the classical field modifies the system before the second scattering takes place. However, recently we showed that this interpretation needs revision in a full quantum theoretical analysis of TDI (QTDI), in which both the system and the incoming pulses are treated quantum mechanically [8]. If the incident field comprises a single x-ray photon, then this photon probes the particle density of the target at either the earlier or the later time, but it does not interact at both times.…”

“…Therefore, in each repetition of the experiment, the system's dynamics is not modified by the probing field before the single interaction takes place. As a result, it was shown in [8] that QTDI provides access to the unperturbed ISF of the quantum system.…”

“…This contribution, therefore, contains information on both possible scattering times, and thereby on two-time information on the target. Analyzing the scattered intensity due to this component as a function of the momentum transfer and the relative phase φ, the desired quantum-mechanical ISF can be measured [8]. However, at present there is no established way to generate single x-ray photons [in the quantum-mechanical sense of Eq.…”