Probing Quantum Dynamical Couple Correlations with Time-Domain Interferometry

Time-domain interferometry (TDI) is a promising method to characterize 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 that allows us 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.

Figure 1

(a) Schematic setup. The incoming wave packet propagating along $\mathbf{k}$ (red) is separated into two parts with a mutual delay by a split unit. The advanced (violet) component is quasielastically scattered by the target at time $t_1$, while the delayed one (blue) scatters at $t_2$. Subsequently, the light scattered in direction $\mathbf{k}+\mathbf{p}$ passes an overlap unit, which acts identical to the split unit. The central component of the outgoing signal contains two indistinguishable contributions, arising from photons which scattered at time $t_1$ or $t_2$, respectively. In our scheme, a phase shifter $\varphi$ controls the interference of these two contributions in the measured intensity of the scattered light, and thus enables one to recover the quantum dynamical couple correlation function of the target. (b) If the split and overlap units are realized using Mössbauer filter foils, then the required phase control is possible using mechanical displacements of the split foil as demonstrated in Ref. [14]. (c) A generic implementation of the phase control is a split-and-delay line, with a phase plate in one of the two arms.