Transfer matrix theory of molecular spin-echo experiments of dynamic surfaces

Molecular spin-echo experiments are able to quantitatively determine both the amplitudes and phases of the quantum state-to-state transition amplitudes in molecule-surface scattering experiments [1]. The available theoretical frameworks describing these molecular spin-echo experiments can only describe scattering by static surfaces, however. Here, we exploit the short-range nature of the time-dependent molecule-surface interactions  to expand the transfer matrix theory of molecular spin-echo experiments to incorporate the effects of surface dynamics. Under the Born approximation and assuming pairwise interactions between the molecule and the adsorbates, we demonstrate that the molecular spin echo signal is a function of the familiar time-dependent pair correlation function of the surface and  of a molecular form factor. We then numerically implement this formalism, demonstrate that it reproduces the expected results for ${}^3$He spin-echo experiments and illustrate how the \emph{o}H$_{2}$ spin echo signal is impacted by surface dynamics. This work provides a fully quantum theoretical framework necessary to interpret molecular spin echo experiments studying dynamic surfaces.

[1] Y. Alkoby, H. Chadwick, O. Godsi, H. Labiad, M. Bergin, J.~T. Cantin, I. Litvin, T. Maniv and G. Alexandrowicz, Nat. Comm., 11, 3110 (2020).