# Probing weak dipole-dipole interaction using phase-modulated non-linear spectroscopy

## TL;DR

This paper explores how phase-modulated non-linear spectroscopy can detect weak dipole-dipole interactions by analyzing peak intensities and phase shifts in the demodulated signals, offering a new approach to measure interaction strength.

## Contribution

It introduces a theoretical framework combining numerical solutions and analytical perturbation theory to identify dipole-dipole interactions through spectral peak intensities and phase differences.

## Key findings

- Dipole-dipole interactions can be detected via peak intensities in the spectrum.
- The phase between harmonic signals depends on the sign of the interaction.
- Parameter dependence of signal intensities provides insights into interaction strength.

## Abstract

Phase-modulated non-linear spectroscopy with higher harmonic demodulation has recently been suggested to provide information on many-body excitations. In the present work we theoretically investigate the application of this method to infer the interaction strength between two particles that interact via weak dipole-dipole interaction. To this end we use full numerical solution of the Schr\"odinger equation with time-dependent pulses. For interpretation purpose we also derive analytical expressions in perturbation theory. We find one can detect dipole-dipole interaction via peak intensities (in contrast to line-shifts which typically are used in conventional spectroscopy). We provide a detailed study on the dependence of these intensities on the parameters of the laser pulse and the dipole-dipole interaction strength. Interestingly, we find that there is a phase between the first and second harmonic demodulated signal, whose value depends on the sign of the dipole-dipole interaction.