# Accumulation effects in modulation spectroscopy with high repetition rate pulses: recursive solution of optical Bloch equations

## TL;DR

This paper investigates how accumulation effects influence modulation spectroscopy with high repetition rate pulses, providing a recursive solution to optical Bloch equations to accurately interpret experimental data.

## Contribution

It introduces a recursive method to account for accumulation effects in quantum two-level systems driven by phase-modulated pulses, enhancing analysis accuracy.

## Key findings

- Accumulation effects significantly alter harmonic amplitudes in fluorescence signals.
- Corrections due to accumulation are essential for precise quantum measurements.
- The recursive solution improves the interpretation of modulation spectroscopy data.

## Abstract

Application of the phase modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the modulations allows to distinguish the contributions of various interaction pathways. The lasers with high repetition rate used in such experiments can lead to appearance of the accumulation effects, which become especially pronounced in systems with long-living excited states. Recently it was shown, that such accumulation effects can be used to evaluate parameters of the dynamical processes in the material. In this work we demonstrate that the accumulation effects are also important in the quantum characteristics measurements provided by modulation spectroscopy. In particular, we consider a model of quantum two-level system driven by a train of phase-modulated light pulses, organised in analogy with the 2D spectroscopy experiments. We evaluate the harmonics' amplitudes in the fluorescent signal and calculate corrections appearing from the accumulation effects. We show that the corrections can be significant and have to be taken into account at analysis of experimental data.