# Symmetry-Based Selective Femtosecond Coherent Control of Transient Two-Photon Absorption

## TL;DR

This paper introduces a symmetry-based pulse shaping method for independent control of transient and final two-photon absorption in Na atoms, enabling tailored population dynamics without affecting the final state.

## Contribution

It presents a novel symmetry-based control scheme using phase transformations to independently manipulate transient populations during two-photon absorption.

## Key findings

- Controlled transient population dynamics in Na atoms.
- Achieved independent manipulation of transient and final populations.
- Demonstrated effectiveness of third-order chirp pulses for duration control.

## Abstract

We present and implement a new scheme for independent control of both the final and the transient population utilizing the symmetry properties of the system. By proper pulse shaping, utilizing the invariance of the two-photon absorption to specific phase transformations of the pulse, different time evolutions of the transient population are photo-induced for a given (fixed) final state population. The model system is the Na atom. The work is conducted in the weak-field regime for which the transient two-photon excitation is described by second-order perturbation theory. One most attractive case is the extended family of third-order chirp pulses which control the population build-up duration independently of the final population.