# High resolution two-dimensional optical spectroscopy of electron spins

## TL;DR

This paper demonstrates high-resolution two-dimensional optical spectroscopy techniques to resolve tiny electron spin energy splittings in semiconductor nanostructures, enabling precise spin state analysis despite broad optical linewidths.

## Contribution

It introduces a novel application of 2D Fourier spectroscopy and Raman coherence spectra for resolving sub-microelectronvolt electron spin splittings in quantum wells.

## Key findings

- Resolved Zeeman splittings in the sub-μeV range.
- Distinguished different electron complexes in ensemble.
- Demonstrated optical retrieval of spin superpositions.

## Abstract

Multidimensional coherent optical spectroscopy is one of the most powerful tools for investigating complex quantum mechanical systems. While it was conceived decades ago in magnetic resonance spectroscopy using micro- and radio-waves, it has recently been extended into the visible and UV spectral range. However, resolving MHz energy splittings with ultrashort laser pulses has still remained a challenge. Here, we analyze two-dimensional Fourier spectra for resonant optical excitation of resident electrons to localized trions or donor-bound excitons in semiconductor nanostructures subject to a transverse magnetic field. Particular attention is devoted to Raman coherence spectra which allow one to accurately evaluate tiny splittings of the electron ground state and to determine the relaxation times in the electron spin ensemble. A stimulated step-like Raman process induced by a sequence of two laser pulses creates a coherent superposition of the ground state doublet which can be retrieved only optically due to selective excitation of the same sub-ensemble with a third pulse. This provides the unique opportunity to distinguish between different complexes that are closely spaced in energy in an ensemble. The related experimental demonstration is based on photon echo measurements in an n-type CdTe/(Cd,Mg)Te quantum well structure detected by a heterodyne technique. The difference in the sub-$\mu$eV range between the Zeeman splittings of donor-bound electrons and electrons localized at potential fluctuations can be resolved even though the homogeneous linewidth of the optical transitions is larger by two orders of magnitude.