High-Resolution Two-Dimensional Optical Spectroscopy of Electron Spins

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 microwaves and radio waves, it has recently been extended into the visible and UV spectral range. However, resolving MHz energy splittings with ultrashort laser pulses still remains 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 steplike 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 because of selective excitation of the same subensemble 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-μeV 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 2 orders of magnitude.

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Plain Language Summary

Interactions between the different parts of a quantum-mechanical system, such as an organic molecule or a semiconductor, can lead to complex behavior. One way to better understand this behavior is by firing short laser pulses at the system and carefully observing how the light is scattered and absorbed. To reveal the relevant dynamics, these pulses need last for only picoseconds, but the short duration hides subtle energy distinctions such as those seen between different spins of an electron exposed to an electric or magnetic field. We have adapted these techniques to measure such tiny differences and use them to identify different optical transitions that can be excited by the pulses.

Specifically, we demonstrate how two-dimensional Fourier transform spectroscopy can be used to evaluate spin splitting of ground-state electrons. As a host system for the electrons, we chose a semiconductor quantum well in which the electrons were provided by doping with impurities. Our approach is based on stimulated steplike Raman processes in a pulsed excitation regime that allow us to probe the splitting of electron energy levels with high selectivity, even for systems with broad optical transitions. This provides the unique opportunity to distinguish between various carrier complexes, such as electron-hole pairs bound to excess electrons in semiconductors, in ensembles hosting different types of optical excitation.

Our approach allows us to measure the spin dynamics of carriers in the ground state without creating a macroscopic spin polarization. This is attractive for fundamental studies of spin ensembles because the energy input in the system, which may destroy spin coherence, is reduced.