Coherent averaging in the frequency domain.

Area of Science:

• Quantum mechanics
• Solid-state physics
• Spectroscopy

Background:

• Periodic time-modulated Hamiltonians are common in quantum systems.
• Effective interactions derived from these Hamiltonians can be challenging to link to experimental observations.
• Existing methods for calculating average Hamiltonians may lack direct experimental relevance.

Purpose of the Study:

• To introduce a novel frequency-domain approach for analyzing quantum systems with time-modulated Hamiltonians.
• To develop a method that better connects theoretical models to measurable quantities.
• To provide a formalism suitable for calculating spectral peak intensities.

Main Methods:

• Development of a frequency-domain formalism.
• Calculation of approximate solutions for the density matrix.
• Application to fast magic-angle-spinning Nuclear Magnetic Resonance (NMR) spectra of solids.

Main Results:

• The proposed frequency-domain approach offers advantages over traditional methods.
• The formalism yields an approximate density matrix solution more amenable to experimental interpretation.
• The method is demonstrated to be effective for calculating intensities of narrowed spectral peaks.

Conclusions:

• The frequency-domain approach provides a more experimentally relevant way to study quantum systems with time-dependent Hamiltonians.
• This method enhances the ability to interpret spectral data, particularly in solid-state NMR.
• The formalism facilitates accurate prediction of spectral peak intensities.