Simulation and design of shaped pulses beyond the piecewise-constant approximation

Area of Science:

• Physics
• Chemistry
• Engineering

Background:

• Resonant circuits exhibit ringing artifacts with rapid input changes, posing challenges in electromagnetic spectroscopies.
• Current methods often use piecewise-constant approximations for control sequences, leading to computational expense in simulations and suboptimal control.
• These limitations hinder the exploration of physical limits in techniques like magnetic resonance.

Purpose of the Study:

• To implement and benchmark Lie-group methods for simulating and optimizing control sequences.
• To address the computational cost and suboptimal control issues arising from ringing artifacts.
• To enable more efficient and accurate exploration of physical limits in electromagnetic spectroscopies.

Main Methods:

• Implementation of recent Lie-group methods for generating smooth control sequences.
• Benchmarking the performance of these methods against traditional piecewise-constant approximations.
• Application to simulation and optimal control problems in resonant circuits.

Main Results:

• Lie-group methods efficiently simulate and optimize smooth control sequences.
• Demonstrated reduction in computational expense for system propagation.
• Identified advantages in designing control pulses resilient to distortions.

Conclusions:

• Lie-group methods offer a superior alternative to piecewise-constant approximations for resonant circuit control.
• These advanced methods enhance simulation accuracy and control optimization in electromagnetic spectroscopies.
• The findings facilitate pushing the physical limits of spectroscopic techniques.