Magneto-optical rotation: accurate approximated analytical solutions for single-probe atomic magnetometers

Area of Science:

• Atomic physics
• Quantum sensing
• Spectroscopy

Background:

• Analytical solutions for atomic magnetometers are limited, especially for multi-state systems.
• Existing models often require complex numerical simulations for accurate predictions.
• Accurate theoretical frameworks are crucial for advancing atomic magnetometer technology.

Purpose of the Study:

• To derive an approximated analytical solution for a single-probe four-state atomic magnetometer.
• To validate the accuracy of the approximated solution against numerical methods.
• To extend the theoretical framework to three-state atomic magnetometers.

Main Methods:

• Developed an approximated analytical solution for a four-state atomic magnetometer.
• Compared the approximated solution with a numerical solution using a 4th order Runge-Kutta solver in MATLAB.
• Extended the theoretical framework to encompass three-state atomic magnetometers.

Main Results:

• The approximated analytical solution shows excellent accuracy over broad probe power and detuning ranges.
• The solution provides a viable alternative to numerical methods for four-state atomic magnetometers.
• The theoretical framework is applicable to three-state atomic magnetometers in small detuning regions.

Conclusions:

• An approximated analytical solution for four-state atomic magnetometers has been successfully developed.
• This solution offers high accuracy and broad applicability, simplifying analysis.
• The work provides a valuable theoretical tool for both four-state and three-state atomic magnetometers.