Duty-Cycle Optimization in a Pulse-Wwidth Modulation Bell--Bloom Pumping

Abstract

We investigate the duty-cycle-dependent atomic response under full-depth intensity pulse-width modulation in Bell--Bloom optical pumping. A time-domain Bloch model explicitly resolves the pump-on/off spin dynamics, yielding piecewise analytical transient solutions and a periodic steady-state description without cycle averaging or harmonic truncation. An extended free-induction-decay method independently determines the effective dark and pump-on transverse-relaxation rates, $W_0$ and $W$. The predicted lock-in responses agree well with experimental results. We find that for each Larmor frequency ${\omega }_0$, the slope is maximized at a finite pump rate that increases with ${\omega }_0$. These results provide a practical framework for sensitivity-oriented optimization of the duty cycle and pump rate in PWM-driven atomic magnetometers.