Active Optical Frequency Measurements with Superradiance Prolonged by a Modulated Magnetic Field

Active optical clocks, which utilize atoms as a laser gain medium, offer high dynamic range and wide detection bandwidth. However, superradiant emission in these systems is typically characterized by rapid, pulsed decay, which limits the spectral resolution and frequency stability of the measurement. This paper investigates whether dynamic control of atomic transition frequencies via a modulated magnetic field can prolong superradiant pulses and enhance the precision of optical frequency measurements.

The researchers model an ensemble of strontium-87 atoms trapped in an optical lattice and coupled to an optical cavity. By applying a time-dependent magnetic field, they induce Zeeman shifts that modulate the transition frequencies of two atomic sub-ensembles. Using a stochastic master equation and a cumulant mean-field approach, the authors simulate the quantum interference between these sub-ensembles. They then analyze the heterodyne detection signal to determine how this modulation affects the spectral linewidth and frequency uncertainty of the emitted light.

The study demonstrates that by applying a series of magnetic pulses or a sinusoidal magnetic field, the destructive and constructive interference of the atomic sub-ensembles can be manipulated to "halt" and "restart" the superradiant emission. This effectively stretches the duration of the superradiant pulse by approximately 30 times compared to unmodulated systems. Consequently, the heterodyne detection spectrum exhibits significantly sharper peaks. Simulations show that this prolonged emission reduces frequency uncertainty by a factor of 26 and improves frequency precision by 7 times over a ten-second integration period compared to standard pulsed superradiance.