intercombination line to several milliseconds, and observe steady parameters suitable for emulating the performance of a continuous superradiant laser by fine tuning the repumping rates. We reach a lasing linewidth of 820 Hz for 1.1 ms of lasing, nearly an order of magnitude lower than the natural linewidth

DOI: 10.48550/arxiv.2302.08977

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Sub-Natural Linewidth Superradiant Lasing with Cold

^{88}

Sr Atoms

^{88}

Sr atoms inside an optical cavity. We extend the superradiant emission on the 7.5 kHz wide

^3P_1

\rightarrow

^1S_0

^{87}\mathrm{Sr}

atoms. Under strong driving of the dipole-forbidden transition ${}^{3}{P}_{1}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of

^{88}\mathrm{Sr}

atoms, the superradiant linewidth narrows further due to the coherent excitation of the cavity field.

μ

Hz range, sustained at the high-power level. This is achieved by incoherently pumping optical lattice clock transitions with ultracold alkaline-earth strontium-87 atoms in the EP of a

\mathcal{PT}

-symmetric system. Physically, the atomic coherence reaches a maximum in the EP, significantly amplifying the superradiance effect and resulting in superradiant lasing with an ultranarrow linewidth. This linewidth is even three orders of magnitude smaller than that of superradiant lasing in the systems without EP. Our work extends the realm of superradiant lasing by introducing the EP property, and offers promising applications for developing atomic clocks with exceptional stability and accuracy.

The prospects of superradiant lasing on the 7.5-kHz-wide $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}$ transition in

^{88}\mathrm{Sr}

is explored by using numerical simulations of two systems based on realistic experimental numbers. One system uses the idea of demonstrating continuous superradiance in a simple, hot atom beam with high flux, and the other system is based on using ultracold atoms in a dipole guide. For the hot-beam system we consider a range of atom beam parameters as well as the impact of a scheme to discard fast atoms along the cavity axis. We find that the system achieves lasing above a flux of $2.5\ifmmode\times\else\texttimes\fi{}{10}^{12}$ atoms/s and that it is capable of outputting hundreds of nanowatts and suppressing cavity noise by a factor of 20--30. The relativistic transverse Doppler shifts cause a shift in the lasing frequency on the order of 500 Hz. For the cold-atom beam we account for decoherence and thermal effects when using a repumping scheme for atoms confined in a dipole guide. This is done by treating recoils and state-dependent forces acting on atoms in the dipole guide within the framework of the stochastic master equation. We find that the output power is on the order of hundreds of picowatts; however, transverse Doppler shifts can be neglected, and cavity noise can be suppressed on the order of a factor of 50--100. Additionally, we show that both systems exhibit local insensitivity to fluctuations in atomic flux.