Prospects of a superradiant laser based on a thermal or guided beam of Sr88

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.