Steady-state superradiance with alkaline-earth-metal atoms

Alkaline-earth-metal-like atoms with ultranarrow transitions open the door to a new regime of cavity quantum electrodynamics. That regime is characterized by a critical photon number that is many orders of magnitude smaller than what can be achieved in conventional systems. We show that it is possible to achieve superradiance in steady state with such systems. We discuss the basic underlying mechanisms as well as the key experimental requirements.

Figure 1

(a) Schematic of a coupled atom-cavity system leading to steady-state superradiance. (b) The parameter space of CQED spanned by the critical atom number $n_0$ and the critical photon number $m_0$. The collective behavior of the coupled atom-cavity system undergoes a crossover from stimulated emission dominated (laserlike) at large $m_0$ to collective spontaneous emission dominated (superradiancelike) for small $m_0$.

Figure 2

Emission rate as a function of repump rate for 10 atoms. The solid orange circles are the expectation values extracted from the Monte Carlo wave-function simulations. The solid blue line shows the semiclassical result obtained from Eqs. (3, 4, 5), and the purple dashed line is the emission rate for uncorrelated particles, $N_e{\Gamma }_c$.

Figure 3

Transition rates between $J$ and $M$ eigenspaces (a–c) and populations $P_{M,J}$ of these subspaces (d–f) for $w=0.1$${\Gamma }_c$ (a, d), $w=2.0$${\Gamma }_c$ (b, e), $w=10.0$${\Gamma }_c$ (c, f), and $N=4$ atoms. Red arrows (downward pointing arrows) indicate decay dominated transitions and blue arrows (upward pointing and diagonal pointing arrows) indicate repump dominated transitions. The transition rates are calculated by averaging over degenerate initial states and summing over final states. In panels (d)–(f) darker shades indicate larger populations.