Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential use
fulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.
Earth-alkaline-like atoms with ultra-narrow 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 co
nventional 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
We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewi
dth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order $10^{-12}W$ is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude.
Interferometry with Heisenberg limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors, and in quantum information science. For experimental implementations the robustness of the phase
resolution is crucial since any experimental realization will be subject to imperfections. In this article we study the robustness of phase reconstruction with two number states as input subject to fluctuations in the state preparation. We find that the phase resolution is insensitive to fluctuations in the total number of particles and robust against noise in the number difference at the input. The phase resolution depends on the uncertainty in the number difference in a universal way that has a clear physical interpretation: Fundamental noise due to the Heisenberg limit and noise due to state preparation imperfection contribute essentially independently to the total uncertainty in the phase. For number difference uncertainties less than one the first noise source is dominant and the phase resolution is essentially Heisenberg limited. For number difference uncertainties greater than one the noise due to state preparation imperfection is dominant and the phase resolution deteriorates linearly with the number difference uncertainty.
