Prospects for a Millihertz-Linewidth Laser

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultranarrow clock transition into the mode of a high $Q$ resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order ${10}^{-12}\mathrm{W}$ 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 2 orders of magnitude.

Figure 1

(a) Experimental scheme and (b) the level structure. The ultranarrow ${}^{3}P_0\mathrm{\text{−}}{}^{1}S_0$ transition indicated by the red arrow is the laser transition. The repumping lasers are indicated by the blue arrows, spontaneous decay into the ${}^{3}P$ states by the gray arrow, and the Raman sideband cooling lasers by the black arrows. The $n$ quantum numbers indicate the vibrational levels of ${}^{3}P_0$ and ${}^{3}P_2$.

Figure 2

Power as a function of pump rate $w$ and atom number $N$. The rapid buildup of power above threshold $w\sim \gamma$ can be seen as well as the decrease of emitted power for too strong a pump. The dashed line shows the boundary of the region of collective emission as determined by the zero of the term in parenthesis in Eq. (6). Here, $\gamma =0.01{\mathrm{s}}^{-1}$, $1/T_2=1{\mathrm{s}}^{-1}$, $\Omega =37{\mathrm{s}}^{-1}$, and $\kappa =9.4\times {10}^5{\mathrm{s}}^{-1}$.

Figure 3

(a) Linewidth vs $w$ and $N$. The white dashed lines indicate (from left to right) the spontaneous decay rate $\gamma$, the inhomogeneous relaxation rate $1/T_2$, and the maximum pump rate $w_{\max }$ [Eq. (7)]. Parameters as in Fig. 2. (b) is a cut through (a) for $N={10}^6$ atoms.