Threshold of a Random Laser with Cold Atoms

We address the problem of achieving an optical random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. The lasing threshold can be defined using the on-resonance optical thickness $b_0$ as a single critical parameter. We predict the threshold quantitatively, as well as power and frequency of the emitted light, using two different light transport models and the atomic polarizability of a strongly pumped two-level atom. We find a critical $b_0$ on the order of 300, which is within reach of state-of-the-art cold-atom experiments. Interestingly, we find that random lasing can already occur in a regime of relatively low scattering.

Figure 1

Threshold of random lasing based on Mollow gain [21], calculated for each pair of pumping parameters $\Delta$ (detuning) and $\Omega$ (Rabi frequency) with Eqs. (1, 2). Only the $\Delta >0$ part is represented. (a) Critical optical thickness $b_{0\mathrm{cr}}$ to allow lasing. (b) Detuning ${\delta }_{\mathrm{RL}}$ of the random laser from the pump frequency. The black area corresponds to a forbidden region (no gain). The hatched part corresponds to parameters for which the diffusion approximation is a priori not reliable.

Figure 2

Critical optical thickness for different geometries and transport models. The lower, red curve corresponds to the slab geometry (width $L$), with RTE model (continuous line) and diffusive model (open circle). The upper, blue curve corresponds to the sphere geometry (diameter $L$), with the diffusive model. The part with $L/{\ell }_{\mathrm{sc}}<3$ is dashed, as the model may not be reliable.

Figure 3

Continuous line: Emitted random laser power normalized to the pump fluorescence power, as a function of the pump intensity. Dashed line: Normalized laser detuning ${\delta }_{\mathrm{RL}}$. The random medium is a spherical cloud of two-level atoms with an on-resonance optical thickness $b_0=650$.