Self-Synchronization and Dissipation-Induced Threshold in Collective Atomic Recoil Lasing

Networks of globally coupled oscillators exhibit phase transitions from incoherent to coherent states. Atoms interacting with the counterpropagating modes of a unidirectionally pumped high-finesse ring cavity form such a globally coupled network. The coupling mechanism is provided by collective atomic recoil lasing, i.e., cooperative Bragg scattering of laser light at an atomic density grating, which is self-induced by the laser light. Under the rule of an additional friction force, the atomic ensemble is expected to undergo a phase transition to a state of synchronized atomic motion. We present the experimental investigation of this phase transition by studying the threshold behavior of this lasing process.

Figure 1

(a) Sectionwise Fourier-transform of the interference signal $P_{beat}$ with the pump laser power being ramped up and down. The dotted line is proportional to the pump laser power. (b) Dependence of the CARL frequency on the intracavity pump power. (c) Dependence of the probe field intensity on the pump power. The CARL laser threshold is around $P_{+}=4\mathrm{W}$ intracavity power. The fitted curves are based on a Fokker-Planck theory outlined in 8. (d)  Calculated bunching parameter. The parameters are ${\gamma }_{fr}=4\kappa$, $N={10}^6$, ${\Delta }_a=-(2\pi )1.7\mathrm{T}\mathrm{H}\mathrm{z}$, and $T=200\mu \mathrm{K}$.

Figure 2

Pump power threshold measured for various laser detunings (a) and atom numbers (b) determined from curves like those shown in Fig. 1. (c) CARL frequency as a function of the laser detuning. (d) Pump power threshold plotted as a function of the temperature derived from the threshold CARL frequency according to Eq. (7).

Figure 3

(a) Evolution of the CARL frequency after molasses has been switched off at time $t=0.5\mathrm{m}\mathrm{s}$. (b) CARL power calculated via Eq. (1). The fits are based on the theoretical formulas Eqs. (2) and (3) of Ref. [2].