Active optical frequency standard using sequential coupling of atomic ensembles

Recently, several theoretical proposals addressed the generation of an active optical frequency standard based on atomic ensembles trapped in an optical lattice potential inside an optical resonator. Using atoms with a narrow linewidth transition and population inversion together with a “bad” cavity allows us to realize the super-radiant photon emission regime. These schemes reduce the influence of mechanical or thermal vibrations of the cavity mirrors on the emitted optical frequency, overcoming current limitation in passive optical standards. The coherence time of the emitted light is ultimately limited by the lifetime of the atoms in the optical lattice potential. Therefore these schemes would produce one light pulse per atomic ensemble without a phase relation between pulses. Here we study how phase coherence between pulses can be maintained by using several inverted atomic ensembles, introduced into the cavity sequentially by means of a transport mechanism. We simulate the light emission process using the Heisenberg-Langevin approach and study the frequency noise of the intracavity field.

Figure 1

Schematic of two atomic ensembles (black dots) in two moving optical lattices during the first stage of the lasing process. The first atomic ensemble emits light into the resonator mode while being slowly pulled through the cavity waist; the second one is prepared and transported towards the cavity.

Figure 2

Time dependence of atom-cavity coupling expressed by the coupling functions ${\Gamma }_1\left(t\right)$ and ${\Gamma }_2\left(t\right)$ for different stages of the lasing cycle.

Figure 3

Phase diffusion coefficient versus the duration of the lasing cycle for different values of the ensemble overlap parameter $R$.

Figure 4

Behavior of amplitude and phase of the intracavity field in a particular realization over several lasing cycles for $R=0.25$ and different durations of lasing cycle. (a) $2({\tau }_1+{\tau }_2)=0.2\mathrm{s}$; (b) $2({\tau }_1+{\tau }_2)=0.5\mathrm{s}$, behavior of the amplitude in the first two lasing cycles and of the phase in established regime are shown in the insets; (c) $2({\tau }_1+{\tau }_2)=1.2\mathrm{s}$.

Figure 5

Power spectral density of the intracavity field for ${\tau }_1=0.0625$ s, ${\tau }_2=0.1775$ s.