Time-dependent spectra of a three-level atom in the presence of electron shelving

We investigate time-dependent spectra of the intermittent resonance fluorescence of a single, laser-driven, three-level atom due to electron shelving. After a quasistationary state of the strong transition, a slow decay due to shelving leads to the steady state of the three-level system. The long-term stationary spectrum consists of a coherent peak, an incoherent Mollow-like structure, and a very narrow incoherent peak at the laser frequency. We find that in the ensemble-average dynamics, the narrow peak emerges during the slow decay regime, after the Mollow spectrum has stabilized but well before an average dark time has passed. The coherent peak, being a steady-state feature, is absent during the time evolution of the spectrum.

Figure 1

Scheme of the three-level atom showing laser excitation of the $|e\rangle -|g\rangle$ transition with Rabi frequency $\mathrm{\Omega }$, detuning $\mathrm{\Delta }$, and spontaneous decay rate $\gamma$, and spontaneous decay via the metastable state $|a\rangle$ at rates ${\gamma }_d,{\gamma }_a$.

Figure 2

Time-dependent spectra $S(\omega ,t,\mathrm{\Gamma })$ for moderate laser field strength, $\mathrm{\Omega }={\gamma }_{+}/4=0.2625\gamma$, ${\gamma }_d=0.05\gamma$, and ${\gamma }_a=0.015\gamma$. The filter's bandwidth is $\mathrm{\Gamma }=0.1\gamma$. The inset shows the spectrum at $\gamma t=150$ in semilogarithmic scale and wider frequency range to reveal the broad component.

Figure 3

Same as Fig. 2, but for strong driving, $\mathrm{\Omega }=3.5\gamma$.

Figure 4

TDS for strong field, $\mathrm{\Omega }=3.5\gamma$, but detuning $\mathrm{\Delta }=1$. The other parameters as in Fig. 2. The inset shows in semilogarithmic scale the diminishing asymmetry of the center of the spectrum for increasing time.