Strong effective saturation by optical pumping in three-level systems

We have studied nonlinear absorption from the In $P_{1/2,3/2}$ ground-state doublet in a resistively heated high-temperature cell and a hollow cathode lamp. Using probe and pump lasers at 410 and 451 nm, respectively, absorption spectra with nonlinear properties caused by saturated absorption, coherent dark resonances, and optical pumping are observed. A theoretical description in terms of a density-matrix theory agrees very well with the observed spectra and identifies optical pumping as a dominating process of broadening in the stepwise contribution rather than velocity-changing collisions. Our experiments suggest that the theory used here is widely applicable in saturation spectroscopy on three-level $\Lambda$ systems.

Figure 1

Energy level scheme of ${}^{115}\text{I}\text{n}$. The lasers in the experiment address $5P_{1/2}$, $F=4$, 5 to $6S_{1/2}$, $F^{\prime }=5$ transitions for ASC experiment and $5P_{1/2}$, $F^{″}=5$, 6 to $6S_{1/2}$, $F^{\prime }=5$ transitions for HCL experiment.

Figure 2

ASC. (a) Absorption spectra of the probe beam with (solid line) and without (dashed line) the pump beam tuned to the center of the Doppler broadened spectrum. The slanted intensity is due to diode laser power variation. (b) Difference (solid line) of the two spectra from (a) compared to absorption signal demodulated by a lock-in amplifier (dotted line).

Figure 3

ASC. Demodulated absorption spectra of the probe beam in the presence of the pump beam as a function of the detuning of the probe-laser frequency in the two-color spectroscopy [6].

Figure 4

Schematic drawing of the hollow cathode lamp. The cathode is made of pure indium which is inserted into a crucible made of nonconducting ceramic (dark gray). The indium pool is grounded by a copper inlet (light gray) at the bottom of the crucible. The crucible has a length of 30 mm and a clearance of 5 mm above the indium pool.

Figure 5

HCL. Doppler-broadened transmission spectrum of the 451 nm probe laser for the $5P_{3/2}$, $F^{″}=6$, $5\to 6S_{1/2}$, $F^{\prime }=5$ transitions. Discharge current 40 mA.

Figure 6

Setup for spectroscopy with the HCL. The incoming laser beam is split in half by a PBSC and guided through the HCL. The pump beam is circular polarized and can be amplitude modulated with a chopper wheel. The polarization of the probe beam behind the HCL is analyzed with photodiodes PD1 and PD2 and demodulated with a lock-in amplifier. An interference filter (IF) blocks light caused by the discharge.

Figure 7

HCL. Doppler-free spectrum of the $5P_{3/2}$, $F^{″}=6\to 6S_{1/2}$, $F^{\prime }=5$ resonance line, demodulated by polarization spectroscopy. The small dispersive signal corresponds to the ${}^{113}\text{I}\text{n}$ isotope.

Figure 8

(a) Simplified energy-level scheme of indium with pump and probe transitions; ${\gamma }_i$, effective decay rate of the ground states; $\Gamma ,{\Gamma }_i$, total and partial decay rate of the excited state; ${\Omega }_i$, Rabi frequencies. (b) The calculated probe beam absorption spectrum with (solid line) and without pump beam (dashed line). Also, the contributions of the coherent two-photon processes (dashed-dotted lines) and step wise contribution (dotted line) are shown.

Figure 9

The FWHM of SW as a function of the Rabi frequency of the pump beam. Data are fitted (solid line) by Eq. (4) yielding $\gamma =1.6\left(0.1\right)\times {10}^{-3}\Gamma$. The dotted line is the FWHM deduced by $s_{\text{eff}}^{\text{RE}}$ in a rate equation model for the same $\gamma$.

Figure 10

The effective saturation parameter deduced by the density-matrix model (solid line) and the rate equation model (dotted line) (see also Fig. 9).