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Physical Review A

Detailed look at aspects of optical pumping in sodium

Jabez J. McClelland, Michael H. Kelley

Published Jun 1, 1985• 78 citations
Publisher

Abstract

Calculations and measurements are presented of the increase in F\ifmmode\bar\else\textasciimacron\fi{}=1 ground-state population as a function of incident laser intensity in optically pumped sodium. The calculations involve numerical integration of a multilevel version of the optical Bloch equations. Agreement between experiment and theory is good when proper account is taken of the residual Doppler width in the atomic beam, which causes a larger increase in the F\ifmmode\bar\else\textasciimacron\fi{}=1 population. The F\ifmmode\bar\else\textasciimacron\fi{}=1 population increases by 3.5% at 35 mW/${\mathrm{cm}}^{2}$, the highest laser intensity investigated.

DOI
10.1103/physreva.31.3704

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Calculations and measurements are presented of the increase in F\ifmmode\bar\else\textasciimacron\fi{}=1 ground-state population as a function of incident laser intensity in optically pumped sodium. The calculations involve numerical integration of a multilevel version of the optical Bloch equations. Agreement between experiment and theory is good when proper account is taken of the residual Doppler width in the atomic beam, which causes a larger increase in the F\ifmmode\bar\else\textasciimacron\fi{}=1 population. The F\ifmmode\bar\else\textasciimacron\fi{}=1 population increases by 3.5% at 35 mW/cm2{\mathrm{cm}}^{2}cm2, the highest laser intensity investigated.
For pt. I see ibid. p. 231, 1994. We consider optical pumping in the multilevel sodium D 1 manifold by several coherent light fields. Coherence between atomic states is taken into account by solving the complete density matrix equations. The manifestation of population trapping and the variation of transmitted light intensity are predicted numerically and verified experimentally for the sodium D 1 line. The influence of relaxation and Doppler broadening is elucidated. The interaction of a strong and a weak field is shown to create electromagnetically induced transparency.
We describe optically pumping a beam of sodium atoms to >96% mS and >92% mS, mI state selection. (We have accurately measured the population of every mS, mI state in the optically pumped beam.) For the optical pumping both ground hyperfine states are pumped, using single-mode cw dye-laser radiation tuned to the 3S1/2–3P1/2 transition that is phase modulated in a LiTaO3 crystal to produce first-order sidebands at approximately the 1772-MHz hyperfine splitting of the ground state. The z-directed optical pumping is performed in a z-directed magnetic field of ~5 G. The state-selected atoms then move, in ~1 cm, into an ~200 G, z-directed field. The downstream probe laser beam is scanned through the 3S1/2 (mS, mI) → 3P3/2 (mS′, mI) transitions, which are spectroscopically resolved at 200 G, and the fluorescence intensities portray the residual populations in each of the eight 3S1/2 states.
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​,F=2--3 2{\mathrm{}}^{2}2P3/2{P}_{3/2}P3/2​,F=3 transition. The intensity profile of the deflected beam was measured at different laser power levels and for different laser polarizations. Calculations using a constant force derived from a two-level atom yield deflections which are too large. The results of more realistic simulation calculations agree very well with the measured deflection. Those calculations incorporate the atomic-beam spatial and velocity distributions as well as the laser frequency distribution and polarization state. Optical pumping, loss of atoms to the nonresonant F=1 ground state, and Doppler shifting of the atoms out of resonance are all considered, as also are the statistics and angular distributions of the spontaneous photons.
By photoionizing hyperfine (HF) levels of the Cs state 62P3/26{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}62P3/2​ in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of ``dark'' and ``bright'' resonances leading to power-dependent branching coefficients.
The D1 line spectrally selective pumping process in Doppler-broadened cesium is analyzed by solving the optical Bloch equations. The process, described by a three-level model with the Λ scheme, shows that the saturation intensity of broadened atoms is three orders of magnitude larger than that of resting atoms. The |Fg = 3〉 → |Fe = 4〉 resonance pumping can result in the ground state |Fg = 4, mF = 4〉 sublevel having a maximum population of 0.157 and the population difference would be about 0.01 in two adjacent magnetic sublevels of the hyperfine (HF) state Fg = 4. To enhance the anisotropy in the ground state, we suggest employing dichromatic optical HF pumping by adding a laser to excite D1 line |Fg = 4〉 → |Fe = 3〉 transition, in which the cesium magnetometer sensitivity increases by half a magnitude and is unaffected by the nonlinear Zeeman effect even in Earth's average magnetic field.
This work is concerned with the temporal evolution of the coherent population trapping (CPT) process in the case of additional optical pumping to states not contributing to the CPT superposition states. Special attention is paid to the influence of weak external magnetic fields that can change the laser-atom interaction considerably. The theoretical analysis is completed by experimental observations on a sodium atomic beam, which show good agreement with our theory. The results obtained are of importance for a realistic picture of CPT schemes in practical applications.