Broadening and intensity redistribution in theNa(3p)hyperfine excitation spectra due to optical pumping in the weak excitation limit

Abstract

Detailed analysis of spectral line broadening and variations in relative intensities of hyperfine spectral components due to optical pumping is presented. Hyperfine levels of sodium 3p 1/2 and 3p 3/2 levels are selectively excited in a supersonic beam at various laser intensities under the conditions when optical pumping time is shorter than transit time of atoms through the laser beam. The excitation spectra exhibit significant line broadening at laser intensities well below the saturation intensity, and redistribution of intensities of hyperfine spectral components is observed, which in some cases is contradicting with intuitive expectations. Theoretical analysis of the dynamics of optical pumping shows that spectral line broadening depends sensitively on branching coefficient of the laser-driven transition. Analytical expressions for branching ratio dependent critical Rabi frequency and critical laser intensity are derived, which give the threshold for onset of noticeable line broadening by optical pumping. The critical laser intensity has its smallest value for transitions with branching coefficient equal to 0.5, and it can be much smaller than the saturation intensity. Transitions with larger and smaller branching coefficients are relatively less affected. The theoretical excitation spectra were calculated numerically by solving density matrix equations of motion using the split propagation technique, and they well reproduce the observed effects of line broadening and peak intensity variations. The calculations also show that presence of dark (i.e., not laser-coupled) Zeeeman sublevels in the lower state results in effective branching coefficients which vary with laser intensity and differ from those implied by the sum rules, and this can lead to peculiar changes in peak ratios of hyperfine components of the spectra.

Hyperfine interaction in the Autler-Townes effect: The formation of bright, dark, and chameleon states

“…This population can be found via asymptotic solution of the Schrödinger equation (2) upon adiabatic switching (3) of the P -field Rabi frequency. At t = 0 the entire population is in state g. The chosen amplitude 0 = 0.1 MHz is too small to cause any notable depletion of state g due to optical pumping [23][24][25]. The relaxation rates α = 1/τ α for the upper and intermediate levels are calculated using the values τ f = 52.4 ns and τ i = 16.3 ns that correspond to the radiative lifetimes of the 4d 5/2 and 3p 3/2 states of Na, respectively [26,27].…”

“…Scanning the P laser frequency across the |g → |i resonance results in excitation of the adiabatic states. To damp Rabi oscillations in the system we introduce weak decay rates α = 2π × 0.2 MHz for all excited levels α = g. The value of the P -laser Rabi frequency P = 10 kHz is chosen small such that optical pumping is negligible within the characteristic observation time τ ∼ 1/ α [23], which implies C g (t) 1. The Rabi frequencies γ = i|E Sd |f γ of all transitions between the intermediate |i and the final states |f γ due to coupling with the S laser field are assumed to be equal to S .…”

“…Rabi frequencies of individual fine {LJ → L J } and HF {LJ F → L J F } transitions are then defined by the tabulated line strength values [35]. The Rabi frequencies for individual transitions {LJ F M → L J F M} between Zeeman sublevels M in the case of linearly polarized excitation are obtained using the formulas provided in [35,36], and the respective values can be found in [23,24]. The calculations are performed for the conditions of the experiment described in [37]: a supersonic beam of sodium atoms with the mean flow velocity of 1160 m/s is crossed by two counterpropagating laser beams at right angles.…”

“…It is convenient to describe the laser-induced couplings using the characteristic Rabi frequencies P ,S that drive the transitions 3s-3p and 3p-4d [23]:…”

Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light

“…It has recently been observed that optical pumping affects the lineshapes in saturated absorption spectroscopy (SAS) [3], electromagnetically induced transparency (EIT) [4], and absorption of cold atoms with a Λ-type three-level scheme [5]. Nonlinear effects in optical pumping have also been investigated [6,7].…”