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Physical Review A

Superfluorescence polarization: Signature of collisional redistribution

Anantharaman Kumarakrishnan, S. Chudasama, Xianming L. Han

Published Sep 10, 2003• 3 citations
Publisher

Abstract

We have studied effects of magnetic sublevel degeneracy on the polarization of superfluorescent pulses generated on the Ca $4s4p{}^{1}{P}_{1}--3d4s{}^{1}{D}_{2}$ transition at $5.5\ensuremath{\mu}\mathrm{m}.$ These pulses were generated from a cell of length 50 cm by optically pumping calcium vapor on the ${4s}^{2}{}^{1}{S}_{0}--4s4p{}^{1}{P}_{1}$ transition in the presence of Ar gas. The axis of ellipticity of superfluorescence (SF) polarization is oriented parallel to the axis of the pump-laser polarization at large detunings, and undergoes an abrupt rotation through $90\ifmmode^\circ\else\textdegree\fi{}$ for detunings close to resonance. The distribution of populations in the magnetic sublevels of the ${}^{1}{P}_{1}$ state can be estimated using a simple model based on previously calculated cross sections for collisionally aided absorption in the presence of an intense (pump) field. For large detunings, these estimates are consistent with the polarized SF intensity measured in the experiment. A direct measurement of the populations of the ${}^{1}{P}_{1}$ magnetic sublevels also supports the collisional redistribution predicted by the calculated cross sections. We therefore suggest that SF polarization can be a useful signature of collisional redistribution. However, the change in ellipticity is unexpected, and probable causes for this effect are discussed.

DOI
10.1103/physreva.68.033801

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We have studied effects of magnetic sublevel degeneracy on the polarization of superfluorescent pulses generated on the Ca 4s4p1P1−−3d4s1D24s4p{}^{1}{P}_{1}--3d4s{}^{1}{D}_{2}4s4p1P1​−−3d4s1D2​ transition at 5.5\ensuremathμm.5.5\ensuremath{\mu}\mathrm{m}.5.5\ensuremathμm. These pulses were generated from a cell of length 50 cm by optically pumping calcium vapor on the 4s21S0−−4s4p1P1{4s}^{2}{}^{1}{S}_{0}--4s4p{}^{1}{P}_{1}4s21S0​−−4s4p1P1​ transition in the presence of Ar gas. The axis of ellipticity of superfluorescence (SF) polarization is oriented parallel to the axis of the pump-laser polarization at large detunings, and undergoes an abrupt rotation through 90\ifmmode∘\else\textdegree\fi90\ifmmode^\circ\else\textdegree\fi{}90\ifmmode∘\else\textdegree\fi for detunings close to resonance. The distribution of populations in the magnetic sublevels of the 1P1{}^{1}{P}_{1}1P1​ state can be estimated using a simple model based on previously calculated cross sections for collisionally aided absorption in the presence of an intense (pump) field. For large detunings, these estimates are consistent with the polarized SF intensity measured in the experiment. A direct measurement of the populations of the 1P1{}^{1}{P}_{1}1P1​ magnetic sublevels also supports the collisional redistribution predicted by the calculated cross sections. We therefore suggest that SF polarization can be a useful signature of collisional redistribution. However, the change in ellipticity is unexpected, and probable causes for this effect are discussed.
We have studied superfluorescence (SF) under highly unfavorable conditions of rapid collisional and radiative distribution in a Doppler-broadened medium. Nanosecond SF pulses at 5.5 \ensuremath{\mu}m were generated on the Ca 4s4p1P1−−3d4s1D24s4p{}^{1}{P}_{1}--3d4s{}^{1}{D}_{2}4s4p1P1​−−3d4s1D2​ transition from a column of calcium vapor buffered with Ar by optically pumping the 4s21S0−−4s4p1P1{4s}^{2}{}^{1}{S}_{0}--4s4p{}^{1}{P}_{1}4s21S0​−−4s4p1P1​ transition. The Rabi frequency associated with the intense pump pulse prevents the occurrence of SF while the pump laser is on. As a result, the predicted scaling laws that describe the properties of SF in a transversely excited system, such as peak heights, pulse widths, and delay times, are shown to apply in our situation in which the conditions resemble swept excitation. The delay times were found to be in agreement with a fully quantum mechanical calculation which describes the initiation of SF. Measurements of the densities of the three levels, the absolute SF photon yield, and the spatial distribution of the excited states indicate that the system has a quantum yield of unity. The SF intensity increases with an increase in Ar pressure due to collisional redistribution until the collisional dephasing rate inhibits SF. The conditions describing the transition of SF to amplified spontaneous emission allow us to measure the collisional broadening rate for the SF transition.
We have studied superfluorescence (SF) in Ca vapor evolving on the 3d4s ^3 D_J -4s4p ^3 P_J-1 transitions at 1.9 µm by exciting the 4s^21 S_0 -4s4p ^1 P_1 with a pulsed dye laser. SF is generated following population transfer by spin-changing collisions with an inert gas Ar from the 4s4p ^1 P_1 and 3d4s ^1 D_2 levels. We show for the first time to our knowledge that the time delay for SF evolution follows the 1/sqrt N dependence expected for the case of uniform excitation of the vapor column by collisional transfer. Here, N is the number of participating atoms that was measured directly from the photon yield. The measured photon yield for the signal as a function of Ar pressure was found to be consistent with rate equations that simulate the buildup of populations in the ^3 D_J levels based on known collisional rates. This suggests that collisional rates can be directly inferred on the basis of SF photon yields and the atomic level populations. The pulse shapes for SF show temporal oscillations that depend on two distinct factors. The first is the presence of a number of independently evolving regions in the gain medium, and the second is the presence of spatial modes. Temporal ringing is a well-known effect related to the exchange of energy between the atoms and the radiation field during pulse propagation. However, the temporal ringing observed in this experiment is far more pronounced than in previous SF experiments due to a particular choice of evolution parameters. This should make it feasible to compare our results with detailed numerical simulations that have been carried out previously.
We have studied Superfluorescence (SF) under highly unfavorable conditions of rapid collisional and radiative distribution in a Doppler broadened medium. Nanosecond SF pulses at 5.5 {mu} were generated from a 50 cm column of calcium vapor buffered with argon by optically pumping the Ca (4s{sup 2} {sup 1}S{sub 0} - 4s4p{sup 1}P{sub 1} - 3d4s{sup 1}D{sub 2}) Raman Amplifier scheme. Power broadening due to an intense 13 nsec pump pulse precludes the evolution of SF for essentially this duration. As a result, the scaling laws which govern the properties of SF in a transversely excited system are shown to apply in our situation in which the conditions resemble swept excitation.
We investigated the polarization properties of superfluorescence (SF) emitted from dense cesium atomic vapor in a cell. The atoms were excited from the 6 S ground to the 8 P state using a femtosecond laser pulse. The SF fields generated on the cascaded decay, 8 P → 8 S → 7 P , mediated the nonlinear optical process. We observed 4.2-µm and 456-nm forward directional emissions generated on the 8 S → 7 P and 7 P → 6 S transitions, respectively. The polarizations of the two fields were correlated in each laser shot, and their directions fluctuated from shot to shot, reflecting the noise that initiated the 4.2-µm emission.
Experimental spectra for excited-state optical collisions between Mg(3p1P1)\mathrm{Mg}(3p{}^{1}{P}_{1})Mg(3p1P1​) atoms and rare-gas atoms are presented. Aligned Mg atoms are produced in the 3p1P13p{}^{1}{P}_{1}3p1P1​ level by excitation with linearly polarized light. Collisions between the excited metal atoms and Ne or Ar rare-gas atoms are probed in a $1000\ensuremath{-}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range in the vicinity of the Mg $3p{}^{1}{P}_{1}\ensuremath{\rightarrow}5s{}^{1}{S}_{0}$ and $3p{}^{1}{P}_{1}\ensuremath{\rightarrow}4d{}^{1}{D}_{2}$ transitions. The probe radiation is linearly polarized either along or perpendicular to the alignment axis, leading to a linear polarization for the optical collision process as a function of detuning of the probe from the atomic resonances. Substantial spectral variation of the linear polarization reflects the different molecular transitions responsible for the excitation process, and the evolution of the atomic alignment into the molecular regime. In the present case, the transitions correspond to excitation from the Mg--rare-gas $3p{}^{1}{\ensuremath{\Pi}}_{1}$ and $3p{}^{1}{\ensuremath{\Sigma}}_{0}^{+}$ molecular terms to the $5s{}^{1}{\ensuremath{\Sigma}}_{0}^{+},$ $4d{}^{1}{\ensuremath{\Delta}}_{2},$ $4d{}^{1}{\ensuremath{\Pi}}_{1},$ and $4d{}^{1}{\ensuremath{\Sigma}}_{0}^{+}$ terms. Experimental details of the approach, and the results obtained, will be described. Discussion of the polarization spectra is made through theoretical modeling focusing on the effects of the symmetry of the molecular states involved in the process. The modeling employs the semiclassical theory developed earlier. For a range of qualitatively correct interaction potentials and corresponding Condon points for the photo-excitation channels, good agreement between experiment and theoretical estimates is obtained.
Cross sections for random collisional reorientation of J within the sublevels of the 62P326^{2}P_{\frac{3}{2}}62P23​​ excited state of cesium have been measured using the D2{D}_{2}D2​ optical-pumping technique. The measured cross sections ${{\ensuremath{\sigma}}_{M}}^{2}$ are: Cs-He (3.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm2{\mathrm{cm}}^{2}cm2, Cs-Ne (2.9\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm2{\mathrm{cm}}^{2}cm2, Cs-Ar (6.0\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm2{\mathrm{cm}}^{2}cm2, Cs-Kr (9.2\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm2{\mathrm{cm}}^{2}cm2, Cs-Xe (11.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ cm2{\mathrm{cm}}^{2}cm2. Simplified equations for D1{\mathrm{D}}_{1}D1​ and D2{\mathrm{D}}_{2}D2​ pumping with zero, partial, and complete excited-state mixing are derived for a hypothetical alkali atom with zero nuclear spin. The calculations are extended to cesium atoms with nuclear spin 72\frac{7}{2}27​ pumped by ${\ensuremath{\sigma}}^{+}$ D2{\mathrm{D}}_{2}D2​ radiation. The equilibrium value 〈Sz〉0{〈{S}_{z}〉}_{0}〈Sz​〉0​ and the time dependence 〈Sz(t)〉〈{S}_{z}(t)〉〈Sz​(t)〉 of the electronic spin polarization are computed for various degrees of excited-state mixing. 〈Sz(t)〉〈{S}_{z}(t)〉〈Sz​(t)〉 is found to be nearly single-exponential in the zero- and the complete-mixing cases, but shows a distinct double-exponential behavior in the intermediate region. 〈Sz〉0{〈{S}_{z}〉}_{0}〈Sz​〉0​ is shown to be dependent on the degree of mixing, and to change sign as the degree of mixing increases. Measurements were performed with a new transmission technique by passing a separate ${\ensuremath{\sigma}}^{+}$-polarized D2{\mathrm{D}}_{2}D2​ pumping beam and an alternately ${\ensuremath{\sigma}}^{+}$- and ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized D1{\mathrm{D}}_{1}D1​ testing beam through the cesium absorption cell. The cross sections for collisionally induced mixing were evaluated by measuring the buffer pressure at which 〈Sz〉0{〈{S}_{z}〉}_{0}〈Sz​〉0​ passed through zero.