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Theoretical and experimental study of the 6S-8S two-photon absorption cross-section in cesium atoms

Michael Caracas Núñez, Miguel A. Gonzalez, Mayerlin Núñez Portela

Published Aug 14, 2023• 4 citations
Publisher

Abstract

The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.

DOI
10.1364/oe.496654

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[Experimental evaluation of the cross sections in Cs (6D(1/2)) + Cs(6S(1/2)) inelastic collisions].

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At a Cs density higher than 9 x 10(14) cm(-3), cesium vapor was irradiated in a glass fluorescence cell with pulses of radiation from an YAG-laser-pumped OPO laser, populating 6D(5/2) state by two-photon absorption. Energy transfer in Cs6(D(5/2)) + Cs (6S) collisions was studied using methods of atomic fluorescence. At the different Cs densities, we have measured the time-integrated intensities of the components and fitted a three-state rate equation model to obtain the cross sections. The experimental points were fitted to a straight line very well. The authors converted the gradient and intercept into cross sections. The cross section for 6D(5/2)-->6D(3/2) transfer is (2.1 +/- 0.4) x 10(14) cm2. The cross section for excitation transfer out of the 6D doublet is sigmaQ = (1.6 +/- 0.4) x 10(-14) cm2. The cross section on contains information on reverse energy pooling collisions [i.e., Cs(6D(3/2)) + Cs (6S(1/2))-->Cs(6P) + 6Cs(P)] and contribution from mining in 6Dj-->7P(J'), This latter contribution could be subtracted out using the results of a second experiment. At a Cs density lower than 6.0 x 10(12) cm3, the laser was used to pump the 6D(3/2) and 6D(5/2) states, respectively. The resulting fluorescence included the direct component emitted in the decay of the 6D(J) state and the sensitized component arising from the collisionally populated 7P(J') state. Relative intensities of the components yielded the cross sections. The cross-sections for the processes Cs(6D(5/2)) + Cs(6S(1/2))-->Cs(7P(J')) + Cs(6S(1/2)) are (1.6 +/- 0.5) x 10(-15) cm2. for J'= 3/2 and (6.5 +/- 2.1) x 10(-16) cm2, for J' = 1/2, respectively. The cross-sections for the processes Cs(6D(3/2) + Cs(6S(1/2))-->Cs (7P(J')) + Cs(6S(1/2)) are (1.9 +/- 0.6) x 10(-15) cm2. for J' = 3/2 and (7.6 + 2.4) x 10(-16) cm2, for J' = 1/2, respectively. The 6D(J) -->7P(J'), energy transfer rate coefficient is small. The total quenching rate coefficient out of the 6D(J) state is much larger. Evidence suggests that the quenching of the 6D(J) state is caused predominantly by reverse energy-pooling process. The cross section for this process, i.e., Cs(6D(3/2))+Cs(6S(1/2))-->Cs(6P) + Cs(6P) is (1.3 +/- 0.4) x 10(-14) cm2.

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By applying the laser absorption and fluorescence method,the cross sections for the fine structure mixing and quenching of the Cs(6P) state,induced by collision with He atoms,have been measured.Cesium atoms were optically excited to the 6P3/2 state.The excited atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single mode laser beam,which was tuned to the 6PJ→8S1/2 transitions.The effective radiative rates were calculated for the 6PJ→6S transitions.The fluorescence intensity I895 of the sensitized 6P1/2→6S1/2 emission was measured as a function of He density in the range 0.5×1018～4×1018cm-3 at constant temperature T=337 K.It was found that the quantity N/I895 exhibited a parabolic dependence on N,confirming that the quenching of the 6PJ states was due to collision with He atoms,not ground state Cs atoms.The coefficients of the second-order polynomial fitted through the measured data yielded the cross sections σ3/2→1/2=(1.46±0.51)×10-19 cm2 and σD=(2.28±0.80)×10-18 cm2 for the 6PJ fine structure mixing and quenching,respectively,due to collision with He atoms.

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Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+:Y3Al5O12using density matrix theory

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The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Journal of Physics Condensed Matter•Oct 5, 1999•0 citations
The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.
The Two-photon absorption processes (TPA) is of great interest due to its variety of technical applications. Two-photon transitions can be excited using light with different statistical properties, such as laser light (coherent light), pseudo-thermal light and entangled photons-pairs (ETPA). For a TPA process driven with entangled photons (ETPA), a linear dependence of the signal with the photon flux has been theoretically predicted and experimentally demonstrated by various groups. The main motivation for studying ETPA relies on the capability of inducing TPA with a low photon flux. This is advantageous to analyze, among other things, biological samples with a reduced probability of destroying them in the process. However, ETPA experiments developed to date raise many questions regarding the difficulty of isolating a signal in organic molecules. One of the main problems in these experiments is the difficulty to study independently all the systematic effects due to the complex structure of organic molecules. An alternative to clarify the origin of the signal is to study the ETPA process in atomic systems. In this case, the possibility to excite narrow band transitions with tunable single frequency lasers can provide a clear signature of the ETPA process. To achieve this objective, the first step consists of understanding TPA with coherent light, or classical TPA, and measuring the corresponding cross-section in atomic systems. Once the classical regime is characterized, the ETPA process can be studied considering decoherence effects and coherence between intermediate states. For this, the ETPA cross section must be calculated and measured. In this work we present a theoretical calculation of the ETPA transition probability and cross-section with the density operator formalism for the transition 62S1/2 →82S1/2. The theoretical results will be complemented with an experiment with atomic Cesium based in a coincidence detection scheme.
At a Cs density higher than 9 x 10(14) cm(-3), cesium vapor was irradiated in a glass fluorescence cell with pulses of radiation from an YAG-laser-pumped OPO laser, populating 6D(5/2) state by two-photon absorption. Energy transfer in Cs6(D(5/2)) + Cs (6S) collisions was studied using methods of atomic fluorescence. At the different Cs densities, we have measured the time-integrated intensities of the components and fitted a three-state rate equation model to obtain the cross sections. The experimental points were fitted to a straight line very well. The authors converted the gradient and intercept into cross sections. The cross section for 6D(5/2)-->6D(3/2) transfer is (2.1 +/- 0.4) x 10(14) cm2. The cross section for excitation transfer out of the 6D doublet is sigmaQ = (1.6 +/- 0.4) x 10(-14) cm2. The cross section on contains information on reverse energy pooling collisions [i.e., Cs(6D(3/2)) + Cs (6S(1/2))-->Cs(6P) + 6Cs(P)] and contribution from mining in 6Dj-->7P(J'), This latter contribution could be subtracted out using the results of a second experiment. At a Cs density lower than 6.0 x 10(12) cm3, the laser was used to pump the 6D(3/2) and 6D(5/2) states, respectively. The resulting fluorescence included the direct component emitted in the decay of the 6D(J) state and the sensitized component arising from the collisionally populated 7P(J') state. Relative intensities of the components yielded the cross sections. The cross-sections for the processes Cs(6D(5/2)) + Cs(6S(1/2))-->Cs(7P(J')) + Cs(6S(1/2)) are (1.6 +/- 0.5) x 10(-15) cm2. for J'= 3/2 and (6.5 +/- 2.1) x 10(-16) cm2, for J' = 1/2, respectively. The cross-sections for the processes Cs(6D(3/2) + Cs(6S(1/2))-->Cs (7P(J')) + Cs(6S(1/2)) are (1.9 +/- 0.6) x 10(-15) cm2. for J' = 3/2 and (7.6 + 2.4) x 10(-16) cm2, for J' = 1/2, respectively. The 6D(J) -->7P(J'), energy transfer rate coefficient is small. The total quenching rate coefficient out of the 6D(J) state is much larger. Evidence suggests that the quenching of the 6D(J) state is caused predominantly by reverse energy-pooling process. The cross section for this process, i.e., Cs(6D(3/2))+Cs(6S(1/2))-->Cs(6P) + Cs(6P) is (1.3 +/- 0.4) x 10(-14) cm2.
The discrepancies between theoretical and experimental results in the process of entangled two-photon absorption (ETPA) are not fully understood. Atomic systems are a promising alternative for investigating this process without the systematic effects present in molecules. We present a theoretical study of the ETPA process in cesium atoms, focusing on the 6S1/2 --> 8S1/2 transition. The ETPA cross section is evaluated both with and without the far-off-resonance (FOR) approximation, including the contributions from intermediate atomic states and decoherence effects. The quantum state of light considered is described by the joint spectral amplitude of photon-pairs produced by the spontaneous parametric down-conversion process. When the FOR approximation is applied, the enhancement factor is constant (36*pi). In contrast, without this approximation the enhancement factor oscillates with the entanglement time, and achieves a maximum value of ~500. These results show the limitations of approximations when calculating the ETPA cross section and contribute to the understanding of the discrepancies between theoretical and experimental values for the ETPA cross section in different samples. The numbers presented in this work can be a starting point for designing experiments aimed at measuring ETPA cross sections in alkali atoms.
By applying the laser absorption and fluorescence method,the cross sections for the fine structure mixing and quenching of the Cs(6P) state,induced by collision with He atoms,have been measured.Cesium atoms were optically excited to the 6P3/2 state.The excited atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single mode laser beam,which was tuned to the 6PJ→8S1/2 transitions.The effective radiative rates were calculated for the 6PJ→6S transitions.The fluorescence intensity I895 of the sensitized 6P1/2→6S1/2 emission was measured as a function of He density in the range 0.5×1018～4×1018cm-3 at constant temperature T=337 K.It was found that the quantity N/I895 exhibited a parabolic dependence on N,confirming that the quenching of the 6PJ states was due to collision with He atoms,not ground state Cs atoms.The coefficients of the second-order polynomial fitted through the measured data yielded the cross sections σ3/2→1/2=(1.46±0.51)×10-19 cm2 and σD=(2.28±0.80)×10-18 cm2 for the 6PJ fine structure mixing and quenching,respectively,due to collision with He atoms.
The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.