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Acta Physica Sinica

V type three-level symmetric second-order coherence theory of attosecond polarization beats

Gan Chen-Li, Zhang Yan-Peng, Yu Feng, Yu Xiao-Jun, Jie Wang, Chuangshe Li, Jianping Song, Keqing Lu, Xun Hou, (1)西安交通大学电子科学与技术系,西安 710049; (2)西安交通大学电子科学与技术系,西安 710049;中国科学院西安光学精密机械研究所瞬态光学技术国家重点实验室,西安 710068; (3)西安市农业学校,西安 710077; (4)中国科学院西安光学精密机械研究所瞬态光学技术国家重点实验室,西安 710068

Published Jan 1, 2005• 1 citation
Publisher

Abstract

Based on the phaseconjugate polarization interference between two onephoton processes, we have studied theoretically the symmetric sumfrequency polarization beat (SFPB) of V type threelevel system in attosecond scale in the case of arbitrary bandwidth or broadband linewidth laser. The homodyne detected SFPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. We have found that the accuracy in the measurement of the energylevel sum of two excited states which are dipolar forbidden transition to each other is determined by the homogeneous linewidths of the optical transitions and exceeds the laser linewidth. A Dopplerfree precision in the measurement of the energylevel sum can be achieved with an arbitrary bandwidth. The field correlation has weakly influence on the SFPB signal when the laser has a narrow bandwidth. When the laser has a broadband linewidth, the SFPB signal shows resonantnonresonant cross correlation. As an attosecond ultrafast modulation process, SFPB can be extended intrinsically to any sumfrequency of energylevels.

DOI
10.7498/aps.54.726

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Based on the phaseconjugate polarization interference between two onephoton processes, we have studied theoretically the symmetric sumfrequency polarization beat (SFPB) of V type threelevel system in attosecond scale in the case of arbitrary bandwidth or broadband linewidth laser. The homodyne detected SFPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. We have found that the accuracy in the measurement of the energylevel sum of two excited states which are dipolar forbidden transition to each other is determined by the homogeneous linewidths of the optical transitions and exceeds the laser linewidth. A Dopplerfree precision in the measurement of the energylevel sum can be achieved with an arbitrary bandwidth. The field correlation has weakly influence on the SFPB signal when the laser has a narrow bandwidth. When the laser has a broadband linewidth, the SFPB signal shows resonantnonresonant cross correlation. As an attosecond ultrafast modulation process, SFPB can be extended intrinsically to any sumfrequency of energylevels.
Based on the phase-conjugate polarization interference between two two-photon processes, we obtained an analytic closed form for the second-order or fourth-order Markovian stochastic correlation of the four-level attosecond sum-frequency polarization beat (FASPB) in the extremely Doppler-broadened limit. The homodyne-detected FASPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. The different roles of the amplitude fluctuations and the phase fluctuations can be understood physically in the time-domain picture. The field correlation has a weak influence on the FASPB signal when the laser has narrow bandwidth. In contrast, when the laser has broadband linewidth, the FASPB signal shows resonant-nonresonant cross-correlation, and drastic difference for three Markovian stochastic fields. The maxima of the two two-photon signals are shifted from zero time delay to the opposite direction, and the signal exhibits damping oscillation when the laser frequency is off-resonant from the two-photon transition. A Doppler-free precision in the measurement of the energy-level sum can be achieved with an arbitrary bandwidth. As an attosecond ultrafast modulation process, it can be extended intrinsically to any sum frequency of energy levels.
Based on the phase-conjugate polarization interference between two-pathway excitations, we obtained an analytic closed form for the second-order or fourth-order Markovian stochastic correlation of the V three-level sum-frequency polarization beat (SFPB) in attosecond scale. Novel interferometric oscillatory behavior is exposed in terms of radiation-radiation, radiation-matter, and matter-matter polarization beats. The phase-coherent control of the light beams in the SFPB is subtle. When the laser has broadband linewidth, the homodyne detected SFPB signal shows resonant-nonresonant cross correlation, a drastic difference for three Markovian stochastic fields, and the autocorrelation of the SFPB exhibits hybrid radiation-matter detuning terahertz damping oscillation. As an attosecond ultrafast modulation process, it can be extended intrinsically to any sum frequency of energy levels. It has been also found that the asymmetric behaviors of the polarization beat signals due to the unbalanced controllable dispersion effects between the two arms of interferometer do not affect the overall accuracy in case using the SFPB to measure the Doppler-free energy-level sum of two excited states.
An analytic closed form for the second-order or fourth-order Markovian stochastic correlation of attosecond sum-frequency polarization beat (ASPB) can be obtained in the extremely Doppler-broadened limit. The homodyne detected ASPB signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. The physical explanation for this is that the Gaussian-amplitude field undergoes stronger intensity fluctuations than a chaotic field. On the other hand, the intensity (amplitude) fluctuations of the Gaussian-amplitude field or the chaotic field are always much larger than the pure phase fluctuations of the phase-diffusion field. The field correlation has weakly influence on the ASPB signal when the laser has narrow bandwidth. In contrast, when the laser has broadband linewidth, the ASPB signal shows resonant-nonresonant cross correlation, and the sensitivities of ASPB signal to three Markovian stochastic models increase as time delay is increased. A Doppler-free precision in the measurement of the energy-level sum can be achieved with an arbitrary bandwidth. The advantage of ASPB is that the ultrafast modulation period 900as can still be improved, because the energy-level interval between ground state and excited state can be widely separated.
Based on the phase-conjugation polarization interference between two two-photon processes, we theoretically investigated the attosecond scale asymmetry sum-frequency polarization beat in four-level system (FASPB). The field correlation has weak influence on the FASPB signal when the laser has narrow bandwidth. Conversely, when the laser has broadband linewidth, the FASPB signal shows resonance-nonresonance cross correlation. The two-photon signal exhibits hybrid radiation-matter detuning terahertz damping oscillation, i. e., when the laser frequency is off resonance from the two-photon transition, the signal exhibits damping oscillation and the profile of the two-photon self-correlation signal also exhibits zero time-delay asymmetry of the maxima. We have also investigated the asymmetry of attosecond polarization beat caused by the shift of the two-photon self-correlation zero time-delay phenomenon, in which the maxima of the two two-photon signals are shifted from zero time-delay point to opposite directions. As an attosecond ultrafast modulation process，FASPB can be intrinsically extended to any level-summation systems of two dipolar forbidden excited states.
Based on the second-order coherence function, we have studied a phase-conjugate ultrafast modulation spectroscopy due to the interference between the fifth- and fifth-order optical polarizations in cascade three-level Doppler-broadened system. It is found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The beat signal depends on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field only affect higher than second-order coherence functions, they have little influence on the general temporal modulation behaviour of the beat signal. The cases that pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases the overall accuracy for the energy-level difference measurement is determined by the homogeneous linewidths of the optical transitions. Finally, the spatial modulation behaviour of the beat signal has also been discussed.
We have employed a second-order coherence function theory to study the effect of laser coherence on polarization beats in four-level system (PBFS). It is found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transition. The cases that pump beams have either narrow band or broadband linewidth are considered and it has been found that for both cases a Doppler-free precision in the measurement of the energy-level splitting between two excited states which are dipolar forbidden from the ground state can be achieved. We have also studied the asymmetric behavior of the polarization beats, and attributed this asymmetry to the shift of the zero time delay which is due to the dispersion of the optical components.