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Acta Physica Sinica

Two-photon asymmetric color-locking second-order stochastic correlation of attosecond polarization beats

Gan Chen-Li, Zhang Yan-Peng, Yu Xiao-Jun, Nie Zhi-Qiang, Li Ling, Jianping Song, Hao Ge, Jiang Tong, Zhang Xiang-Chen, Keqing Lu

Published Jan 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.56.2670

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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 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 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-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.
Based on color-locking noisy field correlation, a time-delayed method is proposed to suppress the thermal effect, and the ultrafast longitudinal relaxation time can be measured even in an absorbing medium. One interesting feature in field-correlation effects is that Rayleigh-enhanced four-wave mixing (RFWM) with color-locking noisy light exhibits spectral symmetry and temporal asymmetry with no coherence spike at $\ensuremath{\tau}=0$. Due to the interference between the Rayleigh-resonant signal and the nonresonant background, RFWM exhibits hybrid radiation-matter detuning with terahertz damping oscillations. The subtle Markovian high-order correlation effects have been investigated in the homodyne- or heterodyne-detected Rayleigh-enhanced attosecond sum-frequency polarization beats (RASPBs). Analytic closed forms of fourth-order Markovian stochastic correlations are characterized for homodyne (quadratic) and heterodyne (linear) detection, respectively. Based on the polarization interference between two four-wave mixing processes, the phase-sensitive detection of RASPBs has also been used to obtain the real and imaginary parts of the Rayleigh resonance.
Based on three stochastic models, the subtle, Markovian field-correlation effects have been investigated in homodyne-detected attosecond sum-frequency Raman-enhanced polarization beating (REPB) and heterodyne-detected femtosecond difference-frequency REPB. The different roles of the amplitude fluctuations and the phase fluctuations have been pointed out in both time and frequency domains. Analytic closed forms of the sixth-order and fourth-order Markovian stochastic correlations are characterized for homodyne (quadratic) and heterodyne (linear) detection, respectively. The attosecond sum-frequency REPB signal shows resonant-nonresonant cross correlation, asymmetric temporal behavior, and drastic difference for three Markovian stochastic fields, and the autocorrelation of REPB exhibits hybrid-radiation-matter-detuning-terahertz damping oscillation. The phase-diffusion model predicts a damping oscillation of the signal around a constant value in the narrowband case. The heterodyne-detected signal of REPB potentially offers rich dynamic information about the homogeneous, broadening, material phase of the third-order nonlinear susceptibility.
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.