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Journal of the Optical Society of America B

Four-level polarization beats with broadband noisy light

Yanpeng Zhang, Chenli Gan, Shahid Munir Farooqi, Keqing Lu, Xun Hou, Tiantong Tang

Published May 1, 2002• 13 citations
Publisher

Abstract

Four-level polarization beats (FLPBs) with broadband noisy light are investigated by use of chaotic field, phase-diffusion, and Gaussian-amplitude models. The polarization beat signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. Different stochastic models of the laser field affect only the fourth-order coherence functions. The constant background of the beat signal originates from the amplitude fluctuation of the Markovian stochastic fields. The Gaussian-amplitude field shows fluctuations larger than the chaotic field, which in turn exhibits fluctuations much larger than for the phase-diffusion field with pure phase fluctuations caused by spontaneous emission. It is also found that the asymmetric behaviors of the polarization beat signals due to the unbalanced dispersion effects between the two arms of an interferometer and to the Doppler width do not affect the overall accuracy when FLPBs are used to measure the energy-level difference between two states that are dipolar forbidden from the ground state.

DOI
10.1364/josab.19.001204

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Journal of Physics B Atomic Molecular and Optical Physics•Apr 21, 2004•3 citations
Four-level polarization beats (FLPBs) with broadband noisy light are investigated by use of chaotic field, phase-diffusion, and Gaussian-amplitude models. The polarization beat signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. Different stochastic models of the laser field affect only the fourth-order coherence functions. The constant background of the beat signal originates from the amplitude fluctuation of the Markovian stochastic fields. The Gaussian-amplitude field shows fluctuations larger than the chaotic field, which in turn exhibits fluctuations much larger than for the phase-diffusion field with pure phase fluctuations caused by spontaneous emission. It is also found that the asymmetric behaviors of the polarization beat signals due to the unbalanced dispersion effects between the two arms of an interferometer and to the Doppler width do not affect the overall accuracy when FLPBs are used to measure the energy-level difference between two states that are dipolar forbidden from the ground state.
The correlation effects of sixth order on cascade three-level polarization beats are investigated using chaotic field, phase-diffusion, and Gaussian-amplitude models. The polarization beat signal is shown to be particularly sensitive to the statistical properties of the Markovian stochastic light fields with arbitrary bandwidth. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence functions. The constant background of the beat signal originates from the amplitude fluctuation of the Markovian stochastic fields. The Gaussian-amplitude field shows fluctuations larger than the chaotic field, which again exhibits fluctuations much larger than for the phase-diffusion field with pure phase fluctuations caused by spontaneous emission. The cases that the pump beams have either narrowband 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 difference of the excited states can be achieved. The sixth-order coherence function theory is of vital importance in cascade three-level polarization beats.
We have employed chaotic and phase-diffusion models to study the effects of laser fourth-order coherence on polarization beats with phase-conjugation geometry in a four-level system (PBFS). We found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the transverse relaxation rate of the transition. The modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Inasmuch as different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of phase fluctuation and amplitude fluctuation are pointed out. The cases that pump beams have either narrow-band or broadband linewidth are considered, and it is found that for both cases a Doppler-free precision in the measurement of the energy-level difference between two states that are dipolar forbidden from the ground state can be achieved. We also discuss the difference between the PBFS and ultrafast modulation spectroscopy from a physical viewpoint.
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.
The correlation effects of fourth-order on polarization beats in a V-type three-level system (PBVTS) are investigated using chaotic and phase-diffusion models. It has been found that the temporal behaviour of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behaviour of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The fourth-order coherence function theory of chaotic field is of vital importance in PBVTS. The cases where the 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 states can be achieved. Finally, the difference between the PBVTS and DeBeer's ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.
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.
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.