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Scientific Reports

Polarization-selective four-wave mixing in a degenerate multi-level system

Jaeuk Baek, Sanghyun Park, Min-Hwan Lee, Heung‐Ryoul Noh, Geol Moon

Published Mar 8, 2024• 7 citations
Publisher

Abstract

Abstract This paper describes the first observation of polarization-selective four-wave mixing signals in conventional coupling-probe spectroscopy, specifically, saturation absorption spectroscopy in 85Rb atoms. The four-wave mixing signal is induced by two counter-propagating laser beams in a degenerate multi-level atomic system, involving the $$F_g=3 \rightarrow F_e =2,3$$ F g = 3 → F e = 2 , 3 , and 4 transitions of the 85Rb D2 line. Consequently, the four-wave mixing signals copropagating along the probe beam induce polarization rotation of a linearly polarized probe beam. To distinguish these four-wave mixing signals from the resulting probe beam, we detect the polarization components orthogonal to the polarization direction of the input probe beam, depending on the linear polarization angles between the probe and coupling beams. The experimental findings demonstrate excellent agreement with theoretical results.

DOI
10.1038/s41598-024-56229-5

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Physical Review A•Aug 12, 2005•2 citations
Abstract This paper describes the first observation of polarization-selective four-wave mixing signals in conventional coupling-probe spectroscopy, specifically, saturation absorption spectroscopy in 85Rb atoms. The four-wave mixing signal is induced by two counter-propagating laser beams in a degenerate multi-level atomic system, involving the Fg=3→Fe=2,3F_g=3 \rightarrow F_e =2,3Fg​=3→Fe​=2,3 F g = 3 → F e = 2 , 3 , and 4 transitions of the 85Rb D2 line. Consequently, the four-wave mixing signals copropagating along the probe beam induce polarization rotation of a linearly polarized probe beam. To distinguish these four-wave mixing signals from the resulting probe beam, we detect the polarization components orthogonal to the polarization direction of the input probe beam, depending on the linear polarization angles between the probe and coupling beams. The experimental findings demonstrate excellent agreement with theoretical results.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
An analytical expression for the degenerate four-wave mixing signal produced in a medium composed of two-level atoms by pump and probe lasers of arbitrary intensities and parallel linear polarization, suffering negligible absorption and depletion, has been derived. The Abrams–Lind approach [Opt. Lett.2, 94 and 3, 205 (1978)] for deriving the phase-matched polarization has been extended to find all the other higher-order polarization terms contributing to the signal. The signal field amplitude is expressed as an infinite series whose convergence rate depends on the intensity of the input fields and their detuning from resonance. The solution is successfully verified by comparison with a full numerical nonperturbative calculation and is found to be equivalent to the Abrams–Lind result in the limit of weak probe intensity. The result is used to calculate the saturation effects on spectral line shape that are relevant to simulation of molecular spectra obtained by degenerate four-wave mixing with saturating pump and probe fields. The result is extended to treat atomic motion in the case of forward geometry of the input beams.
Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field's polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field's polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.
The impact of the pump polarization during the Rb atom degenerate four-wave mixing process on the degenerate four-wave mixing signals is studied.In the experiment,a pump light and the probe light transmitted in the same direction into the air chamber Rb atoms,and the other pump light propagated through the atoms in the opposite direction.Then,by changing the polarization of the two pump lights,the four-wave mixing signal is observed.The result shows that when the two pump light polarization is parallel,a strong four-wave mixing signal can be observed.While the two pump light polarization is orthogonal to each other,the four-wave mixing signal disappear.The theoretical analysis indicates that the population grating induced by the pump beam interference is the physics mechanism of the degenerate four-wave mixing signal.
We report on a new method to achieve the single-scan polarization-resolved degenerate four-wave mixing (DFWM) spectroscopy in a Rb atomic medium using a vector optical field, in which two pump beams are kept linearly polarized and a vector beam is employed as the probe beam. As the polarization and intensity of the DFWM signal are closely dependent on the polarization state of the probe beam, a vector probe beam with space-variant states of polarization is able to generate a DFWM signal with space-variant states of polarization and intensity across the DFWM image. Accordingly, the polarization-resolved spectra can be retrieved from a single DFWM image. To the best of our knowledge, this is the first time that the single-scan polarization-resolved spectrum detection has been realized experimentally with a vector beam. This work provides a simple but efficient single-scan polarization-resolved spectroscopic method, which would be of great utility for the samples of poor light stability and fast optical processes.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.