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Optics Express

Four-wave mixing in a ladder configuration of warm 87 Rb atoms: a theoretical study

Heung‐Ryoul Noh, Han Seb Moon

Published Feb 10, 2021• 10 citations
Publisher

Abstract

We present a theoretical study of the four-wave mixing (FWM) spectra of 5 S 1/2 − 5 P 3/2 − 5 D 5/2 ladder-type transitions of 87 Rb atoms. The density matrix equations are solved by considering all the magnetic sublevels to calculate the FWM signals in the atomic vapor cell. These results are subsequently compared with the experimental results. We observe that the FWM signal propagating exactly opposite to the driving field is measured experimentally. Additionally, we demonstrate the effects of optical depth, laser linewidths, and the coupling field power on the FWM spectra. Finally, the origin of the dispersive-like FWM signal is investigated by intentionally varying the intrinsic atomic properties.

DOI
10.1364/oe.416960

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 24, 2012•2 citations
We present a theoretical study of the four-wave mixing (FWM) spectra of 5 S 1/2 − 5 P 3/2 − 5 D 5/2 ladder-type transitions of 87 Rb atoms. The density matrix equations are solved by considering all the magnetic sublevels to calculate the FWM signals in the atomic vapor cell. These results are subsequently compared with the experimental results. We observe that the FWM signal propagating exactly opposite to the driving field is measured experimentally. Additionally, we demonstrate the effects of optical depth, laser linewidths, and the coupling field power on the FWM spectra. Finally, the origin of the dispersive-like FWM signal is investigated by intentionally varying the intrinsic atomic properties.
Four-wave-mixing (FWM) radiation is generated between the hyperfine structures of the 5D and 5P states in a thermally broadened rubidium atomic vapor using resonant atomic coherence. Background-free unidirectional signals having narrow spectral linewidths are isolated and experimentally studied in the frequency domain, and the effects of the driving beam parameters on the properties of the radiation are discussed. The radiation has several new properties compared to traditional FWM radiations generated between the 5P and 5S states. The high-resolution signals obtained in this method could make it favorable in spectroscopic procedures that rely on two-photon fluorescence.
Rb atoms. By comparing the FWM spectra with the electromagnetically induced transparency (EIT) spectra of the hyperfine states, we confirm that the FWM process is significantly influenced by both ladder-type and V-type two-photon coherences. From the observed FWM signal of each hyperfine structure, we clarify the role of two-photon coherence in the FWM process under EIT, double-resonance optical pumping (DROP), and two-photon absorption (TPA) conditions in a ladder-type atomic system, which is dependent on the open degree of the hyperfine states, the laser intensity, and the laser frequency detuning.
We present investigations of nonlinear optical phenomena using a 87^{87}87Rb thermal vapour in a high magnetic field. The magnetic field (of strength 0.6~T) separates the optical transitions by more than their Doppler-broadened linewidths. This technique provides a high level of control over thermal-vapour systems, which can be used as a simpler alternative to conventional state-preparation methods such as optical pumping. Using this approach, we study electromagnetically induced transparency in a non-degenerate 3-level ladder system. Finding excellent agreement with the numerically modelled transmission spectra, we are able to directly infer the dipole moment of the 5P$_{3/2}\to5D5D5D_{5/2}$ transition ∣⟨5P3/2∣∣er∣∣5D5/2⟩∣=(2.27±0.002stat±0.04syst) ea0|\langle5P_{3/2}||er||5D_{5/2}\rangle|= (2.27\pm0.002_{\rm stat}\pm0.04_{\rm syst})~ea_{0}∣⟨5P3/2​∣∣er∣∣5D5/2​⟩∣=(2.27±0.002stat​±0.04syst​) ea0​. Changing the coupling field to a standing-wave geometry, we observe resonant enhanced absorption: an effect that previously had only been observed in systems involving 4 or more atomic states. We also consider four-wave mixing (FWM) in a diamond level-scheme. Compared to the zero magnetic field case, we find good agreement with the FWM spectra using a simple model, even in the regime of strong laser dressing. Finally, we investigate heralded single-photon generation by spontaneous FWM. With strong laser dressing we observe the appearance of collective quantum beats, a single-photon interference effect due to the relative motion of atoms in a collective spin excitation. A violation of the Cauchy-Schwarz inequality by 6.7 standard deviations is reported.
We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.
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.
We investigated the multi-photon process of each hyperfine-structure dependence on the probe and coupling laser intensities in the closed and open ladder-type atomic configurations in the 5S1/2–5P3/2–5D5/2 transition of 87Rb atoms. When the intensity of the probe laser was comparable to that of the coupling laser, a variation of the closed atomic configuration of the 5S1/2 (F = 2)–5P3/2 (F′ = 3)–5D5/2 (F″ = 4) cycling transition from transmittance to absorption was observed clearly. The spectral features due to multi-photon effects were understood intuitively by using diagrammatic analysis. The observed spectra as functions of the probe and coupling laser intensities were in good agreement with the numerical results calculated with full density matrix equations that included all the degenerate magnetic sublevels of the 5S1/2–5P3/2–5D5/2 transition.