We investigate experimentally and theoretically nondegenerate four-wave mixing in rubidium vapor using a diamond configuration (
5S1/2,
5P1/2,
5P3/2, and
6S1/2 levels). We model this process of three classical fields interacting with a four-level atomic system with the Schr\"odinger equation. The experimental results are in good agreement with theoretical predictions for the generated light as a function of detuning.
We develop a model to calculate nonlinear polarization in a nondegenerate four-wave mixing in diamond configuration which includes the effects of hyperfine structure and Doppler broadening. We verify the model against the experiment with
52S1/2,52P3/2,52D3/2, and
52P1/2 levels of rubidium 85. Treating the multilevel atomic system as a combination of many four-level systems we are able to express the nonlinear susceptibility of a thermal ensemble in a low-intensity regime in terms of Voigt-type profiles and obtain an excellent conformity of theory and experiment within this complex system. The agreement is also satisfactory at high intensity and the analytical model correctly predicts the positions and shapes of resonances. Our results elucidate the physics of coherent interaction of light with atoms involving higher excited levels in vapors at room temperature, which is used in an increasing range of applications.
We present experimental results on nondegenerate four-wave mixing in a thermal vapor cell of rubidium atoms via highly excited Rydberg states. We observe sub-Doppler spectral features and a large sensitivity of the mixed light mode to small electric fields due to the large polarizabilities of the involved Rydberg state. We observe a saturation of the optical response due to the nonlinear four-level physics. The strong interaction between Rydberg atoms and the associated Rydberg blockade could potentially increase the nonlinearity dramatically.
The polarization characteristics of the signal wave produced in Rb vapor by difference-frequency, parametric four-wave mixing (FWM) has been investigated for either ultrafast $(\ensuremath{\sim}150\phantom{\rule{0.3em}{0ex}}\mathrm{fs})$ or nanosecond time-scale excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}5d$,
7s two photon transitions. The electronic configurations of the
5d2D5∕2 and
7s2S1∕2 states of Rb, as well as their energy separation $(\ensuremath{\sim}608\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$, offers the opportunity to examine separately the resonantly enhanced $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}7s$, $5d\ensuremath{\rightarrow}6p\ensuremath{\rightarrow}5s$ FWM pathways on the nanosecond time scale and then to drive both channels simultaneously with an ultrafast pulse of sufficient spectral width. As expected, dye laser $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{ns})$ excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}5d$
(J=5∕2) transition produces a signal wave $({\ensuremath{\lambda}}_{s}\ensuremath{\sim}420\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ having the same ellipticity as the driving optical field. Two photon excitation of Rb
(7s) on the same time scale, however, generates an elliptically polarized signal when the pump is linearly polarized $(\ensuremath{\epsilon}=1)$, a result attributed to $7s\ensuremath{\rightarrow}6p$,
5p amplified spontaneous emission at $\ensuremath{\sim}4\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ and $\ensuremath{\sim}741\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, respectively. Simultaneous excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}7s$,
5d transitions with $\ensuremath{\sim}150\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ pulses centered at $\ensuremath{\sim}770\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ yields polarization characteristics that can be approximated as a superposition of those for the individual transitions, thus displaying weak coupling between the two FWM channels. Also, the influence of molecular contributions to the FWM signal is observed for Rb number densities above $\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.
We report on time-resolved pulsed four-wave mixing (FWM) signals in a thermal Rubidium vapor involving a Rydberg state. We observe FWM signals with dephasing times up to 7 ns, strongly dependent on the excitation bandwidth to the Rydberg state. The excitation to the Rydberg state is driven by a pulsed two-photon transition on ns timescales. Combined with a cw de-excitation laser, a strongly directional and collective emission is generated according to a combination of the phase matching effect and averaging over Doppler classes. In contrast to a previous report (Huber et al. in Phys Rev A 90: 053806, 2014) using off-resonant FWM, at a resonant FWM scheme we observe additional revivals of the signal shortly after the incident pulse has ended. We infer that this is a revival of motion-induced constructive interference between the coherent emissions of the thermal atoms. The resonant FWM scheme reveals a richer temporal structure of the signals, compared to similar, but off-resonant excitation schemes. A simple explanation lies in the selectivity of Doppler classes. Our numerical simulations based on a four-level model including a whole Doppler ensemble can qualitatively describe the data.
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.