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Physical Review A

Four-wave mixing involving Rydberg states in thermal vapor

A. Kölle, G. Epple, Harald Kübler, R. Löw, Tilman Pfau

Published Jun 21, 2012• 58 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.85.063821

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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.
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 52S1/2,52P3/2,52D3/25{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},5{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2},5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}52S1/2​,52P3/2​,52D3/2​, and 52P1/25{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}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 investigate the transient response of the generated light from four-wave mixing (FWM) in the diamond configuration using a step-down field excitation. The transients show fast decay times and oscillations that depend on the detunings and intensities of the fields. A simplified model taking into account the thermal motion of the atoms, propagation, absorption, and dispersion effects shows qualitative agreement with the experimental observations with the energy levels in rubidium (5S1/25{S}_{1/2}5S1/2​, 5P1/25{P}_{1/2}5P1/2​, 5P3/25{P}_{3/2}5P3/2​, and 6S1/26{S}_{1/2}6S1/2​). The atomic polarization comes from all the contributions of different velocity classes of atoms in the ensemble modifying dramatically the total transient behavior of the light from FWM.
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 new results on the coherent control of a four-wave mixing signal in rubidium vapor involving Rydberg levels. By varying the relative polarizations of the laser beams responsible for the nonlinear process, we control atomic excitation routes and thus quantum interference in the medium. We observed interference fringes as a function of the relative polarizations and further developed a theoretical model based on the density-matrix formalism that is in very good agreement with our experimental results.
We report on observations of four-wave mixing in rubidium vapor via two-photon resonant excitation with nd and (n+2)s states, for n=14–20. The intensity of the generated beam is studied in a collinear configuration, and the results are consistent with the predictions of a theoretical model based on the semiclassical Maxwell–Bloch equations, considering interference effects associated with multiple excitation pathways and with internally generated fields. We have also observed spectral broadening of the two-photon resonant lines, which is well described by a linear dependence on atomic density, in accordance with collision-induced broadening.
We present resonant four-wave mixing (FWM) signals involving a Rydberg state in a thermal Rb vapor. The dynamic behavior of the FWM signals exhibits revival peaks shortly after the incident pulse, which are due to coherent collective emission among all Doppler classes. The FWM signals have dephasing times up to 7 ns, and strongly depend on the excitation bandwidth to the Rydberg state. Our numerical simulations based on a four-level model including the whole Doppler broadened ensemble can describe the data quite well.