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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Signal revivals in pulsed Rydberg four-wave mixing in thermal ensembles

Yi‐Hsin Chen, Fabian Ripka, Robert Löw, Tilman Pfau

Published Mar 7, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2222353

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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.
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 a pulsed four-wave mixing scheme via a Rydberg state to create, store, and retrieve collective Rydberg polaritons. The storage medium consists of a gas of thermal Rb atoms confined in a $220\ensuremath{-}\ensuremath{\mu}\mathrm{m}$-thick cell, which is heated above room temperature. The experimental sequence consists of a pulsed excitation of Rydberg polaritons via the D1{D}_{1}D1​ line, a variable delay or storage time, and a final retrieval pulse via the D2{D}_{2}D2​ line. The lifetime of the Rydberg polaritons is around 1.2 ns, almost entirely limited by the excitation bandwidth and the corresponding motional dephasing of the atoms. The presented scheme combined with a tightly confined atomic ensemble is a good candidate for a deterministic single-photon source, as soon as strong interactions in terms of a Rydberg blockade are added.
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.
In this work, we present a set of experiments involving four-wave mixing processes in rubidium atoms. We employ several experimental configurations exploring two- and three-level systems in cascade or Λ configurations, all of which are in a copropagating geometry, to investigate different physical phenomena present in each scenario. In the first experiment, we combine a cw diode laser and a 1 GHz femtosecond pulse train to generate coherent blue light through the four-wave mixing process in hot rubidium vapor. The generated coherent signal is analyzed by scanning either the diode frequency or the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler- Townes splitting with a wide separation in the doublet structure due to the configuration of copropagating fields. To model these results, we employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to explore other cases beyond those involving our experimental setup, comparing the response of the upper-level population and the generated signal coherence for homogeneously and non-homogeneously broadened systems. Moreover, in this same experiment, we also observed an unexpected interference effect between excitation routes of the four-wave mixing process when the repetition rate of the pulse train is scanned. The theoretical model demonstrates that the interfering effect appears only when the repetition rate is carefully chosen to produce a pair of modes of the frequency comb resonant with both one- and two-photon transitions for the same atomic velocity group. In the second experiment, still with a hot rubidium vapor, we explore two symmetrical degenerate four- wave mixing signals induced by two almost copropagating laser beams, with~ka and~kb wave-vectors, and detected simultaneously in the 2~ka −~kb and 2~kb −~ka directions. Each spectrum has a single peak with a short frequency separation between them, which our model indicates is due to the nonlinear behavior of the refractive indexes, a consequence of the high intensity of both input fields. Finally, we use the same experimental setup for the two symmetrical signals to study the field intensity fluctuations of the degenerate four-wave mixing signals and the transmission signals. In this case, the sample is an ensemble of cold rubidium atoms in a magneto-optical trap. There is an intensity- intensity cross-correlation between the signals due to the resonant phase-noise to amplitude-noise conversion. In this type of cold system, we can neglect the Doppler- broadening, allowing a straightforward study of the dependency of the correlations on the laser detuning. In these measurements, we observe a type of oscillation in the correlation curves that the theoretical model indicates to be connected with Rabi oscillations, revealed by the fluctuations long after the transient period.
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.