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arXiv:1512.04843 · Applied Physics B

Pulsed Rydberg four-wave mixing with motion-induced dephasing in a thermal vapor

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

Published Jan 1, 2016• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1007/s00340-015-6277-8

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Journal of the Optical Society of America B•Jun 27, 2014•18 citations
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 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 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.
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 present a theoretical model of a four-photon excitation process to the Rydberg state in thermal atomic vapor where the motion-induced dephasing in the system is eliminated. This is achieved by arranging the four laser beams in a suitable geometry such that the residual wave vector is reduced to zero. The method of adiabatic elimination has been used to reduce the complex five-level system to an effective three-level system to study electromagnetically induced transparency (EIT) where the transition from ground state to second excited state can be considered as the effective probe and second excited state to the Rydberg state as the effective coupling transition. The effect of the blockade phenomenon is observed in the strong interaction regime, where the two atoms are considered to be moving with independent velocities and the system is Doppler averaged using Monte Carlo simulation technique. Also, the dephasing mechanisms in the system are investigated in detail. Though the system is not frozen during the excitation process, a strong blockade effect is still observed similar to the cold atom system. We conclude the paper with a proposal for experimentally investigating the four-photon excitation process to the Rydberg state in thermal rubidium vapor.
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.