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arXiv:1611.02158 · Optics Express

Phase matching alters spatial multiphoton processes in dense atomic ensembles

Adam Leszczyński, Michal P. Parniak, Wojciech Wasilewski

Published Jan 4, 2017• 11 citations
arXivHTMLPDF

Abstract

Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.

DOI
10.1364/oe.25.000284

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Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.
Nondegenerate forward four-wave mixing in hot atomic vapors has been shown to produce strong quantum correlations between twin beams of light [McCormick et al., Opt. Lett. 32, 178 (2007)], in a configuration which minimizes losses by absorption. In this paper, we look at the role of the phase-matching condition in the trade-off that occurs between the efficiency of the nonlinear process and the absorption of the twin beams. To this effect, we develop a semiclassical model by deriving the atomic susceptibilities in the relevant double-$\ensuremath{\Lambda}$ configuration and by solving the classical propagation of the twin-beam fields for parameters close to those found in typical experiments. These theoretical results are confirmed by a simple experimental study of the nonlinear gain experienced by the twin beams as a function of the phase mismatch. The model shows that the amount of phase mismatch is key to the realization of the physical conditions in which the absorption of the twin beams is minimized while the cross coupling between the twin beams is maintained at the level required for the generation of strong quantum correlations. The optimum is reached when the four-wave mixing process is not phase matched for fully resonant four-wave mixing.
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 describe several novel experimental effects resulting from optical coherences in multilevel atoms driven with coherent laser fields. Four configurations were explored using Rb vapor cells: lambda dark-line resonances, single beam double-lambda oscillations, and cascade two-photon transitions in co- and counter-propagating geometries. Experiments were performed with high spectral-resolution using low-power diode lasers sources and optically thick cells. Two of the most striking effects we observed are: (1) a self-oscillation that occurs at 3.0 GHz on the 85Rb hyperfine frequency when a single laser field pumps the atoms, and (2) a coherent blue-beam emission that we observe in the co-propagating cascade two-photon case. These phenomena lead to complex lineshapes, and the effects sometimes dominate the well-known 3-level coherence effects. Additional higher-order mixing or cascaded interferences are apparent in all four experimental configurations. Many of these can be viewed as multi-wave mixing enhanced by optical coherences around closed-loop paths of atomic energy levels. The effects are particularly strong when four-photon closed-loop paths with resonant energy levels are possible, as in, the double-lambda system or as a four-wave mixing “box.”
We have measured -3.5 dB (-8.1 dB corrected for losses) relative intensity squeezing between probe and conjugate beams generated by stimulated, nondegenerate four-wave mixing in hot rubidium vapor. Unlike early observations of squeezing in atomic vapors based on saturation of a two-level system, our scheme uses a resonant nonlinearity based on ground-state coherences in a three-level system. Since this scheme produces narrowband, squeezed light near an atomic resonance, it is of interest for experiments involving cold atoms or atomic ensembles.