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arXiv:quant-ph/0412190 · Physical Review Letters

Four-Wave Mixing with Self-Phase Matching due to Collective Atomic Recoil

Gordon R. M. Robb, Brian W J McNeil

Published Jan 18, 2005• 9 citations
arXivHTMLPDF

Abstract

We describe a method for nondegenerate four-wave-mixing in a cold sample of four-level atoms. An integral part of the four-wave-mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Because of the generation of this density modulation, phase matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur; rather the density modulation acts to "self-phase match" the fields during the course of the wave-mixing process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment which would involve pumping a sample of cold Cs atoms with three infrared pump fields to produce blue light.

DOI
10.1103/physrevlett.94.023901

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We describe a method for nondegenerate four-wave-mixing in a cold sample of four-level atoms. An integral part of the four-wave-mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Because of the generation of this density modulation, phase matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur; rather the density modulation acts to "self-phase match" the fields during the course of the wave-mixing process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment which would involve pumping a sample of cold Cs atoms with three infrared pump fields to produce blue light.
We describe a method for sum-frequency generation via non-degenerate four-wave mixing in classical (thermal) and quantum ultracold atomic gases (BEC). An integral part of the sum-frequency generation process is a collective instability which spontaneously generates a periodic density modulation in the atomic gas with a period comparable to the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase matching between the pump and generated fields is not a necessary initial condition for this sum-frequency generation process to occur: rather the density modulation acts to 'self-phase-match' the fields during the course of the sum-frequency generation process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment to demonstrate a regime where the sum-frequency generation process evolves quantum mechanically, with discrete emission of sum-frequency photons. This experiment would involve pumping ultracold Cs atoms in a high-finesse unidirectional cavity with three infrared pump fields to produce blue light as a series of hyperbolic secant pulses.
Nondegenerate four-wave mixing (FWM) in diamond-type atomic systems has important applications in a wide range of fields, including quantum entanglement generation, frequency conversion, and optical information processing. Although the efficient self-seeded nondegenerate FWM with amplified spontaneous emission (ASE) has been realized extensively, the seeded nondegenerate FWM without ASE is inefficient in reported experiments so far. Here we present the experimental realization of the seeded nondegenerate FWM in cesium atoms with a significantly improved efficiency. Specifically, with two pump lasers at 852 and 921 nm and a seed laser at 895 nm, a continuous-wave laser at 876 nm is efficiently generated via FWM in a cesium vapor cell with a power up to 1.2 mW, three orders of magnitude larger than what has been achieved in previous experiments. The improvement of the efficiency benefits from the exact satisfaction of the phase-matching condition realized by an elaborately designed setup. Our results may find applications in the generation of squeezing and entanglement of light via nondegenerate FWM.
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.