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arXiv:quant-ph/0203076 · Physical Review A

Consequences of induced transparency in a double-Λ scheme: Destructive interference in four-wave mixing

M. G. Payne, L. Deng

Published Jun 3, 2002• 53 citations
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Abstract

We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.

DOI
10.1103/physreva.65.063806

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We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.
We present a time-dependent calculation for four-wave mixing using a combination of long, short, and time delayed laser pulses in the context of electromagnetically induced transparency. Two transform limited nanosecond lasers are used to create a highly coherent mixture of the ground state and an excited state via a two-photon process. Once the induced transparency is established, a laser with short pulse length is injected after a suitable delay to generate four-wave mixing. We show that the wave mixing process is phase matched for all detunings, and with appropriately selected atomic coherence and populations, near 100% photon flux conversion efficiency can be obtained, independent of the intensity of the short pulse laser. In addition, we show that for small detunings for the short pulse laser, the four-wave mixing field travels with the speed of light in vacuum and suffers no pulse distortion even though the medium is highly dispersive at the frequency of the generated wave. These advantages open a door for future applications of the scheme for highly efficient, very stable UV generation.
Using room-temperature 87Rb atoms we demonstrate a quantum destructive interference between two one-photon excitation pathways in an inelastic two-wave mixing scheme that corresponds to the "strong-storage and weak-retrieval" of an optical field. This destructive interference is fundamentally different from the usual electromagnetically induced transparency because it is critically dependent on the generation and propagation of a wave-mixing field. We also show that contrary to the common belief, the maximum atomic coherence in general does not lead to the maximum mixing-wave conversion efficiency.
We show that in a two-mode, three-level, double-$\ensuremath{\Lambda}$ system an efficient multiphoton destructive interference involving one- and three-photon pumping pathways occurs, leading to a unique type of induced transparency. Unlike the conventional electromagnetically induced transparency achieved with a three-state $\ensuremath{\Lambda}$ system, the induced transparency is critically dependent upon two distinctive relaxation processes involving the production and propagation of an internally generated field. When a two-mode probe field is injected under suitable conditions, we show that the two probe pulses, after a characteristic propagation distance, evolve into a pair of temporal, amplitude, and group velocity matched pulse, traveling loss free in a highly dispersive medium.
We investigate the propagation dynamics of a two-mode probe field traveling with ultraslow group velocities. We show that a strong cross-beam coupling occurs between the two modes of the probe wave in the presence of a two-mode control laser field that maintains two-photon resonance excitations in a three-level system. In the adiabatic limit and under appropriate conditions, both modes can travel with matched temporal profiles, amplitudes, and greatly reduced group velocities, and one mode can grow and take on features of the other mode. When only one mode of probe field is injected, the generation and growth of the second mode has the characteristics of four-wave mixing, resulting in a tunable, ultraslow four-wave mixing field with nearly 100% photon flux conversion efficiency. We further show a type of induced transparency resulting from an efficient one- and three-photon destructive interference. This is to be contrasted with the conventional one-mode, three-level electromagnetically induced transparency where the interference involves two one-photon pathways.
The effect of electromagnetically induced transparency in resonant four-wave-mixing schemes is investigated in an analysis that goes beyond perturbation theory in the coherent driving field. In addition we examine the case where the two-photon pump field is sufficiently strong to necessitate a nonperturbative treatment. This allows us to examine the cases where either one or both of the driving fields are strong. Phase matching is included in a plane-wave propagation treatment that matches the situation most likely to be encountered in actual experiments. The calculations are in part intended to model real experimental situations and thus incorporate driving and pump-field linewidths via the phase-diffusion model and Doppler broadening. With a strong pump-field laser, large enhancements in the efficiency of light generation occur at frequencies corresponding to the Autler-Townes satellites induced by the strong driving field. In this situation gain and high four-wave-mixing efficiency are simultaneously present, resulting in the production of a large intensity of coherent radiation. \textcopyright{} 1996 The American Physical Society.
Electromagnetically-induced-transparency-based four-wave mixing (FWM) in a resonant four-level double-Λ system has a maximum conversion efficiency (CE) of 25% due to spontaneous emission. Herein, we demonstrate that spontaneous emission can be considerably suppressed by arranging the applied laser beams in a backward configuration. With the backward double-Λ FWM scheme, we observe a CE of 63% in cold rubidium atoms with an optical depth (OD) of 48. To the best of our knowledge, this is the first observation of a CE exceeding the conversion limit in resonant FWM processes. Furthermore, we present a theoretical model that includes the phase-mismatch effect in the backward double-Λ FWM system. According to the theoretical model, the present scheme can achieve 96% CE using a medium with a large OD of 200 under ideal conditions. Such an efficient frequency conversion scheme has potential applications in optical quantum information technology.