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Physical Review A

Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system

Haitao Zhou, Dawei Wang, Dan Wang, Jun-Xiang Zhang, Shi-Yao Zhu

Published Nov 17, 2011• 45 citations
Publisher

Abstract

We experimentally demonstrate the high-efficiency reflection of a probe field in \ensuremath{\Lambda}-type three-level atoms of cesium vapor driven by two counterpropagating coupling fields. More than 60$%$ of reflection efficiency is observed at the phase-matching angle. The underlying mechanism theoretically is investigated as the four-wave mixing is enhanced by the electromagnetically-induced transparency. Both of the two Doppler-free two-photon resonances (one for the probe and co-propagating fields, the other for the reflected and the counterpropagation fields) play an important role in satisfying the phase matching in the reflection direction. The phase compensation due to the anomalous dispersion and the decrease of effective absorption length in the atomic system allow the efficient reflection to be observed in a wide range of incident angles of the probe field and detunings of the coupling field.

DOI
10.1103/physreva.84.053835

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We experimentally demonstrate the high-efficiency reflection of a probe field in \ensuremath{\Lambda}-type three-level atoms of cesium vapor driven by two counterpropagating coupling fields. More than 60% of reflection efficiency is observed at the phase-matching angle. The underlying mechanism theoretically is investigated as the four-wave mixing is enhanced by the electromagnetically-induced transparency. Both of the two Doppler-free two-photon resonances (one for the probe and co-propagating fields, the other for the reflected and the counterpropagation fields) play an important role in satisfying the phase matching in the reflection direction. The phase compensation due to the anomalous dispersion and the decrease of effective absorption length in the atomic system allow the efficient reflection to be observed in a wide range of incident angles of the probe field and detunings of the coupling field.
The phase compensation mechanism induced by anomalous dispersion in the reflection process of four-wave mixing (or reflection from a grating) in a three-level system is investigated, where the four wave vectors do not match in vacuum. An efficiency of the reflected signal of as high as 43% from a hot atomic cell of Cs is observed. The maximum reflection occurs when the frequency of the probe beam (and consequently the frequency of the reflected signal) is slightly red detuned from the transition frequency, which is attributed to the phase compensation from the steep anomalous dispersion accompanied with a strong probe absorption. The dependences of the efficiency on the angle between the coupling and probe lights, on the intensity of the coupling, field and on atomic density are studied. A theoretical model is presented and it is in good agreement with the experimental results.
The reflection spectrum of a probe light in a -type three-level atomic system coupled by an off-resonant standing-wave is investigated experimentally and theoretically. We show that the maximum value of reflection coefficient occurs when both of the coupling and probe lights are tuned off resonances from the atomic transitions. The nature of enhanced reflection is attributed to the phase compensation caused by the anomalous dispersion, which leads to a significant reduction of nonlinear phase mismatch in atomic four-wave mixing. At certain detuning of coupling and probe frequencies near two-photon resonance, there exits a best compensation, so the reflection efficiency reaches its maximum. The dependences of efficiency on the intensity of coupling fields and the density of atoms are also studied.
The Goos-H\"anchen shift of the system composed by two cavity walls and an intracavity atomic sample is presented. The atomic sample is treated as a four-level double-$\ensuremath{\Lambda}$ system, driven by the two counterpropagating coupling fields. The probe field experiences the discontinuous refractive index variation and is reflected. Moreover, under the phase-matching condition, the four-wave mixing effect based on electromagnetically induced transparency can cause effective reflection. The Goos-H\"anchen shifts appear in both situations and are carefully investigated in this article. We refer to the first one with the incident and reflected light having identical wavelength as the linear Goos-H\"anchen shift, and the second one with the reflection wavelength determined by the phase-matching condition as the nonlinear Goos-H\"anchen shift. The differences between the two kinds of shifts, such as the incident angle range, conditions for the shift peaks, and controllability, are discussed.
We report the experimental manipulation of the group velocities of reflected and transmitted light pulses in a degenerate two-level atomic system driven by a standing wave, which is created by two counter-propagating light beams of equal frequencies but variable amplitudes. It is shown that the light pulse is reflected with superluminal group velocity while the transmitted pulse propagates from subluminal to superluminal velocities via changing the power of the backward coupling field. We find that the simultaneous superluminal light reflection and transmission can be reached when the power of the backward field becomes closer or equal to the forward power, in this case the periodical absorption modulation for photonic structure is established in atoms. The theoretical discussion shows that the anomalous dispersion associated with a resonant absorption dip within the gain peak due to four-wave mixing leads to the superluminal reflection, while the varying dispersion from normal to anomalous at transparency, transparency within absorption, and electromagnetically induced absorption windows leads to the subluminal to superluminal transmission.
Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double- Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of 91.2 % ± 0.6 % by using this backward FWM system at an optical depth of 130 in cold 87 Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.