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Physical Review Letters

Frequency Mixing Using Electromagnetically Induced Transparency in Cold Atoms

Danielle Braje, Vlatko Balić, S. N. Goda, G. Y. Yin, Stephen E. Harris

Published Oct 29, 2004• 232 citations
Publisher

Abstract

We report the first experimental demonstration of four-wave mixing using electromagnetically induced transparency in cold atoms. Backward-wave, phase-matched difference-frequency conversion is achieved at optical powers of a few nanowatts and at energies of less than a picojoule.
DOI
10.1103/physrevlett.93.183601

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Electromagnetically induced transparency (EIT) in a four-level atomic system suppresses linear absorption and leads to resonantly enhanced slow-light four-wave mixing at low light intensities. We analyse the backward four-wave mixing in the four-level system under the EIT conditions, derive the four-wave-mixing efficiency and discuss slow-light propagation conditions. We present experimental measurements of resonant four-wave mixing with the backward scheme in cold Rb atoms and compare the experimental results with the theoretical calculations.
We observed electromagnetically induced transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of 3.8(9)3.8(9)%3.8(9) was observed in a four-level system of cold 87Rb{}^{87}\mathrm{Rb}87Rb atoms using a driving laser pulse with a peak intensity of $\ensuremath{\approx}80$ $\ensuremath{\mu}\mathrm{W}/{\mathrm{cm}}^{2}$, corresponding to an energy of $\ensuremath{\approx}60$ photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of 46(2)46(2)%46(2) was demonstrated when applying this scheme using a driving laser intensity of $\ensuremath{\approx}1.8$ mW/cm2\mathrm{mW}/{\mathrm{cm}}^{2}mW/cm2. According to our theoretical predictions, this FWM scheme can achieve a conversion efficiency of nearly 100100%100 when using a dense medium with an optical depth of 500.
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.
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.
Long-distance quantum optical communications usually require efficient wave-mixing processes to convert the wavelengths of single photons. Many quantum applications based on electromagnetically induced transparency (EIT) have been proposed and demonstrated at the single-photon level, such as quantum memories, all-optical transistors, and cross-phase modulations. However, EIT-based four-wave mixing (FWM) in a resonant double-$\mathrm{\ensuremath{\Lambda}}$ configuration has a maximum conversion efficiency (CE) of 25% because of absorptive loss due to spontaneous emission. An improved scheme using spatially modulated intensities of two control fields has been theoretically proposed to overcome this conversion limit. In this study, we first demonstrate wavelength conversion from 780 to 795 nm with a 43% CE by using this scheme at an optical density (OD) of 19 in cold 87Rb^{87}\mathrm{Rb}87Rb atoms. According to the theoretical model, the CE in the proposed scheme can further increase to 96% at an OD of 240 under ideal conditions, thereby attaining an identical CE to that of the previous nonresonant double-$\mathrm{\ensuremath{\Lambda}}$ scheme at half the OD. This spatial-light-modulation-based FWM scheme can achieve a near-unity CE, thus providing an easy method of implementing an efficient quantum wavelength converter for all-optical quantum information processing.