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Scientific Reports

High-efficiency backward four-wave mixing by quantum interference

Ziyu Liu, Jian-Ting Xiao, Jia-Kang Lin, Junjie Wu, Jz-Yuan Juo, Chin-Yao Cheng, Yong‐Fan Chen

Published Nov 13, 2017• 21 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-017-16062-5

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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.
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.
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.
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.
We have analyzed a five-level Λ-configuration four-wave mixing (FWM) scheme for obtaining high-efficiency FWM based on the two-electromagnetically induced transparency (EIT) in the ultraslow propagation regime. We find that the maximum FWM efficiency is nearly 30%, which is orders of magnitude larger than previous schemes based on the two-EIT. Our scheme allows the possibility for new technological applications such as nonlinear spectroscopy at very low light intensity, quantum single-photon nonlinear optics and quantum information science.
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.
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.