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arXiv:2009.11021 · Physical Review A

Quantum frequency conversion based on resonant four-wave mixing

Chin-Yao Cheng, Jia-Juan Lee, Ziyu Liu, Jiun‐Shiuan Shiu, Yong‐Fan Chen

Published Feb 15, 2021• 18 citations
arXivHTMLPDF

Abstract

Quantum frequency conversion (QFC), a critical technology in photonic quantum information science, requires that the quantum characteristics of the frequency-converted photon must be the same as the input photon except for the color. In nonlinear optics, the wave mixing effect far away from the resonance condition is often used to realize QFC because it can prevent the vacuum field reservoir from destroying the quantum state of the converted photon effectively. Under conditions far away from resonance, experiments typically require strong pump light to generate large nonlinear interactions to achieve high-efficiency QFC. However, strong pump light often generates additional noise photons through spontaneous Raman or parametric conversion processes. Herein, we theoretically study another efficient QFC scheme based on a resonant four-wave mixing system. Due to the effect of electromagnetically induced transparency (EIT), this resonant QFC scheme can greatly suppress vacuum field noise at low light levels; consequently, the converted photon can inherit the quantum state of the input photon with high fidelity. Our research demonstrates that if the conversion efficiency of the EIT-based QFC is close to 100%, the wave function and quadrature variance of the converted photon are almost the same as the input probe photon.

DOI
10.1103/physreva.103.023711

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Quantum frequency conversion (QFC), a critical technology in photonic quantum information science, requires that the quantum characteristics of the frequency-converted photon must be the same as the input photon except for the color. In nonlinear optics, the wave mixing effect far away from the resonance condition is often used to realize QFC because it can prevent the vacuum field reservoir from destroying the quantum state of the converted photon effectively. Under conditions far away from resonance, experiments typically require strong pump light to generate large nonlinear interactions to achieve high-efficiency QFC. However, strong pump light often generates additional noise photons through spontaneous Raman or parametric conversion processes. Herein, we theoretically study another efficient QFC scheme based on a resonant four-wave mixing system. Due to the effect of electromagnetically induced transparency (EIT), this resonant QFC scheme can greatly suppress vacuum field noise at low light levels; consequently, the converted photon can inherit the quantum state of the input photon with high fidelity. Our research demonstrates that if the conversion efficiency of the EIT-based QFC is close to 100%, the wave function and quadrature variance of the converted photon are almost the same as the input probe photon.
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 present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics, this Hamiltonian does not have a power expansion in the fields and the conversion length decreases with decreasing input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to 103{10}^{3}103 input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.
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.
Single-photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at subwatt pump powers. We present a detailed theoretical analysis of the conversion dynamics in these systems and show that they are capable of converting single- and multiphoton quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability density, and pump-power requirements are derived which are in good agreement with previous theoretical and experimental results. We show that with only modest improvement to the state of the art, efficiencies exceeding 95% are achievable using less than 100 mW of pump power. At the critical driving strength that yields maximum conversion efficiency, the spectral conversion probability density is shown to exhibit a flat-topped peak, indicating a range of insensitivity to the spectrum of a single-photon input. Two alternate theoretical approaches are presented to study the conversion dynamics: a dressed-mode approach that yields a better intuitive picture of the conversion process, and a study of the temporal dynamics of the participating modes in the resonator, which uncovers a regime of Rabi-like coherent oscillations of single photons between two different frequency modes. This oscillatory regime arises from the strong coupling of distinct frequency modes mediated by coherent pumps.
In this paper, we present a novel single stage quantum frequency conversion (QFC) scheme based on an enhancement cavity, which allows for high conversion efficiencies with record low noise levels, 100 times smaller than in previous systems and close to the thermal background. Our approach represents a significant improvement over traditional QFC methods that rely on periodically poled waveguide crystals, which typically produce high levels of noise with input wavelengths in the visible spectrum. One of the key challenges in QFC is the generation of noise photons - photons that are not part of the desired output state. Those noise photons are one of the major limitations of today’s quantum network experiments. It has been widely believed that single stage QFC of qubit photons in the visible range would result in too many noise photons in the telecom band, because of SPDC induced by the short wavelength driver laser. However, using the enhancement cavity design, we are able to overcome this challenge and demonstrate high-fidelity QFC from the visible to telecom band. Our results have important implications for the development of practical QFC devices for a range of applications, including quantum communication and quantum networks, where low noise levels are critical.