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arXiv:2406.03484 · Physical Review A

Raman effects in quantum frequency conversion using Bragg scattering

Mathias Linde Holst Korsgaard, Jacob G. Koefoed, Karsten K. Rottwitt

Published Sep 4, 2024• 5 citations
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Abstract

We present a quantum-mechanical model that describes fiber-based frequency conversion by four-wave-mixing Bragg scattering in the presence of Raman interactions. In the case of continuous-wave pumps, we find closed-form expressions for the conversion efficiency and photon statistics characterized by the second-order correlation function. For pulsed pumps, we derive a highly general model based on Green functions and provide a numerical solution method using a split-step scheme. In both cases, we find that noise from spontaneous Raman scattering can pose a serious challenge to this type of frequency conversion if the pumps are less than 30 THz from the quantum fields. However, this impact can be mitigated with cross-polarized pumps and, on the anti-Stokes side, through fiber cooling.

DOI
10.1103/physreva.110.033508

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We present a quantum-mechanical model that describes fiber-based frequency conversion by four-wave-mixing Bragg scattering in the presence of Raman interactions. In the case of continuous-wave pumps, we find closed-form expressions for the conversion efficiency and photon statistics characterized by the second-order correlation function. For pulsed pumps, we derive a highly general model based on Green functions and provide a numerical solution method using a split-step scheme. In both cases, we find that noise from spontaneous Raman scattering can pose a serious challenge to this type of frequency conversion if the pumps are less than 30 THz from the quantum fields. However, this impact can be mitigated with cross-polarized pumps and, on the anti-Stokes side, through fiber cooling.
Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise-less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here. We find that Raman scattering induces a NF in the BS process that is comparable to the 3-dB NF associated with linear amplifiers
Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise-less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here. We find that Raman scattering induces a NF in the BS process that is comparable to the 3-dB NF associated with linear amplifiers.
We experimentally demonstrate frequency translation of a non-classical optical field by Bragg-scattering four-wave mixing, driven by orthogonally polarized pump pulses in a birefringent optical fiber. Heralded single photons are up- and down-translated by 6.8 THz between bands at 688.1 nm and 678.2 nm, each with efficiency > 97%. The input and output spectral shape and bandwidth show negligible modulation. Second-order auto-correlation measurements of the 678.2 nm and 688.1 nm fields at maximum conversion yield values of 0.0302 ± 0.0005 and 0.028 ± 0.001, respectively, compared with the input second-order correlation of 0.026 ± 0.001; this indicates that the frequency translation process preserves the non-classical nature of the field. The high efficiency, broad bandwidth, and low noise render this scheme useful for quantum networks and sources.
In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.
Hybrid quantum networks will be based on nodes that operate at different wavelengths, requiring quantum channel standardization via quantum frequency conversion (QFC). QFC is typically based on highly efficient sum- or difference-frequency generation in second-order nonlinear materials, such as periodically poled lithium niobate waveguides. The presence of the strong pump beam in such a nonlinear medium leads to unwanted nonlinear processes that produce noise. One of these noise processes is spontaneous Raman scattering (SRS). Typically, the pump is chosen to be the longest wavelength in the second-order nonlinear mixing process so that noise photons at the signal wavelength are produced by the less efficient anti-Stokes Raman scattering process rather than the Stokes scattering process. Since SRS is a temperature-dependent process, lowering the temperature reduces the Raman-scattered photons. We discuss the theory of temperature-dependent Raman scattering and present experimental results of the temperature dependence of dark count rates in a guided-wave QFC device.