Resonator-assisted single-photon frequency convertion in a conventional waveguide with a giant V-type atom

TL;DR

This paper addresses deterministic single-photon frequency conversion in a 1D waveguide by employing a V-type giant atom nonlocally coupled to the waveguide and to a single-mode resonator. The authors use a real-space scattering framework to derive the n+1 excitation subspace dynamics, where the GA-resonator coupling creates dressed states |n_±> with energies $\lambda_{n±} = n \omega_c + \nu_±^n$ and mixing angle $\tan\theta_n = 2\sqrt{n} g / \omega_{fc}$, leading to an effective $\Lambda$-type interaction for $n \ge 1$. Key results show that zero conversion arises from complete suppression of emission to the lower states (forming bound states in the continuum), while the maximal conversion under reciprocal conditions is 1/2; nonreciprocity and unit conversion become possible by tuning the resonator photon number $n$, the inter-coupling phase $\varphi_J$, and the delay $\tau$, with non-Markovian dynamics yielding multiple peaks/dips and enhanced nonreciprocity. The findings offer a route to on-chip frequency routing and nonreciprocal photon transport in quantum networks, leveraging phase-controlled interference and reservoir-induced memory effects.

Abstract

We propose a scheme to achieve efficient frequency conversion for a single photon propagating in a 1D conventional waveguide by exploiting the quantum interference induced by the scale of a V-type giant atom (GA) characterized by the distance between the two coupling points as well as single-photon transition pathways originated from the coupling between the GA and the resonator. The presence of photons in the resonator triggers the frequency conversion of photons. The scattering spectra and the conversion contrast are studied in both the Markovian and the non-Markovian regimes. The disappearance of frequency conversion is rooted in the complete suppression of the emission from the excited state to either of lower states in the $n+1$ subspace where $n$ is the photon number of the resonator, and the non-Markovicity-induced nonreciprocity is found under specific conditions. Altering the photon number $n$ induces the non-reciprocal transmission of single photons in the waveguide, hence, enhance the conversion probability.

Figures (7)

• Figure 1: Sketch of a $V$-type three-level atom coupled to a one-dimensional waveguide. The transition $|g\rangle \leftrightarrow |e\rangle$ is coupled to the waveguide at positions $x = \pm d/2$, while the transition $|g\rangle \leftrightarrow |f\rangle$ is coupled to a single-mode cavity.
• Figure 2: (a) The spontaneous damping rates $\Gamma _{\pm }^{n}$ and (b) the accumulated phases $\phi _{\pm }^{n}$ versus photon number $n$ with $g=5\Gamma ,\omega _{e}=1015\Gamma$, and $\Gamma \tau =0.01$.
• Figure 3: (a,c,e) The transmittance $T_{-}^{\,n}$ and (b,d,f) the conversion probability $T_{c}^{\,n}$ verse the scaled detuning $\Delta _{k}^{\,n}$ and the scaled phase (a,b) $\phi _{-}^{\,n}/\pi$, (c,d) $\phi _{+}^{\,n}/\pi$, (e,f) $\varphi _{J}/\pi$ when $n=1$, $|J_{1}|=|J_{2}|$ and $\omega _{fc}=0$. Other parameters are setting as follow: (a,b) $\varphi _{J}=0$ and $\phi _{+}^{\,n}=\pi /3$; (c,d) $\varphi _{J}=0$ and $\phi _{-}^{\,n}=\pi /3$; (e,f) $\phi _{-}^{\,n}=0$ and $\phi _{+}^{\,n}=\pi$.
• Figure 4: The transmittance (a) $T_{-}^{n}$, reflectance (b) $R_{-}^{n}$, and conversion probability (c) $T_{c}^{n}$ versus photon number $n$ and the scaled detuning $\Delta _{k}^{n}/\Gamma$ when $|J_{1}|=|J_{2}|$, $\omega _{fc}=0$, $\omega _{e}/\Gamma =1015$, $g/\Gamma =15$, $\varphi _{J}=0$, $\tau \Gamma =0.1\pi$. (d-f) The profile of the scattering spectra at $n=1,4,9,17,25$.
• Figure 5: The conversion contrast $I_{2}^{n}$ versus photon number $n$ and the scaled detuning $\Delta _{k}^{n}/\Gamma$ when $|J_{1}|=|J_{2}|$, $\omega _{fc}=0$, $\omega _{e}/\Gamma =1015$, $g/\Gamma =5$, $\tau \Gamma =0.1\pi$. (a) $\varphi _{J}=0.25\pi$, (c) $\varphi _{J}=0.5\pi$. (b,d) The profile of the conversion contrast at $n=1,3,4,9,11,16$.