Group delay controlled by the decoherence of a single artificial atom

Abstract

The ability to slow down light at the single-photon level has applications in quantum information processing and other quantum technologies. We demonstrate two methods, both using just a single artificial atom, enabling dynamic control over microwave light velocities in waveguide quantum electrodynamics (waveguide QED). Our methods are based on two distinct mechanisms harnessing the balance between radiative and non-radiative decay rates of a superconducting artificial atom in front of a mirror. In the first method, we tune the radiative decay of the atom using interference effects due to the mirror; in the second method, we pump the atom to control its non-radiative decay through the Autler--Townes effect. When the half the radiative decay rate exceeds the non-radiative decay rate, we observe positive group delay; conversely, dominance of the non-radiative decay rate results in negative group delay. Our results advance signal-processing capabilities in waveguide QED.

Figures (3)

• Figure 1: Illustrations of the atom--mirror systems. For detailed experimental setups and device images, see Sec. S1 of Ref. SupMat. The probe tone $\Omega_p$ can be either continuous-wave (CW) or pulsed. The reflected signal $r \Omega_p$ is measured by either a vector network analyzer or a digitizer. (a) Setup for Device 1, where $\Gamma_{10}$ is tuned by changing the atom frequency. (b) Setup for Device 2, where $\Gamma^n_{10}$ is tuned by CW pumping with $\Omega_c$ on the $|1\rangle \leftrightarrow |2\rangle$ transition.
• Figure 2: Tuning $\Gamma_{10}$ in Device 1 to modify $\tau_d$. Red arrows and data points indicate an example of positive $\tau_d$ at $\omega_{10} / 2\pi = \unit[7.7990]{GHz}$, while the orange arrows and data points show an example of negative $\tau_d$ at $\omega_{10} / 2\pi = \unit[7.6057]{GHz}$. Solid curves represent theoretical simulations based on Eqs. (\ref{['eq:refl_coeff']})--(\ref{['eq:delay_two_tone']}) in panels (c)--(e) and the optical Bloch equation (provided in Ref.~Lin2022) in panel (f), using extracted parameters given in Tables S1 and S2 of Ref. SupMat. Arrow $A$ indicates the singularity of $\tau_d$ at $\unit[7.650]{GHz}$, while arrow $B$ corresponds to the node at $\unit[7.534]{GHz}$, where $|r| = 1$ and $\tau_d$ vanishes. (a) Measured $|r|$ as a function of bias current $I$ (magnetic field) and probe frequency $\omega_p$, where $\omega_{10}$ is set by $I$. (b) Numerically calculated $\tau_d$ from the measured $\mathrm{Arg}(r)$ using Eq. (\ref{['eq:delay_two_tone']}). Colored arrows indicate line cuts corresponding to data points in (c,d). (c,d) Line cuts of $\mathrm{Arg}(r)$ and $\tau_d$, respectively, for different $\omega_{10}$. We observe a sign change between the slopes of the red and orange $\mathrm{Arg}(r)$ curves at $\delta_{p,10} = 0$, indicating the switching between positive and negative $\tau_d$. (e) $|r|$ (black data points) and $\tau_d$ (blue data points) versus $\omega_{10}$ when $\delta_{p,10} = 0$. These values are obtained from fine-grained measurements conducted near the singularity [arrow A in (a,b)]. The extracted $\tau_d$ from time-domain measurements are shown as pink data points. (f) Time-domain results. The green (purple) curve serves as the reference for the red (orange) curve, measured under far-detuned conditions.
• Figure 3: Tuning $\tau_d$ through pump-induced $\Gamma_{10}^n$ in Device 2. Deep blue arrows indicates the $\delta_{p,10} = 0$ vertical line cut. The arrows $A$ and $B$ indicate the location of the singularity ($r = 0$) at $\unit[-139.4]{dBm}$ and $\tau_d = 0$ at $\unit[-136.0]{dBm}$, respectively. Solid curves correspond to simulations based on the two-tone reflection formula (Eq. (S5) in Ref. SupMat) in (c)--(e), and formulas for time evolution (Eqs. (S6)--(S8) and (S16) in Ref. SupMat) in (f). These simulations utilize the extracted parameters given in Tables S1 and S2 in Ref. SupMat. (a) Measured $|r|$ as a function of $P_c \propto \Omega_c^2$ and $\delta_{p,10}$. (b) Numerically calculated $\tau_d$ from the measured $\mathrm{Arg}(r)$ according to Eq. (\ref{['eq:delay_two_tone']}). The black boundary curves represent $\tau_d = 0$. Colored horizontal arrows indicate different line cuts [$P_c = \unit[-127.1]{dBm}$ (cyan), $\unit[-138.1]{dBm}$ (orange), and $\unit[-152.1]{dBm}$ (red)] corresponding to those in (c,d); $\delta_{p,10} = 0$ (deep blue) corresponds to the one in (e). The simulations for (a,b) are shown in Fig. S7(b,c) of Ref. SupMat. (c,d) Line cuts of $\mathrm{Arg}(r)$ and $\tau_d$, respectively, for different $P_c$. (e) Power dependence of $|r|$ (black data points) and $\tau_d$ (blue data points) when $\delta_{p,10} = 0$. The extracted $\tau_d$ from time-domain measurements are shown as pink data points note1. (f) Time-domain results for $P_c=\unit[-115.1]{dBm}$ (purple), $\unit[-138.1]{dBm}$ (orange), and $\unit[-152.1]{dBm}$ (red). The green curve serves as the reference for the red and orange curves, measured under far-detuned condition. Additional details for different $P_c$ are provided in Fig. S7(d,e) of Ref. SupMat.