Controllable Scattering of a Single Photon inside a One-Dimensional Resonator Waveguide

We analyze the coherent transport of a single photon, which propagates in a one-dimensional coupled-resonator waveguide and is scattered by a controllable two-level system located inside one of the resonators of this waveguide. Our approach, which uses discrete coordinates, unifies low and high energy effective theories for single-photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of a single photon. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators and qubits.

Figure 1

Schematic configuration for the coherent transport of a single photon in a coupled-resonator waveguide (a) coupled to a two-level system (b), which is located in one of the resonators. (c) Schematic diagram of coupled superconducting transmission line resonators with one resonator coupled to a dc-SQUID-based charge qubit.

Figure 2

The reflection coefficient $R$ (blue solid line) and the transmission coefficient, $1-R$ (red dashed line) as a function of either the momentum $k$ or the detuning $\Delta ={\Omega }_k-\Omega$, when $\omega =\Omega =5$ with intercavity coupling $\xi =2$, [for (a),(b)]; and $\omega =5$, $\Omega =6$ with $\xi =1$ [for (c),(d)]. Parameters are in units of $J$.

Figure 3

Comparison between the Fano-like line shape (blue solid line) in Eq. (7) and the Fano line shape (red dashed line) given by $F(\Delta )=(\Delta /{\delta }_{\xi }+y_0-q\Gamma {)}^2[(\Delta /{\delta }_{\xi }+y_0{)}^2+{\Gamma }^2{]}^{-1}$ at ${\delta }_{\xi }=-3$ and $\xi =0.01$, where all the parameters are in units of $J$. The detunings are $\Delta ={\Omega }_k-\Omega$ and ${\delta }_{\xi }=\omega -\Omega -2\xi$.

Figure 4

Phase diagrams of the reflection spectrum $R(\Delta )$ in Eq. (7): (a) with respect to the intercavity coupling $\xi$ and the detuning $\delta =\omega -\Omega$, in units of $J$; (b) with respect to $J$ and $\delta$, in units of $\xi$; both at $k=\pi /8$.