Phase-modulated single-photon router

The single-photon routing properties in the system composed of two waveguides and two coupled cavities interacting with a two-level system are investigated theoretically. The phases of the coupling strengths are considered. The analytical expressions for the single-photon routing probabilities are obtained. The study shows that single-photon routing in a single waveguide or between two waveguides can be switched on or off by modulating the phase difference between the coupling constants. The analytical results also exhibit that the coupling between the two nanocavities plays an important role in the phase-dependent single-photon routing. We also show numerically the influence of the dissipation of cavities and atoms on routing properties. Our results may be useful in controlling and manipulating light-matter interactions based on waveguides at the single-photon level.

Figure 1

Phase-controlled single-photon routing configuration considered in this paper. Waveguide M and waveguide N couple, respectively, to cavity A and cavity B. The two cavities are linked by a two-level system. There is a direct interaction between the two cavities.

Figure 2

Phase-controlled resonant single-photon scattering probabilities for the case of a single waveguide without decays. (a) Transmission probability $T_m^r$. (b) Reflection probability $R_m^r$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, $|g_a|=|g_b|=J={10}^{-5}{\omega }_e$.

Figure 3

Single-photon scattering properties as a function of $G_m$ and detuning $\mathrm{\Delta }$ for the case of a single waveguide without decays. The left column shows (a) $T_m$ and (b) $R_m$ when $\mathrm{\Delta }\theta =\pi /2$, while the right column exhibits (c) $T_m$ and (d) $R_m$ when $\mathrm{\Delta }\theta =\pi$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, $J=|g_a|=|g_b|={10}^{-5}{\omega }_e$.

Figure 4

Phase-dependent resonant single-photon scattering probability for the case of two waveguides without decays. (a) Transmission probability $T_m^r$. (b) Reflection probability $R_m^r$. (c) Transfer probability $P_n^r$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, $G_m=|g_a|=|g_b|=0.1J={10}^{-5}{\omega }_e$.

Figure 5

Single-photon scattering properties as a function of $G_m$ and detuning $\mathrm{\Delta }$ without decays. The left column shows (a) $T_m$, (b) $R_m$, and (c) $P_n\left(c\right)$ when $\mathrm{\Delta }\theta =\pi /2$, while the right column exhibits (d) $T_m$, (e) $R_m$, and (f) $P_n$ when $\mathrm{\Delta }\theta =\pi$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, $|g_a|=|g_b|={10}^{-5}{\omega }_e$. $G_m=G_n$, $J=|g_a|=|g_b|={10}^{-5}{\omega }_e$.

Figure 6

Resonant photon transmission and reflection probabilities as a function of dissipation for the case of a single waveguide. The left column shows resonant photon transmission probabilities as a function of (a) ${\gamma }_a$ and (b) ${\gamma }_e$ with $\mathrm{\Delta }\theta =\pi$. The right column exhibits resonant photon reflection probabilities as a function of (c) ${\gamma }_a$ and (d) ${\gamma }_e$ with $\mathrm{\Delta }\theta =\pi /2$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, ${\gamma }_a={\gamma }_b$, $J=|g_a|=|g_b|={10}^{-5}{\omega }_e$. $G_m=0.1\left|g_a\right|$.

Figure 7

Resonant photon routing probabilities as a function of dissipations for the case of two waveguides. The left column shows resonant photon transmission probabilities $T_m^r$ as a function of (a) ${\gamma }_a$ and (b) ${\gamma }_e$ with $\mathrm{\Delta }\theta =\pi$. While the right column exhibits probabilities of resonant photon $P_n^r$ routed to the WN as a function of (c) ${\gamma }_a$ and (d) ${\gamma }_e$ with $\mathrm{\Delta }\theta =\pi /2$. In the calculations, ${\omega }_a={\omega }_b={\omega }_e$, ${\gamma }_a={\gamma }_b$, $G_m=G_n=0.1J=|g_a|=|g_b|={10}^{-5}{\omega }_e$.