Manipulating single-photon transport in a waveguide-QED structure containing two giant atoms

We investigate coherent single-photon transport in a waveguide-QED structure containing two giant atoms. The unified analytical expressions of the single-photon scattering amplitudes applicable for different topological configurations are derived. The spectroscopic characteristics in different parameter regimes, especially the asymmetric Fano line shapes and the electromagnetically induced transparency (EIT)-like spectra, are analyzed in detail. Specifically, we find that the appearance of Fano line shapes is influenced by not only the phase delays between coupling points but also the topologies of system. We also summarize the general conditions for appearance of EIT-like spectra by analyzing the master equation and verify these conditions by checking the corresponding analytical expressions of the scattering spectra. These phenomena may provide powerful tools for controlling and manipulating photon transport in future quantum networks.

Figure 1

Sketches of two giant atoms coupled to an open waveguide for three distinct topologies: (a) two separate giant atoms, (b) two braided giant atoms, and (c) two nested giant atoms.

Figure 2

(a) Reflectance $R$ for two separate giant atoms as functions of detuning $\mathrm{\Delta }$ and phase $\varphi$. The black dashed line is used to label the locations of the reflection peaks. The white dashed lines are used to label the reflection minima. The curves in (b)–(i) show cross sections of panel (a) at phases (b) $\varphi =0$, (c) $\varphi =0.05\pi$, (d) $\varphi =\pi /4$, (e) $\varphi =0.45\pi$, (f) $\varphi =\pi /2$, (g) $\varphi =0.55\pi$, (h) $\varphi =3\pi /4$, and (i) $\varphi =0.92\pi$.

Figure 3

(a) Reflectance $R$ for two braided giant atoms as functions of detuning $\mathrm{\Delta }$ and phase $\varphi$. The black dashed line is used to label the locations of the reflection peaks. The white dashed lines are used to label the reflection minima. The curves in (b)–(d) show cross sections of panel (a) at phases (b) $\varphi =0$, (c) $\varphi =\pi /10$, and (d) $\varphi =0.47\pi$.

Figure 4

(a) Reflectance $R$ for two nested giant atoms as functions of detuning $\mathrm{\Delta }$ and phase $\varphi$. The black dashed line is used to label the locations of the reflection peaks. The white dashed lines are used to label the reflection minima. The curves in (b)–(g) show cross sections of panel (a) at phases (b) $\varphi =0$, (c) $\varphi =\pi /10$, (d) $\varphi =\pi /3$, (e) $\varphi =2\pi /3$, (f) $\varphi =0.71\pi$, and (g) $\varphi =4\pi /5$.

Figure 5

Individual decays ${\mathrm{\Gamma }}_{\mathrm{S}}$ (red solid lines), ${\mathrm{\Gamma }}_{\mathrm{A}}$ (black dashed lines), and collective decay ${\mathrm{\Gamma }}_{\mathrm{SA}}$ (orange dot-dashed lines) as functions of $\varphi$ for three topologies: (a) two separate atoms, (b) two braided atoms, and (c) two nested atoms. The insets are the reflection spectra as functions of ${\mathrm{\Delta }}_a$ (in unit of $\gamma$) at the phase delay indicated by the blue arrows, where EIT phenomena appear. The detunings between two atoms are chosen as ${\mathrm{\Delta }}_{ab}=-\gamma$ in the leftmost inset in panel (c), and ${\mathrm{\Delta }}_{ab}=\gamma$ in the other insets.

Figure 6

EIT-like spectra caused by waveguide-mediated interactions between single-atom states. (a)–(c) Two braided atoms with parameters ${\varphi }_{a1}=0$, ${\varphi }_{a2}=\pi$, ${\varphi }_{b1}=0.25\pi$, ${\varphi }_{b2}=2.25\pi$, and ${\gamma }_a={\gamma }_b=\gamma$. The detunings between two atoms are (a) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}-2.5\gamma$, (b) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}$, and (c) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}+2.5\gamma$, respectively. (d)–(f) Two nested atoms with parameters ${\varphi }_{a1}=0$, ${\varphi }_{a2}=\pi$, ${\varphi }_{b1}=0.25\pi$, ${\varphi }_{b2}=0.75\pi$, ${\gamma }_a=\gamma$, and ${\gamma }_b=10\gamma$. The detunings between two atoms are (d) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}-2.5\gamma$, (e) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}$, and (f) ${\mathrm{\Delta }}_{ab}={\mathrm{\Delta }}_{\mathrm{L},b}+2.5\gamma$, respectively.

Figure 7

Transmission coefficient (solid lines), reflection coefficient (dashed lines), and inelastic photon flux (dotted lines) as a function of probe detuning ${\mathrm{\Delta }}_a$ for three different configurations. All systems are in the parameter regime where they fulfill the EIT criteria given in Sec. 4a. (a) Two separate giant atoms; the system parameters are the same as those used in the left inset in Fig. 5, the coherent drive amplitude is ${\left|\alpha \right|}^2=0.04\gamma$. (b) Two braided giant atoms; the system parameters are the same as those used in the left inset in Fig. 5, the coherent drive amplitude is ${\left|\alpha \right|}^2=0.04\gamma$. (c) Two nested giant atoms; the system parameters are the same as those used in the left inset in Fig. 5, the coherent drive amplitude is ${\left|\alpha \right|}^2=0.01\gamma$.

Figure 8

Transmission coefficient (solid lines), reflection coefficient (dashed lines), and inelastic photon flux (dotted lines) as a function of probe detuning ${\mathrm{\Delta }}_a$ for the braised and the nested configurations. All systems are in the parameter regime where they fulfill the EIT criteria given in Sec. 4b. (a) Two braided giant atoms; the system parameters are the same as those used in Fig. 6, the coherent drive amplitude is ${\left|\alpha \right|}^2=0.01\gamma$. (b) Two nested giant atoms; the system parameters are the same as those used in Fig. 6, the coherent drive amplitude is ${\left|\alpha \right|}^2=0.04\gamma$.