Correlation Functions and Photon-Photon Interactions Controlled by a Giant Atom

Abstract

Waveguide quantum electrodynamics (WQED) provides a powerful platform for exploring quantum optical phenomena by enhancing atom-photon interactions through photon confinement in a waveguide. Here we investigate the photon-scattering dynamics of a weak coherent pulse incident from the left on a giant atom coupled to a bidirectional waveguide, focusing on effects absent in the small-atom approximation. Using an extended input-output formalism, we calculate the relevant correlation functions and show that the competition between two scattering processes is governed by the ratio of the pulse width to the atomic lifetime, leading to time-dependent switching between bunching and antibunching. In addition, tuning the phase accumulated between the two coupling points of the giant atom allows the photon statistics to be switched among three distinct regimes, each with a finite phase bandwidth. We also discuss the experimental feasibility in superconducting circuits. Our results provide a route toward giant-atom-based control of photon pulses and potential applications in quantum control.

Figures (7)

• Figure 1: Schematic of a two-level giant atom coupled to a waveguide at two points with coupling strengths $g_1$ and $g_2$. A weak coherent pulse is incident from the left.
• Figure 2: Second-order correlation functions of both photons are transmitted for different giant atom lifetime $\tau$ relative to the pulse width $\delta_t$. (a)-(e) Unnormalized second-order correlation function. (f)-(j) Corresponding product of the single-photon intensity spectrum.
• Figure 3: Transitions between bunching and antibunching in the second-order correlation function. (a) Normalized second-order correlation function. (b) Equal-time normalized second-order correlation function (blue curve, indicated by the black dashed line in panel (a)) and the product of the single-photon intensities (orange curve).
• Figure 4: Normalized equal-time second-order correlation functions for different ratios of the giant atom lifetime $\tau$ to the pulse width $\delta_t$. The left and right insets zoom in on $C^{(2)}_{tt}(t,t)$ in the ranges from $-1.1$ to $0.6$ and from $2.0$ to $3.0$, respectively. The blue, orange, green, red, purple, and brown curves correspond to $\delta_t=0.3\tau,~0.5\tau,~0.8\tau,~1\tau,~1.5\tau,~3\tau$.
• Figure 5: Normalized second-order correlation function for different phases $\phi_0$. (a) $\phi_0=0$. (b) $\phi_0=\pi/2$. (c) $\phi_0=2\pi/3$. (d) $\phi_0=\pi$. (e) Normalized second-order correlation function as a function of $\phi_0$ and $t_1-t_2$, with $t_1+t_2=-0.5\delta_t$. (f) Line cut of panel (e) at $t_1-t_2=0$, plotted as a function of $\phi_0$.