Giant atoms coupled to waveguide: Continuous coupling and multiple excitations

Abstract

We propose a stochastic Schrödinger equation (SSE) approach to investigate the dynamics of giant atoms coupled to a waveguide, addressing two critical gaps in existing research, namely insufficient exploration on continuous coupling and multiple excitations. A key finding is that continuous coupling, unlike discrete coupling at finite points, breaks the constant phase difference condition, thereby weakening the interference effects in giant atom-waveguide systems. In addition, a key technical advantage of the SSE approach is that auto- and cross-correlation functions can directly reflect the complex photon emission/absorption processes and time-delay effects in giant atom-waveguide systems. Moreover, the SSE approach also naturally handles multiple excitations, without increasing equation complexity as the number of excitations grows. This feature enables the investigation of multi-excitation initial states of the waveguide, such as thermal and squeezed initial states. Overall, our approach provides a powerful tool for studying the dynamics of giant atoms coupled to waveguide, particularly for continuous coupling and multi-excitation systems.

Figures (10)

• Figure 1: Schematic diagram of the two giant atoms (labeled “$a$” and “$b$” ) coupled to a waveguide. (a) Single coupling (small atom) with vacuum initial state of the waveguide. (b) Discrete coupling (two coupling points) with vacuum initial state of the waveguide. (c) Continuous coupling with multiple-excitation (e.g. thermal or squeezed) initial states of the waveguide.
• Figure 2: (a)-(c) Discrete coupling distributions for $m=1$, $m=2$, and $m=10$ coupling points, respectively. (d)-(f) Auto- and cross-correlation functions for $m=1$, $m=2$, and $m=10$, respectively.
• Figure 3: Time evolution of concurrence $C(t)$ for single-point (orange dotted), two-point (green dashed), and multi-point (blue solid) coupling cases. The parameters are identical to those in Fig. \ref{['fig:2']}.
• Figure 4: Gaussian distribution $g_{\mu}(x)$ for $s_{\mu}=0.01$, 0.1, and 2 (assuming $s_{a}=s_{b}$) are plotted in panels (a), (b), (c). The correlation functions $\alpha_{\mu\nu}(\tau)$ for $s_{\mu}=0.01$, $0.1$, and $2$ (assuming $s_{a}=s_{b}$) are plotted in panels (d), (e), (f).
• Figure 5: The weakening of interference effects as a consequence of the broadening of the continuous coupling. (a) Entanglement generation for different spatial distributions of the continuous coupling $g_{\mu}(x)$ given in Eq. (\ref{['eq:gx_2peak']}). (b) and (c) are the distribution functions $g_{a}(x)$ and $g_{b}(x)$ for the case $s_{\mu}=0.1$ and $s_{\mu}=1$ (assuming $s_{a}=s_{b}$), respectively.