Controlling entanglement by phase engineering in giant-atom waveguide

Abstract

We investigate the entanglement dynamics of two giant atoms coupled to a common waveguide. By introducing additional phase modulation at each coupling point, every photon propagation path is jointly controlled by two distinct coupling phases, enabling precise and flexible manipulation of the entanglement evolution. This phase engineering induces destructive interference among different paths, leading to entanglement dynamics in nested giant atoms that become equivalent to those of small atoms, as well as dynamical equivalence between separated and braided configurations. Furthermore, the proposed scheme significantly enhances the robustness of entanglement against variations in the phase shift, offering a practical route to generate stable entanglement and enabling quantum devices with programmable propagation and controllable memory effects.

Figures (8)

• Figure 1: Three typical configurations of two two-level giant atoms with transition frequencies $\omega_a$ and $\omega_b$ coupled to a common waveguide. (a) Separate coupling, (b) Braided coupling, and (c) Nested coupling. Each giant atom interacts with the waveguide via two coupling points labeled $x_{jn}$, where $j = a, b$ denotes the atom and $n = 1,2$ indexes its coupling points. The atom–waveguide coupling coefficient at position $x_{jn}$ is $g e^{i\varphi_{jn}}$, with $\varphi_{jn}$ the coupling phase.
• Figure 2: (a) Nested giant-atom configuration. For specific coupling phases, only a few propagation paths remain active (blue solid lines), while most are suppressed by destructive interference (red dashed lines). (b) Entanglement dynamics of two small atoms coupled to a waveguide with phase shift $\theta_{\alpha}$ between them, identical to the corresponding case in (a). (c) Entanglement dynamics of two small atoms with phase shift $\theta_{\alpha}+\theta_{\beta}$, matching the case in (d). (d) Another set of coupling-phase conditions leading to a different pattern of active and suppressed paths.
• Figure 3: Concurrence $C_N^{\mathrm{I}}$ ($C_N^{\mathrm{II}}$) as a function of the evolution time $\Gamma t$ and the phase shift $\theta_0$ for different coupling phases and time delays $\Gamma \tau_0$. (a) and (c): $\Gamma\tau_0=0$; (b) and (d): $\Gamma\tau_0=0.8$. Case I: $\varphi _{a1}=\varphi _{b1}=0$, $\varphi _{a2}=\varphi _{b2}=\pi/2$. Case II: $\varphi _{a1}=\varphi _{b2}=0$, $\varphi _{a2}=\varphi _{b1}=\pi/2$. Initial state: $|+\rangle = (|eg\rangle + |ge\rangle)/\sqrt{2}$.
• Figure 4: Concurrence $C_{N}^{\mathrm{I}}$ as a function of evolution time $\Gamma t$ and partial phase shift $\theta_\alpha$ for different $\theta_\beta$. Initial state $|+\rangle$ and time delay $\Gamma \tau_0=0.8$. The Time delay associated with $\theta_\alpha$ is $\tau_\alpha = \theta_\alpha \tau_\beta/\theta_\beta$. Coupling phases follow Case I.
• Figure 5: (a), (c), and (e) Concurrence $C_{S}^{+}$ as a function of the phase shift $\theta_0$ and the evolution time $\Gamma t$ for different time delays $\Gamma \tau_0$. (b), (d), and (f) Corresponding time traces. Parameters: initial state $|+\rangle$; coupling phases $\varphi_{a1}=\varphi_{b1}=0$ and $\varphi_{a2}=\varphi_{b2}=\pi/2$.