Decoherence-free interaction and maximally entangled state generation in giant-atom semi-infinite waveguide systems

TL;DR

This work shows that decoherence-free interaction (DFI) between giant atoms can be realized in semi-infinite 1D waveguides for braided and nested configurations, enabling maximally entangled states in these setups. It derives a Markov master equation for M giant atoms with multiple connection points, analyzes the DFI conditions and entanglement dynamics using a non-Hermitian effective Hamiltonian in the single-excitation subspace, and demonstrates phase-tunable entanglement properties that surpass those in infinite-waveguide systems. The study further generalizes to multiple atoms, identifying specific phase values where DFI persists and multipartite entanglement (including W states with Q = 8/9) is achievable, while noting limitations in the nested configuration for some multipartite targets. These results establish a theoretical framework and practical pathway for DFI-based quantum information processing in giant-atom waveguide-QED platforms.

Abstract

Giant atoms are artificial atoms that can couple to a waveguide non-locally. Previous works have shown that two giant atoms in a braided configuration can interact through one-dimensional (1D) infinite and chiral waveguides, with both individual and collective atomic relaxation being fully suppressed. In this paper, however, we show that the decoherence-free interaction (DFI) between two giant atoms can be realized in both braided and nested configurations when the waveguide is semi-infinite. This protected interaction fails to appear in semi-infinite waveguide systems containing two separate giant atoms or two small atoms. We also study the entanglement generation between two giant atoms coupled to a 1D semi-infinite waveguide. The results show that the maximally entangled state is generated in both braided and nested configurations due to the formation of DFI, and in the separate configuration, the maximally achievable entanglement can exceed 0.5. Finally, we generalize the discussion on DFI and entanglement generation to the case involving multiple giant atoms coupled into a semi-infinite waveguide. This study presents a new scheme for realizing DFI and generating maximally entangled states in giant-atom waveguide-QED systems.

Figures (12)

• Figure 1: (Color online) Two giant atoms in a braided configuration coupled to a 1D semi-infinite waveguide. The connection points are located at coordinates $x_{j1}$ and $x_{j2}$, where $j = a, b$. In our work, we consider the case where the two giant atoms share the same transition frequency, i.e., $\omega_a = \omega_b = \omega_0$.
• Figure 2: (Color online) Exchange interaction and decay rates as a function of $\theta/\pi$ for two braided giant atoms.
• Figure 3: (Color online) $(a)$ Concurrence $C_{eg}^{B}$ as a function of $\theta/\pi$ and $\gamma t$. $(b)$ Concurrence $C_{eg}^{B}(t)$ as a function of $\gamma t$ at a given value of phase shift.
• Figure 4: (Color online) $(a)$ Two giant atoms in a separate configuration coupled to a 1D semi-infinite waveguide. $(b)$ Exchange interaction and decay rates as a function of $\theta/\pi$ for two separate giant atoms. $(c)$ Concurrence $C_{eg}^{S}$ as a function of $\theta/\pi$ and $\gamma t$.
• Figure 5: (Color online) $(a)$ Two giant atoms in a nested configuration coupled to a 1D semi-infinite waveguide. $(b)$ Exchange interaction and decay rates as a function of $\theta/\pi$ for two nested giant atoms. $(c)$ Concurrence $C_{eg}^{N}$ as a function of $\theta/\pi$ and $\gamma t$.