Doublon bound states in the continuum through giant atoms

Abstract

Bound states in the continuum (BICs) are spatially localized modes embedded in the spectrum of extended states, typically stabilized by symmetry or interference. While extensively studied in single-particle and linear systems, the many-body regime of BICs remains largely unexplored. Here, we demonstrate that giant atoms, quantum emitters coupled nonlocally to structured waveguides, can host robust doublon BICs, i.e., two-photon bound states stabilized by destructive interference and interactions. We first analyze a driven two-photon emission process and show how doublon BICs arise and mediate decoherence-free interaction between distant atoms. We then demonstrate that these many-body BICs also emerge under natural, undriven dynamics via a virtual two-photon emission process in three-level giant atoms. Our results reveal an interference-based mechanism for stabilizing many-body localization in open quantum systems, with potential applications in quantum simulation, non-ergodic dynamics, and protected quantum information processing.

Figures (3)

• Figure 1: Overview of the system. (a) Schematic of two three-level GAs coupled to a structured waveguide with nearest-neighbor hopping rate $J$ and on-site two-photon interaction $U$. Each atom has level spacings detuned by $\Delta_{1,2}$ from the band center and is coupled to the waveguide at two points, spatially separated with distance $\Delta x=2$, forming a braided configuration. The coupling strength at each connection point is $g$. For appropriate level spacings, doublon bound states in the continuum (BICs) emerge via interference between emission pathways. The overlap of these doublon BICs between the two atoms mediates a decoherence-free interaction (orange arrow). (b) Band structure of the nonlinear waveguide, for two different values of U.
• Figure 2: Doublon BIC and DFI between GAs, for two-photon interaction [Eq. (\ref{['eq:HDC']})]. Parameters: $U = 10J$, $g = 0.04 J$, and $\Delta x = 2$. (a) The doublon BIC for a single GA with the DF frequency $\Delta_1 = 10.392J$. The plot shows the bound state's overlap $P_b(n,n)$ with the two-photon states $|0,nn \rangle$, while the inset also shows the off-diagonal elements $P_b(m,n)$. (b) Time evolution of the population $n^{(1)}(t)$ of the GA's $|1 \rangle$ level for three values of $\Delta_1$: at the DF frequency (blue), inside the doublon band (orange), and outside the doublon band (green). (c) Population dynamics $n^{(1)}_{1,2}(t)$ of two braided GAs at the DF frequency. (d) Heatmap of the doublon population $P(n,t)=\langle \psi(t)|a^\dag_na^\dag_na_na_n|\psi(t) \rangle$ in the waveguide. (e, f) Same as in (c, d), but for a non-DF frequency inside the doublon band.
• Figure 3: Doublon BIC and DFI between GAs, for single-photon coupling [Eq. (\ref{['eq:Hnat']})]. Parameters: $U = 10J$, $g = 0.25 J$, and $\Delta x = 2$. (a) The doublon BIC for a single GA with the DF condition $\Delta_1 = 5.338J$ and $\Delta_2 = 5J$. The plot shows the diagonal overlap $P_b(n,n)$, indicating strong localization in real space. The inset shows the full two-photon amplitude $P_b(m,n)$, with vanishing off-diagonal elements confirming the doublon nature. (b) Time evolution of the population $n^{(2)}(t)$ of the GA's $|2 \rangle$ level for fixed $\Delta_1 = 5.338J$ and varying $\Delta_2$: at the DF condition (blue), inside the doublon band (orange), and outside the doublon band (green). (c) Population dynamics $n^{(1)}_{1,2}(t)$ of two braided GAs at the DF frequency. (d) Heatmap of the doublon population $P(n,t)=\langle \psi(t)|a^\dag_na^\dag_na_na_n|\psi(t) \rangle$ in the waveguide. (e, f) Same as in (c, d), but for a non-DF frequency inside the doublon band.