A bound state in the continuum is a quantum state that exists within the energy range of propagating modes but does not decay into them. In principle, any state whose energy overlaps with a continuum should radiate — it has degenerate states to decay into, and nothing forbids the transition. Bound states in the continuum survive because of destructive interference: the amplitudes for emission into different continuum channels cancel exactly, trapping the state despite the available decay pathways. The cancellation is geometric — it depends on the spatial structure of the coupling, not on energy barriers or material properties.
Legon, Miranda Rojas, Orellana, and Norambuena (arXiv 2602.23082, February 2026) show that in a system of two giant atoms coupled to a one-dimensional waveguide, the bound states in the continuum are maximally entangled Bell-like states, and which Bell state emerges is controlled entirely by the geometric parameters of the setup.
Giant atoms are quantum emitters that couple to the waveguide at multiple spatial points, unlike point-like atoms that couple at a single location. The multiple coupling points create interference between emission pathways. An atom that couples to the waveguide at two points separated by a distance d has two channels for emitting a photon — one from each coupling point — and the relative phase between these channels depends on d times the photon wavevector. At specific geometric configurations, the emissions cancel and the atom becomes dark — it cannot radiate into the waveguide. This is the single-atom bound state in the continuum.
With two giant atoms, each coupling at multiple points, the interference pattern is richer. The authors find that maximally entangled two-atom states — Bell states with concurrence equal to 1 — coincide with bound states in the continuum of the coupled system. The entanglement is not created by a quantum gate or a measurement protocol. It is a property of the bound state itself: the only states that satisfy the destructive interference condition for non-decay are the maximally entangled ones.
Two geometric parameters control the entanglement. The ratio of intra-atomic connection lengths — the distances between coupling points within each atom — determines the concurrence, the quantitative measure of entanglement. The propagation phase between atoms — set by the inter-atomic separation — determines which Bell state is realized. By adjusting these two lengths, the experimentalist selects both the degree and the type of entanglement.
The entangled states are stable because they are bound states. They cannot decay into the waveguide because the destructive interference that makes them bound also makes them dark. The entanglement persists indefinitely in the absence of other decoherence mechanisms, because the state has no channel through which to lose its quantum correlations. The geometry that prevents radiation also preserves entanglement.
The result connects three concepts that are usually studied separately. Bound states in the continuum are studied in photonics and wave physics. Maximal entanglement is studied in quantum information. Giant atoms are studied in quantum optics. The connection between them is geometric: the same spatial structure that cancels radiation also selects entanglement. The architecture of the coupling points, not the dynamics of the interaction, determines the quantum state.