Counterdiabatic quasi-Floquet control for the generation of entangled BICs using giant atoms

Abstract

Bound states in the continuum (BICs) provide a mechanism for preserving entanglement in waveguide quantum electrodynamics. Here, using quantum control techniques in a configuration of two braided giant atoms, we propose a robust approach to create high-fidelity entangled BICs. The protocol combines quasi-Floquet modulation of the effective atom--waveguide couplings with an independent phase-controlled atomic exchange, which provides restricted counterdiabatic assistance for preparing the complete dressed BIC. In the lossless effective model, we obtain a full-state BIC fidelity of $0.99992$ and an unconditional atomic Bell fidelity of $0.99588$ using a fast control protocol. Microscopic finite-mode simulations validate the central-sideband description during the passage, while static calibration-error scans quantify its control tolerances. A separate microscopic study with relaxation and dephasing, using experimentally motivated component scales, identifies a finite useful entanglement window and a benefit from shaping the coupling envelopes. These results support controlled preparation, retention, and retrieval of dressed entanglement within the stated control and noise assumptions.