Floquet Engineering and Harnessing Giant Atoms in Frequency-Comb Emission and Bichromatic Correlations in Waveguide QED

The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency-encoded light-matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here we consider a dynamically modulated qubit array, and realize frequency-controlled single-photon emission focusing on the generation of a frequency comb constituted solely of even-parity or anti-Stokes sidebands. Our system also offers parity-dependent bunching and antibunching in frequency-filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non-local coupling architectures, thereby enhancing its versatility in Floquet engineering. Our proposal also supports the predictable generation of high-dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi-photon dynamics, in which the non-Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency-encoded quantum information processing and many-body quantum simulation.