Quantum dynamics of microwave photons in synthetic frequency dimension

Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.