Doubly Modulated Optical Lattice Clock Interference and Topology

The quantum system under periodical modulation is the simplest path to understand the quantum non-equilibrium system, because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase can not be gauged out, so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to ultra-high precision and ultra-stability of OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigen-energies, we demonstrate the relation between effective Floquet Hamiltonian and 1-D topological insulator with high winding number. Our experiment not only provides a direction for detecting the phase effect, but also paves a way in simulating quantum topological phase in OLC platform.