Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the quantum nature of light, i.e., solely related to the quantized Fock states and the inhomogeneous coupling strengths between them. The Hamiltonian of two cavities coupled with a two-level atom is an intrinsic one-dimensional Su-Schriefer-Heeger model of Fock states. By adding another cavity, the Fock-state lattice is extended to two dimensions with a honeycomb structure, where the strain due to the inhomogeneous coupling strengths of the annihilation operator induces a Lifshitz topological phase transition between a semimetal and three band insulators within the lattice. In the semimetallic phase, the strain is equivalent to a pseudomagnetic field, which results in the quantization of the Landau levels and the valley Hall effect. We further construct an inhomogeneous Fock-state Haldane model where the topological phases can be characterized by the topological markers. With d cavities being coupled to the atom, the lattice is extended to d − 1 dimensions without an upper limit. This study demonstrates a fundamental distinction between the topological phases in quantum and classical optics and provides a novel platform for studying topological physics in dimensions higher than three.

Mesoscopic superposition states of photons can be prepared in three cavities interacting with the same two-level atom. By periodically modulating the three cavity frequencies around the transition frequency of the atom with 2π/3 phase difference, the time reversal symmetry is broken and an optical circulator is generated with chiralities depending on the quantum state of the atom. A superposition of the atomic states can guide photons from one cavity to a mesoscopic superposition of the other two cavities. The physics can be understood in a finite spin-orbit-coupled Fock-state lattice where the atom and the cavities carry the spin and the orbit degrees of freedom, respectively. This scheme can be realized in circuit QED architectures and provides a new platform for exploring quantum information and topological physics in novel lattices.

We measure the superradiant emission in a one-dimensional (1D) superradiance lattice (SL) in ultracold atoms. Resonantly excited to a superradiant state, the atoms are further coupled to other collectively excited states, which form a 1D SL. The directional emission of one of the superradiant excited states in the 1D SL is measured. The emission spectra depend on the band structure, which can be controlled by the frequency and intensity of the coupling laser fields. This work provides a platform for investigating the collective Lamb shift of resonantly excited superradiant states in Bose-Einstein condensates and paves the way for realizing higher dimensional superradiance lattices.

Topological phases of matters are of fundamental interest and have promising applications. Fascinating topological properties of light have been unveiled in classical optical materials. However, the manifestation of topological physics in quantum optics has not been discovered. Here we study the topological phases in a two-dimensional momentum-space superradiance lattice composed of timed Dicke states (TDS) in electromagnetically induced transparency (EIT). By periodically modulating the three EIT coupling fields, we can create a Haldane model with in-situ tunable topological properties, which manifest themselves in the contrast between diffraction signals emitted by superradiant TDS. The topological superradiance lattices provide a controllable platform for simulating exotic phenomena in condensed matter physics and offer a basis of topological quantum optics and novel photonic devices.Comment: 11 pages, 10 figure

We have synthesized the anti-symmetric spin exchange interaction (ASI), which is also called the Dzyaloshinskii-Moriya interaction, in a superconducting circuit containing five superconducting qubits connected to a bus resonator, by periodically modulating the transition frequencies of the qubits with different modulation phases. This allows us to show the chiral spin dynamics in three-, four-and five-spin clusters. We also demonstrate a three-spin chiral logic gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our results pave the way for quantum simulation of magnetism with ASI and quantum computation with chiral spin states.