Topological phases of quantized light

Abstract

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.

Synthetic frequency dimensions in dynamically modulated ring resonators

“…In the past decade, synthetic dimensions have been extensively explored in systems including cold atoms [18][19][20][21][22][23][24][25][26][27][28][29][30][31] , hot atomic gases 32,33 , photonic platforms [34][35][36][37][38][39][40][41] , superconducting circuits [42][43][44] , and optomechanics 45 . In the photonic implementations, for the quantum (few-photon) regime, synthetic a) Electronic mail: yuanluqi@sjtu.edu.cn b) Electronic mail: shanhui@stanford.edu lattices with arbitrary dimensions were constructed using the Fock-state ladder formed by an atom coupled to several multimode cavities 46,47 . For classical light, several internal degrees of freedom can be utilized to synthesize new dimensions 16 .…”

Synthesizing five-body interaction in a superconducting quantum circuit

“…The anti-symmetric spinexchange interaction (Dzyaloshinskii-Moriya interaction) [9,10] has been synthesized by breaking the time-reversal symmetry through Floquet modulation [11], enabling a three-qubit chiral quantum gate for entangling qubits more efficiently than the two-qubit gates [12]. Similar techniques have been applied to the synthesis of effective gauge field [13] and three-spin chirality Hamiltonian [14], which is a necessary element in simulating chiral spin liquid [15] and promising to realize the topological states of quantized light [16][17][18]. Four-spin ring-exchange interaction, which has been synthesized in optical lattices of cold atoms [19], is essential for toric codes in topological quantum computing [20].…”

Unification of valley and anomalous Hall effects in a strained lattice

“…Lattice dynamics beyond real space has been investigated in cold atoms [1] and photonic systems [2,3] with synthetic extra dimensions. By using the Fock states of multiple cavities coupled to a two-level atom, lattices in arbitrary dimensions can be synthesized [4][5][6][7]. These Fock-state lattices offer a new tool for engineering quantum states (such as the preparation of mesoscopic superposition states [6]) and investigating high dimensional topological physics [7].…”

“…By using the Fock states of multiple cavities coupled to a two-level atom, lattices in arbitrary dimensions can be synthesized [4][5][6][7]. These Fock-state lattices offer a new tool for engineering quantum states (such as the preparation of mesoscopic superposition states [6]) and investigating high dimensional topological physics [7]. In particular, the inhomogeneous coupling strengths between the Fock states, which are proportional to √ n with n being the photon number in the Fock states, resemble strain in real-space lattices.…”

“…To demonstrate that relation, we construct a tightbinding model of exactly flat bands for arbitrary size of lattices [41][42][43][44] by borrowing the coupling strengths in the Fock-state lattice of a multi-mode Jaynes-Cummings (JC) model [6,7,45],…”