Tamm-Hubbard surface states in the continuum

Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Chiral edge states are highly sought after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate chiral topological propagation that is induced by suitably designed interactions, instead of flux or spin-orbit coupling. Also different from conventional 2D realizations, our effective Chern lattice is implemented on a much smaller equivalent 1D spin chain, with sequences of entangling gates encapsulating the required time-reversal breaking. By taking advantage of the quantum nature of the platform, we circumvented difficulties from the limited qubit number and gate fidelity in present-day noisy intermediate-scale quantum era quantum computers, paving the way for the quantum simulation of more sophisticated topological states on very rapidly developing quantum hardware.

Higher-Order Topological Phase of Interacting Photon Pairs

Topological phases open a door to such intriguing phenomena as unidirectional propagation and disorder-resilient localization at a stable frequency. Recently discovered higher-order topological phases further extend the concept of topological protection enabling versatile control over localization in multiple dimensions. Motivated by the recent advances in quantum technologies such as large coherently operating qubit ensembles, we predict and investigate the higher-order topological phase of photon pairs emerging due to effective photon-photon interaction and described by the extended version of Bose-Hubbard model. Being feasible for state-of-the-art experimental capabilities, the designed model provides an interesting example of interaction-induced topological transitions in the few-particle two-dimensional system.

Quantum Chaos Driven by Long-Range Waveguide-Mediated Interactions

We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave function in real space. This indicates the Bethe ansatz breakdown and the onset of quantum chaos, in stark contrast to the conventional integrable problem of two interacting bosons in a box. We identify the long-range waveguide-mediated coupling between the atoms as the key ingredient of chaos and nonintegrability. Our results provide new insights in the interplay between order, chaos, and localization in many-body quantum systems and can be tested in state-of-the-art setups of waveguide quantum electrodynamics.

Photon-Mediated Localization in Two-Level Qubit Arrays

We predict the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide. This localization can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons, where one photon creates a standing wave that traps the other photon. The localization is caused by the interplay between on-site repulsion due to the photon blockade and the waveguide-mediated long-range coupling between the qubits.

Exceptional points for photon pairs bound by nonlinear dissipation in cavity arrays

We theoretically study the dissipative Bose-Hubbard model describing the array of tunneling-coupled cavities with non-conservative photon-photon interaction. The bound two-photon states are formed in this system either in the limited range of the center-of-mass wave vectors or in the full Brillouin zone, depending on the strength of the dissipative interaction. Transition between these two regimes is manifested as an exceptional point in the complex energy spectrum. This improves fundamental understanding of the interplay of non-Hermiticity and interactions in the quantum structures and can potentially be used for on-demand nonlinear light generation in photonic lattices.

Observation of surface states with algebraic localization

We introduce and experimentally demonstrate a class of surface bound states with algebraic decay in a one-dimensional tight-binding lattice. Such states have an energy embedded in the spectrum of scattered states and are structurally stable against perturbations of lattice parameters. Experimental demonstration of surface states with algebraic localization is presented in an array of evanescently coupled optical waveguides with tailored coupling rates.

Floquet bound states in the continuum

Quantum mechanics predicts that certain stationary potentials can sustain bound states with an energy buried in the continuous spectrum of scattered states, the so-called bound states in the continuum (BIC). Originally regarded as mathematical curiosities, BIC have found an increasing interest in recent years, particularly in quantum and classical transport of matter and optical waves in mesoscopic and photonic systems where the underlying potential can be judiciously tailored. Most of our knowledge of BIC is so far restricted to static potentials. Here we introduce a new kind of BIC, referred to as Floquet BIC, which corresponds to a normalizable Floquet state of a time-periodic Hamiltonian with a quasienergy embedded into the spectrum of Floquet scattered states. We discuss the appearance of Floquet BIC states in a tight-binding lattice model driven by an ac field in the proximity of the dynamic localization regime.