Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

TL;DR

This paper explores how superconducting qubits coupled to hyperbolic lattices can simulate quantum physics in negatively curved space, revealing photon bound states, boundary effects, and frustrated spin models with potential for quantum simulation.

Contribution

It demonstrates the experimental feasibility of using hyperbolic lattices in circuit QED to realize and analyze complex quantum phenomena, including photon bound states and frustrated spin interactions.

Findings

Photon-qubit bound states have a curvature-limited size.

Spectral density matches continuum theory despite boundary effects.

Hyperbolic bath mediates geometrically-frustrated spin models.

Abstract

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincar\'{e} disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.