Simulation of the Su-Schrieffer-Heeger model using a superconducting parametric cavity

While large-scale universal quantum computers are on the way, analog quantum simulators (AQSs) can be used right now to study complex natural phenomena. By simulating the Su-Schrieffer–Heeger (SSH) model that describes particles hopping on a one-dimensional lattice with staggered hopping amplitudes, we demonstrate that superconducting parametric cavities are a versatile platform for programable AQS. Our device is a 100 mm-long superconducting quarter-wave coplanar waveguide resonator which is shorted by an asymmetrical Superconducting Quantum Interference Device (SQUID). Multiple resonant modes of the cavity are used as a photonic lattice arrayed in a synthetic dimension. Parametric couplings between sites are generated by pumping the SQUID with microwave signals at the difference frequencies of pairs of modes. We perform transport measurements that allow us to reconstruct the full scattering matrix of the SSH chain, observing many of the features of the SSH model. For instance, depending on the ratio between hopping amplitudes and the site number parity, we can observe 0, 1 and 2 edge states which live within the bulk energy gap of the system. Complementary to our published work on the bosonic Creutz ladder [1], this result highlights the power and programmability of superconducting parametric cavities for quantum simulation.

1. J.S.C. Hung, J.H. Busnaina, C.W.S. Chang, A.M. Vadiraj, I. Nsanzineza, E. Solano, H. Alaeian, E. Rico, and C.M. Wilson, Phys. Rev. Lett., 127, 100503 (2021).