Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

Abstract

Superconducting metamaterials are a promising resource for quantum information science. In the context of circuit QED, they provide a means to engineer on-chip, novel dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum reservoir engineering, and as an element for quantum simulation architectures.Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line (LHTL) that is compatible with circuit QED architectures. We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conducted using both microwave transmission measurements and laser scanning microscopy (LSM). Results are observed to be in good quantitative agreement with numerical simulations and also an analytical model based upon current-voltage relationships for a discrete transmission line. In particular, we demonstrate that the metamaterial mode frequencies, spatial profiles of current and charge densities, and damping due to external loading can be readily modeled and understood, making this system a promising tool for future use in quantum circuit applications and for studies of complex quantum systems.

Superconducting circuit optomechanics in topological lattices

“…Form the optomechanical damping rate, the unnormalized participation ratio η k i is experimentally obtained by Eq. (22). Using the relation described in Eq.…”

“…Using the on-site optomechanical interactions, we are able to perform a direct measurement of the collective microwave mode shapes, reconstruct the full Hamiltonian of such multimode system beyond the tightbinding approximation, and demonstrate exceptionally low disorder in our devices. Such optomechanical mode shape measurements equally addresses an experimental challenge in large-scale multimode superconducting circuits as a platform for quantum simulation [55][56][57] and many-body physics studies [12,13,58], where only indirect approaches were performed by near field scanning probes [19], laser scanning microscopy [22,23], or dispersive coupling to qubits [54].…”

Superconducting circuit optomechanics in topological lattices

“…We demonstrate non-trivial topological microwave modes in 1-D optomechanical chains as well as 2-D honeycomb lattices, realizing the canonical Su-Schrieffer-Heeger (SSH) model [16][17][18]. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the bulk band modes, as well as the topologically protected edge states, without using any local probe [19][20][21] or inducing perturbation [22,23]. This enables us to reconstruct the full underlying lattice Hamiltonian beyond tight-binding approximations, and directly measure the existing residual disorder.…”

“…Using the on-site optomechanical interactions, we are able to perform a direct measurement of the collective microwave mode shapes, reconstruct the full Hamiltonian of such multimode system beyond the tight-binding approximation, and demonstrate exceptionally low disorder in our devices. Such optomechanical mode shape measurements equally addresses an experimental challenge in large-scale multimode superconducting circuits as a platform for quantum simulation [55][56][57] and many-body physics studies [12,13,58], where only indirect approaches were performed by near field scanning probes [19], laser scanning microscopy [22,23], or dispersive coupling to qubits [54].…”

Observation of topological valley Hall edge states in honeycomb lattices of superconducting microwave resonators

“…In this manuscript, we use a laser scanning imaging technique in order to map the spatial distribution of the resonant modes across the lattice. This technique is similar to the laser scanning microscopy developed to observe the current density in superconductor films [14] and has already been used to characterize single a superconducting resonator [15,16] or coupled resonators [17]. It is an alternative to the scanning technique developed in [9].…”