[Paper Review] Topological lattices realized in superconducting circuit optomechanics

Amir Youssefi, S. Kono+5 more|arXiv (Cornell University)|Nov 17, 2021

Mechanical and Optical Resonators4 citations

TL;DR

This paper demonstrates topological microwave modes in superconducting circuit optomechanical lattices by realizing the Su-Schrieffer-Heeger (SSH) model in a 1D chain and the strained graphene model in a 2D honeycomb lattice. Using intrinsic optomechanical interactions, the authors directly measure collective mode functions without local probes, enabling full Hamiltonian reconstruction and disorder characterization, achieving a hybridization factor of ζ = 0.98, indicating minimal frequency disorder (σΔω ≈ 0.01–0.38%).

ABSTRACT

Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction, and has contributed to the quantum control of engineered mechanical systems ranging from kg scale LIGO mirrors to nano-mechanical systems, enabling ground-state preparation, entanglement, squeezing of mechanical objects, position measurements at the standard quantum limit and quantum transduction. Yet, nearly all prior schemes have employed single- or few-mode optomechanical systems. In contrast, novel dynamics and applications are expected when utilizing optomechanical lattices, which enable to synthesize non-trivial band structures, and have been actively studied in the field of circuit QED. Superconducting microwave optomechanical circuits are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here, we overcome this challenge and demonstrate topological microwave modes in 1D circuit optomechanical chains realizing the Su-Schrieffer-Heeger (SSH) model. Furthermore, we realize the strained graphene model in a 2D optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offers an avenue to explore collective, quantum many-body, and quench dynamics, topological properties and more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedoms. (Keywords: Quantum Optomechanics, Superconducting Circuit Electromecahnics)

Motivation & Objective

• To overcome scaling limitations in superconducting optomechanical lattices by enabling site-by-site engineering of identical optomechanical units.
• To realize topological band structures—specifically the SSH model in 1D and strained graphene model in 2D—using superconducting microwave circuits.
• To develop a direct, non-invasive method for measuring collective microwave mode shapes using on-site optomechanical interactions.
• To reconstruct the full lattice Hamiltonian and quantify residual disorder in multimode optomechanical systems without relying on indirect probes.

Proposed method

• Fabricated a 1D chain of 10 superconducting optomechanical units with staggered couplings to realize the SSH model, enabling topological edge states.
• Constructed a 2D honeycomb optomechanical lattice to emulate the strained graphene model, supporting topologically protected edge modes.
• Utilized intrinsic optomechanical coupling to map microwave mode profiles via mechanical displacement measurements, avoiding external probes.
• Applied a hybridization factor ζ to quantify edge mode localization, defined as the ratio of minimum to maximum participation at chain ends.
• Performed statistical analysis over 4000 random disorder realizations to correlate measured ζ with cavity frequency disorder σΔω.
• Used vector network analyzer (VNA) S-parameters in both transmission and reflection to experimentally verify edge state localization from opposite ends.

Experimental results

Research questions

• RQ1 Can topological phases be realized in superconducting circuit optomechanical lattices with site-resolved control?
• RQ2 Can intrinsic optomechanical interactions enable direct measurement of collective microwave mode functions without local probes?
• RQ3 To what extent does disorder in cavity frequencies affect the hybridization and localization of topological edge modes?
• RQ4 Can the full Hamiltonian of a multimode optomechanical lattice be reconstructed from measured mode shapes?
• RQ5 How does the length of the SSH chain influence the robustness of topological edge states against frequency disorder?

Key findings

• The 10-cell SSH chain exhibited a measured hybridization factor of ζ^meas = 0.98, indicating strong co-localization of topological edge modes.
• This corresponds to a cavity frequency disorder range of σΔω = (0.01%, 0.38%) with 90% confidence, implying extremely low residual disorder.
• Edge states were experimentally confirmed via reflection measurements: only one peak was visible from each end, confirming single-edge localization.
• Transmission spectra showed abnormally low transmission for edge modes due to their localization at one end, despite high edge current density.
• The hybridization factor ζ decreased sharply with increasing disorder, and was more sensitive in longer chains (e.g., 20-cell chain) at the same disorder level.
• The method enabled full reconstruction of the lattice Hamiltonian from direct mode shape measurements, overcoming limitations of indirect probing techniques.