Topological lattices realized in superconducting circuit optomechanics

Abstract

Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction [1][2][3], and has contributed to the quantum control of engineered mechanical systems ranging from kg scale LIGO mirrors to nano-mechanical systems, enabling entanglement [4, 5], squeezing of mechanical objects [6], to position measurements at the standard quantum limit [7], non-reciprocal [8] and quantum transduction [9]. Yet, nearly all prior schemes have employed single-or few-mode optomechanical systems. In contrast, novel dynamics and applications are expected when utilizing optomechanical arrays and lattices [10], which enable to synthesize non-trivial band structures, and have been actively studied in the field of circuit QED [11][12][13][14]. Superconducting microwave optomechanical circuits are a promising platform to implement such lattices [15], but have been compounded by strict scaling limitations. Here we overcome this challenge and realize superconducting circuit optomechanical 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. The latter is found to be sufficiently small to observe fully hybridized topological edge modes. Such optomechanical lattices, accompanied by the measurement techniques introduced, of-fers an avenue to explore out of equilibrium physics in optomechanical lattices such as quan-tum [24] and quench [25] dynamics, topological properties [10,26,27] and more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedoms [28][29][30][31].

Generation of stable Gaussian cluster states in optomechanical systems with multifrequency drives

“…To achieve higher fidelities one should either reduce the value of squeezing r or select larger mechanical frequencies and/or larger values of g. However, increasing both g and r simultaneously may be problematic due to the requirements for the validity of the rotating wave approximation expressed in equation (27). This condition remains valid for all the values of r reported in figures 7 and 8 (where for r = 4, we find g e r 2 Ω ∼ 0.09), and for all the values of g used in figure 9 (which is evaluated for r = 2).…”

“…The temperature of 10 mK used in figures 2, 3 and 6-9 is demanding, but we observe that in figure 5, a high level of squeezing (and thus good cluster state preparation) is achieved even at temperatures around 100 mK. Moreover, the temperature requirement can be further relaxed by employing higher mechanical frequencies in the GHz range [15,21,26,27,29].…”

Topological phononic metamaterials

“…Looking into the future, topological phononic metamaterials will continue to have important impacts on research in metamaterials, as they could provide new mechanisms for robust wave manipulations that may lead to superior functional devices and systems. This is particularly important as topological phononic metamaterials go smaller and smaller and merging with micromechanical systems, nanomechanical systems, and optomechanical systems [587,722]. Developing high-quality on-chip phononic topological systems and their applications is still a prior target in future research.…”

Interplay between topology and localization on superconducting circuits

“…Quasi-periodic disorder and dimer lattice structures have emerged as noteworthy avenues for inducing localization and topological states, respectively. The renowned Aubry-André (AA) [32][33][34][35] and Su-Schrieffer-Heeger (SSH) [36][37][38][39][40][41][42] models have been successfully implemented in superconducting circuits. [34,41] Consequently, the appeal lies in the design of a qubit chain featuring staggered coupling strengths and controllable off-diagonal quasi-periodic modulations.…”