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].

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Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction [1–3], 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 [11–14]. 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 SuSchrieffer-Heeger (SSH) model [16–18]. 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 [19–21] 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 [28–31].

We demonstrate a fully packaged hybrid integrated laser and a soliton microcomb with frequency actuation bandwidth of more than 10 MHz and ultra-low laser frequency noise. The flat frequency response in the range of >1 MHz and the optical laser frequency chirp range of >1 GHz are compatible with high-resolution continuous wave frequency modulated distance ranging and distributed fiber optic sensing without any linearization or pre-distortion. The features of a novel laser system assembled in 14-pin butterfly package are enabled by the ultra-low loss silicon nitride platform and monolithically integrated piezo-electric actuators.

Recent advances in the development of ultralow loss silicon nitride integrated photonic circuits have heralded a new generation of integrated lasers capable of reaching fiber laser coherence. However, these devices presently are based on self-injection locking of distributed feedback (DFB) laser diodes, increasing both the cost and requiring tuning of laser setpoints for their operation. In contrast, turn-key legacy laser systems use reflective semiconductor optical amplifiers (RSOA). While this scheme has been utilized for integrated photonics-based lasers, so far, no cost-effective RSOA-based integrated lasers exist that are low noise and simultaneously feature fast, mode-hop-free and linear frequency tuning as required for frequency modulated continuous wave (FMCW) LiDAR or for laser locking in frequency metrology. Here we overcome this challenge and demonstrate a RSOA-based, frequency agile integrated laser, that can be tuned with high speed, with high linearity at low power. This is achieved using monolithic integration of piezoelectrical actuators on ultra-low loss silicon nitride photonic integrated circuits in a Vernier filter-based laser scheme. The laser operates at 1550 nm, features 6 mW output power, 400 Hz intrinsic laser linewidth, and allows ultrafast wavelength switching within 7 ns rise time and 75 nW power consumption. In addition, we demonstrate the suitability for FMCW LiDAR by showing laser frequency tuning over 1.5 GHz at 100 kHz triangular chirp rate with nonlinearity of 0.25% after linearization, and use the source for measuring a target scene 10 m away with a 8.5 cm distance resolution.

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We demonstrate a Vernier ring laser with linear frequency tuning of 1.5 GHz at 100 kHz chirp rate and wavelength switching with 7 ns rise time and 75 nW power consumption using Si3N4 photonic chip with integrated PZT actuators.