Extended Data Fig. 7: Limitation of the on-chip loss and parasitic sidebands.

a, Predicted two-resonator on-chip loss with varied \({Q}_{{\rm{intrinsic}}}\) for different waveguide–ring couplings γ. The theoretical curve of on-chip loss is calculated under the optimal condition of both pump and microwave detunings are zero. The measured on-chip loss of the \(11.0\,{\rm{GHz}}\), \(12.5\,{\rm{GHz}}\) and \(28.2\,{\rm{GHz}}\) devices used in this work are labelled with a triangle, square, and diamond, respectively. b, Simulation of the normalized power of the parasitic sidebands as a function of the shift frequency. The waveguide–cavity coupling rate \(\gamma \) is varied from \(2{\rm{\pi }}\times 1\,{\rm{GHz}}\) to \(2{\rm{\pi }}\times 7\,{\rm{GHz}}\). Waveguide–cavity coupling rates that are as high as \(2{\rm{\pi }}\times 7\,{\rm{GHz}}\) can still keep the parasitic sidebands suppressed below \(20\,{\rm{dB}}\) for shift frequencies \( > 10\,{\rm{GHz}}\) and below \(30\,{\rm{dB}}\) for shifts that are \( > 30\,{\rm{GHz}}\). In this work, the parasitic sidebands are lower than \(25\,{\rm{dB}}\) in devices at shift frequencies of \(10\,-\,30\,{\rm{GHz}}\).