Stability of resonator vacuum state
This protocol is extracted from research article:
Qubit parity measurement by parametric driving in circuit QED
Sci Adv, Nov 30, 2018; DOI: 10.1126/sciadv.aau1695

When parametrically driven on resonance, the classical equations of motion for the field quadratures of the nonlinear resonator x = 〈â + â〉/2 and y = − iââ〉/2 are given byEmbedded Image(7)Embedded Image(8)

Computing the eigenvalues of the evolution matrix linearized around vacuum (x, y) = (0, 0), we obtained λ± = ± Embedded Image − κ/2. Small fluctuations around vacuum will thus make the system leave this unstable point on a time scale given by Embedded Image.

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