Fig. 4: Dispersive coupling of the cavity to a short channel and overview of the resulting frequency shift and detuning for different transparencies.
a Pair transition energies (hfA) for the short junction limit for two different transparencies. Magenta and dark purple traces indicate the quasi-particle transition energy hfA for transparencies of τ = 0.987 and 0.988, respectively. b, c Cavity frequency shift δf from the bare cavity frequency f0 normalized by the frequency corresponding to the gap edge fΔ = Δ/h for both τ = 0.987 and 0.988, respectively. The effective coupling strength at φ = π is geff = 0.0139fΔ for both transparencies. As can be seen in b, when the bound states and cavity detuning remains positive the cavity frequency is dispersively shifted downward. If however the detuning is shifted through zero via the phase as in c the cavity frequency exhibits both up and down shifts. Model parameters for b and c are: ωc = 0.2235fΔ, γ = 0.0067fΔ, κ = 6.7 × 10−6fΔ, Z = 2 × 10−5. Model details can be found in the methods section. d Cavity frequency shift δf as a function of τ at φ = π. Simulation parameters are ωc = 0.2235fΔ, γ = 0.0067fΔ, κ = 6. 7 × 10−6fΔ, Z = 2 × 10−5. The detuning of Andreev bound state transition and cavity (hfA − hf0) is also plotted to highlight the point of reversal of frequency shift.
