Abstract
We consider a quarter wave coplanar microwave cavity terminated to ground via asuperconducting quantum interference device. By modulating the flux through the loop,the cavity frequency is modulated. The flux is varied at twice the cavity frequencyimplementing a parametric driving of the cavity field. The cavity field also exhibitsa large effective nonlinear susceptibility modelled as an effective Kerrnonlinearity, and is also driven by a detuned linear drive. We show that thesemi-classical model corresponding to this system exhibits a fixed point bifurcationat a particular threshold of parametric pumping power. We show the quantum signatureof this bifurcation in the dissipative quantum system. We further linearise about thebelow threshold classical steady state and consider it to act as a bifurcationamplifier, calculating gain and noise spectra for the corresponding small signalregime. Furthermore, we use a phase space technique to analytically solve for theexact quantum steady state. We use this solution to calculate the exact small signalgain of the amplifier.
Highlights
Superconducting circuit quantum electrodynamics [ ] is increasingly being used to study systems in the quantum regime
The microwave resonator is made from aluminium on a silicon substrate, and Josephson junctions are created by allowing the aluminium to oxidise before adding more aluminium
7 Conclusion In this paper we detailed the quantum and semi-classical structure of a superconducting microwave resonator connected through a superconducting quantum interference device (SQUID) loop to ground
Summary
Superconducting circuit quantum electrodynamics (circuit QED) [ ] is increasingly being used to study systems in the quantum regime. The existence and components of the semi-classical fixed points are functions of the two non-dimensional ratios of the parametric pumping magnitude κ, detuning Δ, and dissipation rate γ of the system: κ. The noise will drive the dynamics off the semi-classical subspace Despite this we can find a very close correspondence between the semi-classical fixed points and the form of the steady state Positive P function. In particular the additional fixed points of the non classical dimension are present As they describe, the non classical subspace allows the noise to drive a stochastic process that corresponds to the nonclassical features of the steady state solution.
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