Abstract
We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting λ/4 resonator, and is terminated by a flux-tunable superconducting quantum interference device. We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity, α, is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity, β, related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in situ by the applied dc flux. We also suggest how to cancel the effect of β by adding a small dc flux and a pump tone at twice the pump frequency.
Highlights
Both nonlinearities depend on the parameters of the device and can be tuned in situ by the applied dc flux
In addition to the Duffing nonlinearity present in the Josephson bifurcation amplifier (JBA), the magnetic-flux modulation of the Josephson inductance adds an additional degree of freedom, and a nonlinearity to the system dynamics
Our measured devices consist of a distributed λ/4 coplanar waveguide resonator of length l, with a flux-tunable inductance realized by terminating one end to ground via two parallel Josephson junctions forming a dc-superconducting quantum interference device [12, 16,17,18, 20], see figure 1(a)
Summary
The intracavity dynamics of the underdamped, parametrically driven nonlinear oscillator can be mapped onto the Duffing oscillator, studied in detail by Dykman [5]. To investigate the resonator response upon parametric pumping of the flux at frequency ωp, we adopt the formalism developed by Wustmann and Shumeiko [9]. |A|2 gives the number of photons in the resonator, whereas B(t) is the probe field amplitude such that. Α denote the effective pump strength and Duffing parameter, respectively. The full F-dependence of these coefficients can be express in terms of resonator parameters as [9]. Where δ f = π 1/ 0 is the ac-flux amplitude, Z0 = 50 is the resonator’s characteristic impedance, RK = h/e2 is the quantum resistance and α0 = π 2ωλ/4 Z0/RK. In the following two sections we will investigate the Duffing nonlinearity as well as the order pump-induced nonlinearity
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