Nondegenerate parametric oscillations in a tunable superconducting resonator

Abstract

We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.

Period multiplication in a parametrically driven superconducting resonator

“…Instead of breaking the symmetry of the overall triplet pattern, the individual round spots deform into crescents with a size that increases with increasing probe intensity. Such a behavior resembles the phase locking effect observed in non-degenerate parametric oscillators 8,10 , where the oscillator state possesses continuous phase degeneracy. This resemblance leads us to interpret our observation as the result of a deformation of each stable stationary state of the triplet into a stable cycle with simultaneous phase locking.…”

“…Furthermore, low temperatures in the range of 10 mK allows to investigate the quantum properties of the oscillator states. Using this technique, both the degenerate (pumping at twice a resonator mode frequency) and nondegenerate (pumping at the sum of two resonator mode frequencies) parametric oscillations, have been experimentally investigated 7,8 .…”

“…The non-degenerate oscillator has a continuous phase degeneracy [8][9][10] , while the degenerate oscillator exhibits a discrete, two-fold degeneracy, which is manifested by two correlated π-shifted steady states 7,11 . In the quantum regime these states form coherent superpositions of optical coherent states, cat states 12,13 , which can be used as building blocks for a photonic quantum processor 14 .…”

Injection Locking and Parametric Locking in a Superconducting Circuit

“…As parametric oscillation is stabilized, the resulting outgoing field amplitudes a out and b out exhibit similar properties as in previously studied spatially degenerate Josephson amplifiers 11,23 . Performing repeated heterodyne quadrature measurements of the outgoing field amplitudes reveals a statistics of quadratures that is characteristic of parametric oscillation (see Figs.…”

A general characterization method for nonlinearities in superconducting circuits

“…truncation to second order in a Taylor expansion). Higher order nonlinear terms also affect the dynamic range of parametric amplifiers [11,19] and oscillators [20,21]. In principle, the high order nonlinear terms can be calculated if the individual circuit elements are accurately known [22][23][24][25] e.g.…”