Period multiplication in a parametrically driven superconducting resonator

Abstract

We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength resonator, with frequencies nω close to multiples, n = 2, 3, 4, 5, of the resonator fundamental mode and observe intense output radiation at ω. The output field manifests n-fold degeneracy with respect to the phase, the n states are phase shifted by 2π/n with respect to each other. Our demonstration verifies the theoretical prediction by Guo et al. 1 , and paves the way for engineering complex macroscopic quantum cat states with microwave photons.The technology of circuit quantum electrodynamics 2,3 offers an excellent platform for observation and exploration of parametric oscillation phenomena in the quantum domain. By connecting Josephson elements to superconducting resonators, one is able to induce nonlinearity of the electromagnetic field and realise temporal high frequency control of the resonator parameters 4-6 . This in combination with high quality factors of the superconducting resonators makes the parametric oscillation regime, above the instability threshold, easily accessible with relatively small modulation intensities. 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 .An inherent property of parametric oscillations is phase degeneracy of the oscillator states.The non-degenerate oscillator has a continuous phase degeneracy 8-10 , 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 .Quantum properties of the degenerate parametric oscillations motivate a great interest in finding ways to engineer more complex multiply degenerate oscillator states. The period multiplication phenomenon in nonlinear oscillators 15,16 offers an attractive approach to the problem. In recent papers, an experimental demonstration of the period tripling in a superconducting resonator was reported 17 , and quantum properties of the emerging three-fold degenerate state were theoretically investigated 18 . In that experiment, the self-sustained oscillations of the resonator mode were excited by injecting an external signal with a frequency close to three times a) ida-maria.svensson@chalmers.se b) per.delsing@chalmers.se the fundamental mode frequency; the excitation mechanism involves, first, an excitation of a higher resonator mode with frequency close to the driving frequency, and then a parametric down-conversion of thi...

Classical Many-Body Time Crystals

“…Our paradigm of a many-body time crystal is straightforwardly generalizable to quantum resonator networks [38,[56][57][58][59]. Higher-period TTSB is also realizable in these systems through a judicious choice of modulated nonlinearities [60][61][62]. The simple view of TTSB proposed in this Letter can be putatively applied to the recently seen TTSB in quantum spin systems [13,14].…”

Transformative resonant moderation of geomagnetic polarity and strata

“…Additionally, discrete time translation symmetry has been experimentally observed in a resonator forced externally by another quarter-wavelength resonator -both as period multiplication, but mainly as doubling, halving, and tripling (all in parametrically driven tunable superconducting resonators) and as 2π/n phase shifts accompanied by intensely magnified radiation (in resonators with frequencies n•ω close to multiples n = 2, 3, 4, and 5, of the resonator's fundamental mode) (Svensson et al, 2018). Here, the period multiplication (including doubling, halving, and tripling), the 2π/n phase shifts (of both p and p'), and the ¼ lockstep (to p'), all characterize the above find from the GVSA of CKGPTS95 calibration, as well.…”

Injection locking and synchronization in Josephson photonics devices

“…Equivalent processes in ac-driven Josephson devices 47 have very recently been observed for p = 3 downconversion. [48][49][50] In the classical description these processes, which based on a quantum picture may be called p-photon creation processes, materialize as (higher-order) parametric resonances in the equations-of-motion. Setting R 0 ≡ 0 and = 0 for the moment, Eq.…”