829 research outputs found
On a family of integrable systems on with a cubic integral of motion
We discuss a family of integrable systems on the sphere with an
additional integral of third order in momenta. This family contains the
Coryachev-Chaplygin top, the Goryachev system, the system recently discovered
by Dullin and Matveev and two new integrable systems. On the non-physical
sphere with zero radius all these systems are isomorphic to each other.Comment: LaTeX, 8 page
Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device
A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons
in a way that they are well confined and immune to suspension losses so they
exhibit extremely high acoustic -factors at low temperature, with products of order Hz. In this work we couple such a resonator to a
SQUID amplifier and investigate effects in the strong signal regime. Both
parallel and series connection topologies of the system are investigated. The
study reveals significant non-Duffing response that is associated with the
nonlinear characteristics of Josephson junctions. The nonlinearity provides
quasi-periodic structure of the spectrum in both incident power and frequency.
The result gives an insight into the open loop behaviour of a future Cryogenic
Quartz Oscillator in the strong signal regime
Extremely Low-Loss Acoustic Phonons in a Quartz Bulk Acoustic Wave Resonator at Millikelvin Temperature
Low-loss, high frequency acoustic resonators cooled to millikelvin
temperatures are a topic of great interest for application to hybrid quantum
systems. When cooled to 20 mK, we show that resonant acoustic phonon modes in a
Bulk Acoustic Wave (BAW) quartz resonator demonstrate exceptionally low loss
(with -factors of order billions) at frequencies of 15.6 and 65.4 MHz, with
a maximum product of 7.8 Hz. Given this result, we show
that the -factor in such devices near the quantum ground state can be four
orders of magnitude better than previously attained. Such resonators possess
the low losses crucial for electromagnetic cooling to the phonon ground state,
and the possibility of long coherence and interaction times of a few seconds,
allowing multiple quantum gate operations
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