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Stochastic resonance in RF SQUIDs and superconducting circuits

  • Stochastic resonance (SR) is a universal paradoxical phenomenon ordering various dynamic and threshold systems by a noise of certain intensity making them much more sensitive to weak periodic signals.
  • Taking in mind a wide range of applications of superconducting quantum interferometers (SQUIDs) for high-sensitive measurements in industry, biomedicine, geology, scientific researches, etc., we study manifestation of SR in single-Josephson-junction superconducting quantum interferometers (RF SQUIDs) in order to find an optimal set of SQUID and signal parameters that enables high amplification of a weak periodic signal on a noisy background.
  • Using a mathematical model of the RF SQUID loop containing a Josephson junction (not obviously a tunnel-type one), we simulate stochastic dynamics of magnetic flux in the SQUID loop affected by noise with various statistics and various weak periodic signals.
  • For experimental studies, we built a low-temperature (liquid helium) measuring setup with self-shielded 3D toroidal RF SQUIDs made of bulk niobium incorporating adjustable Josephson junctions.
  • Several results obtained are indicated below.
Stochastic amplification of weak signals in an RF SQUID with ScS contact at 0<T<Tc
SR in RF SQUID with an near-atomic-size point contact (ScS ASC) is modified with the temperature rise due to smearing of the energy barrier between adjacent metastable current states of the loop thus resulting a change in the gain of the stochastically amplified weak signal. At high enough temperature, the SQUID behavior of ScS-SQUID resembles that of a SIS-SQUID.
O. G. Turutanov, V. Yu. Lyakhno, V. I. Shnyrkov.
Stochastic amplification of weak signals in an RF SQUID with ScS contact.
SR in RF SQUID with shunted ScS junction
Using a point (ScS) contact of near-atomic size (or quantum point contact, QPC) in RF SQUID provides SR conditions at any, arbitrary small, value of loop inductance and contact critical current unlike SQUIDs with tunnel (SIS) junctions. This is due to unusual sharp-top potential (at near-zero temperature) which always has a barrier between two wells thus making the ScS RF SQUID bistable.
O. G. Turutanov, V. A. Golovanevskiy, V. Yu. Lyakhno, V. I. Shnyrkov.
Stochastic resonance in an RF SQUID with shunted ScS junction. Physica A 396, 1 (2014)
Induced stochastic transitions in multi-well potential
In addition to the usual scenario of the SR in a bistable system with Gaussian noise, the transitions between multiple metastable states of the multi-well SQUID loop potential under the influence of a binary noise is observed experimentally. This can be interpreted as a kind of noise ”spectroscopy” of the metastable states of the SQUID loop with different values of the trapped magnetic flux.
O. G. Turutanov, V. U. Lyakhno, and V. I. Shnyrkov. Experimental observation of induced stochastic transitions in a multiwall potential of an rf-SQUID loop. Low Temp. Phys. 40, 1026 (2014)
Stochastic-parametric resonance
Numerical solution of Langevin equations for a single-junction superconducting quantum interfero-meter shows that cooperative action of noise and a regular high-frequency electromagnetic field results in the deterministic-assisted SR amplification of weak harmonic signal similar to the common SR effect. This new effect which we call parametric-stochastic resonance (PSR) gives a possibility of maximizing gain for an arbitrary noise level.
O. G. Turutanov, V. I. Shnyrkov, and A. M. Glukhov.
Stochastic-parametric amplification of narrow-band signals in a single-junction SQUID interferometer.
Low Temp. Phys. 34, 37 (2008)
SR in coupled SQUIDs
A numerical simulation of the SR in the adiabatic approximation in overdamped superconducting loops closed by a weak link shows that coupling of single SQUID loops in pair enhances the gain of weak sine signal and the signal-to-noise ratio. These effects can be used to create new stochastic SQUID antennas for measurements of harmonic and quasi-harmonic signals.
A. M. Glukhov, O. G. Turutanov, V. I. Shnyrkov, A. N. Omelyanchouk.
Stochastic resonance in superconducting loops containing Josephson junctions. Numerical simulation.
Low Temp. Phys. 32, No. 12, 1123-1130 (2006)
Stochastic amplifier for flux qubit readout
Basing on SR 4-terminal SQUID, a fully superconducting detector of a flux qubit states id proposed. Absence of high-frequency and quasiparticle current in the qubit-measuring circuit weakly coupled with the qubit provides little back action and prevents fast qubit decoherencing durin weak continuous measurements of quantum states.
O. G. Turutanov, V. I. Shnyrkov, A. N. Omelyanchouk
Stochastic amplifier based on superconducting interferometer with 4-terminal Josephson junction for flux qubit readout.
MSMW’07 Symposium Proceedings, Kharkov, Ukraine, p.822-824

Tunable SR-based input circuits for SQUIDs
The potential barrier between metastable states in a SQUID loop with incorporated 4-terminal mesoscopic weak link is governed by control current driven through two leads of the 4-terminal weak link. The effect enables, with presence of thermal or external noise, building novel superconducting SR amplifiers with tunable gain and frequency band for SQUID input circuits.
O. G. Turutanov, A. N. Omelyanchouk, V. I. Shnyrkov, Yu. P. Bliokh.
Stochastic resonance-based input circuits for SQUIDs.
Physica С 372, 239 (2002)
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