^{1}, O. G. Turutanov

^{1,a)}, V. I. Shnyrkov

^{1}and A. N. Omelyanchouk

^{1}

### Abstract

A numerical simulation of the stochastic resonance is carried out in the adiabatic approximation in overdamped systems based on superconducting loops closed by a weak link. The systems under consideration include a single-ring rf SQUID, two rings coupled by a common magnetic flux, and a ring closed by a 4-terminal Josephson junction. It is shown that coupling of single SQUID rings enhances the gain and the signal-to-noise ratio. These effects can be used to create new stochastic SQUIDantennas for measurements of harmonic and quasi-harmonic signals. The stochastic resonance in 4-terminal SQUIDS exists even at values of the dimensionless inductance.

INTRODUCTION

MODEL OF STOCHASTIC RESONANCE IN A SINGLE rf SQUID RING

NUMERICAL SIMULATION TECHNIQUE AND THE RESULTS FOR A SINGLE RING

SIMULATION OF THE STOCHASTIC RESONANCE IN COUPLED RINGS

MODELING THE STOCHASTIC RESONANCE IN A 4-TERMINAL SQUID

STOCHASTIC ANTENNAS

CONCLUSION

### Key Topics

- Josephson junctions
- 26.0
- Superconducting quantum interference devices
- 23.0
- Antennas
- 15.0
- Stochastic processes
- 12.0
- Magnetic flux
- 11.0

## Figures

Potential function of a superconducting loop containing a Josephson junction. The hysteresis parameter , the external magnetic flux . Inset: scheme of the rf SQUID ring; is the inductance of the ring, is the magnetic flux through the ring, and and are the critical current and the capacitance of the Josephson junction, respectively.

Potential function of a superconducting loop containing a Josephson junction. The hysteresis parameter , the external magnetic flux . Inset: scheme of the rf SQUID ring; is the inductance of the ring, is the magnetic flux through the ring, and and are the critical current and the capacitance of the Josephson junction, respectively.

Symmetric bistable potential of the rf SQUID ring for and ; the values of the flux corresponding to the minima of the potential , the middle of the barrier , and the potential barrier height (a). A diagram of the transition of the system from one stable state to another upon the warping of the potential by an external magnetic flux (b).

Symmetric bistable potential of the rf SQUID ring for and ; the values of the flux corresponding to the minima of the potential , the middle of the barrier , and the potential barrier height (a). A diagram of the transition of the system from one stable state to another upon the warping of the potential by an external magnetic flux (b).

Time series of a periodic input signal (white curves), the signal with noise, (black), and the output signal (gray) (a); the Fourier spectra of the output signal at different noise levels (b).

Time series of a periodic input signal (white curves), the signal with noise, (black), and the output signal (gray) (a); the Fourier spectra of the output signal at different noise levels (b).

Dependence of the flux gain and signal-to-noise ratio on the noise level in a one-ring rf SQUID. Parameter , input signal amplitude , signal frequency , noise cutoff frequency , and number of points in the time series 32768. The curve of the SNR does not appear smooth because of the scatter in the determination of the position of the noise shelf.

Dependence of the flux gain and signal-to-noise ratio on the noise level in a one-ring rf SQUID. Parameter , input signal amplitude , signal frequency , noise cutoff frequency , and number of points in the time series 32768. The curve of the SNR does not appear smooth because of the scatter in the determination of the position of the noise shelf.

Even and odd harmonics in the Fourier spectrum of the output signal at different levels of the constant bias flux. The noise intensity is equal to that value at which the maximum stochastic amplification of the signal is observed.

Even and odd harmonics in the Fourier spectrum of the output signal at different levels of the constant bias flux. The noise intensity is equal to that value at which the maximum stochastic amplification of the signal is observed.

Values of the first three harmonics of the main signal in the output Fourier spectrum as a function of the input bias flux ; . The noise intensity is equal to that value at which the maximum stochastic amplification of the signal is observed.

Values of the first three harmonics of the main signal in the output Fourier spectrum as a function of the input bias flux ; . The noise intensity is equal to that value at which the maximum stochastic amplification of the signal is observed.

Potential surface for two coupled rf SQUID rings in the absence of additional bias, input signal, and noise at the following parameter values: , (a); , , (b), , (c); , (d), and with biasing by an external signal for , , (e); , , (f).

Potential surface for two coupled rf SQUID rings in the absence of additional bias, input signal, and noise at the following parameter values: , (a); , , (b), , (c); , (d), and with biasing by an external signal for , , (e); , , (f).

Flux gain as a function of the noise level and coupling coefficient for identical rings (a) and different rings (b). Signal amplitude , signal frequency , hysteresis parameters (a); , (b).

Flux gain as a function of the noise level and coupling coefficient for identical rings (a) and different rings (b). Signal amplitude , signal frequency , hysteresis parameters (a); , (b).

Potential of a 4-terminal SQUID for , , .

Potential of a 4-terminal SQUID for , , .

Flux gain as a function of the noise level in the ring of a 4-terminal SQUID. Parameters: , , .

Flux gain as a function of the noise level in the ring of a 4-terminal SQUID. Parameters: , , .

Possible configurations of stochastic antennas for receiving weak quasi-harmonic signals with the use of SQUIDs: a,b—antennas for SQUID microscopes, c—antennas for low-frequency radar, geophysical magnetometry, and biomagnetic measurements.

Possible configurations of stochastic antennas for receiving weak quasi-harmonic signals with the use of SQUIDs: a,b—antennas for SQUID microscopes, c—antennas for low-frequency radar, geophysical magnetometry, and biomagnetic measurements.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content