# Josephson phase diffusion in the superconducting quantum interference device ratchet

## Abstract

We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. Łuczka, New J. Phys. 17, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified several times by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially non-chaotic and possesses an unexpected simplicity of attractors.

- Authors:

- Institute of Physics, University of Silesia, 40-007 Katowice (Poland)
- (Poland)

- Publication Date:

- OSTI Identifier:
- 22402558

- Resource Type:
- Journal Article

- Journal Name:
- Chaos (Woodbury, N. Y.)

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ATTRACTORS; CHAOS THEORY; DIFFUSION; EFFICIENCY; ELECTRIC CURRENTS; ELECTRIC POTENTIAL; JOSEPHSON EFFECT; MAGNETIC FLUX; MATHEMATICAL EVOLUTION; PERIODICITY; SQUID DEVICES; TIME DEPENDENCE

### Citation Formats

```
Spiechowicz, Jakub, Łuczka, Jerzy, E-mail: jerzy.luczka@us.edu.pl, and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów.
```*Josephson phase diffusion in the superconducting quantum interference device ratchet*. United States: N. p., 2015.
Web. doi:10.1063/1.4921211.

```
Spiechowicz, Jakub, Łuczka, Jerzy, E-mail: jerzy.luczka@us.edu.pl, & Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów.
```*Josephson phase diffusion in the superconducting quantum interference device ratchet*. United States. doi:10.1063/1.4921211.

```
Spiechowicz, Jakub, Łuczka, Jerzy, E-mail: jerzy.luczka@us.edu.pl, and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów. Fri .
"Josephson phase diffusion in the superconducting quantum interference device ratchet". United States. doi:10.1063/1.4921211.
```

```
@article{osti_22402558,
```

title = {Josephson phase diffusion in the superconducting quantum interference device ratchet},

author = {Spiechowicz, Jakub and Łuczka, Jerzy, E-mail: jerzy.luczka@us.edu.pl and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów},

abstractNote = {We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. Łuczka, New J. Phys. 17, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified several times by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially non-chaotic and possesses an unexpected simplicity of attractors.},

doi = {10.1063/1.4921211},

journal = {Chaos (Woodbury, N. Y.)},

issn = {1054-1500},

number = 5,

volume = 25,

place = {United States},

year = {2015},

month = {5}

}