# Axion Field Influence on Josephson Junction Quasipotential

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## Abstract

**:**

## 1. Introduction

## 2. Model

#### 2.1. RCSJ Model

#### 2.2. Axion

#### 2.3. Axion–JJ System

## 3. Calculation of the Quasipotential

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

JJ | Josephson junction |

RCSJ | resistively and capacitively shunted junction |

## References

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**Figure 1.**Schematic illustration of the device. (

**a**) The physical process: An axion field a enters the normal barrier between two superconducting electrodes. (

**b**) The mathematical model: The phase particle in a minimum of the washboard potential U, tilted by a bias current, is perturbed by the axion (represented by the arrow that hits the particle-phase $\phi $). Under the combined effect of thermal noise and axion–JJ coupling, the JJ phase can overcome the barrier $\Delta U$ and roll down along the potential. In this case, a detectable voltage $\propto \langle d\phi /dt\rangle $ appears.

**Figure 2.**Behavior of the average value (

**top**panels) and the root mean square (

**bottom**panels) of the switching time distributions as a function of the inverse noise intensity, for different values of the axion–JJ coupling, $\gamma $, and three different bias current, ${i}_{b}=\{0.1,0.5,\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}0.8\}$, see panels (

**a**,

**d**), (

**b**,

**e**), and (

**c**,

**f**), respectively. The black solid line without symbols in the top panels denotes the full Kramers theory for the dissipative Josephson escape [73]. The other parameters of the system are $\epsilon =1$, ${\beta}_{c}=100$, ${t}_{max}={10}^{6}$, and $N={10}^{4}$. The legend in panel (

**c**) refers to all panels.

**Figure 3.**Behavior of the quasipotential effective barrier, $\Delta {\mathcal{U}}_{eff}$, retrieved from the data shown in Figure 2, as a function of the axion–JJ coupling $\gamma $. Panels (

**a**–

**c**) refer to different bias current values, i.e., ${i}_{b}=\{0.1,0.5,\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}0.8\}$, respectively.

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**MDPI and ACS Style**

Grimaudo, R.; Valenti, D.; Spagnolo, B.; Troisi, A.; Filatrella, G.; Guarcello, C.
Axion Field Influence on Josephson Junction Quasipotential. *Materials* **2023**, *16*, 5972.
https://doi.org/10.3390/ma16175972

**AMA Style**

Grimaudo R, Valenti D, Spagnolo B, Troisi A, Filatrella G, Guarcello C.
Axion Field Influence on Josephson Junction Quasipotential. *Materials*. 2023; 16(17):5972.
https://doi.org/10.3390/ma16175972

**Chicago/Turabian Style**

Grimaudo, Roberto, Davide Valenti, Bernardo Spagnolo, Antonio Troisi, Giovanni Filatrella, and Claudio Guarcello.
2023. "Axion Field Influence on Josephson Junction Quasipotential" *Materials* 16, no. 17: 5972.
https://doi.org/10.3390/ma16175972