@article{20324,
  abstract     = {We report relaxation oscillations in a one-dimensional array of Josephson junctions, wherein the array dynamically switches between low-current and high-current states. The oscillations are current-voltage dual to those ordinarily observed in single junctions. The current-voltage dual circuit quantitatively accounts for temporal dynamics of the array, including the dependence on biasing conditions. Injection locking of the oscillations results in well-developed current plateaux. A thermal model explains the self-consistent reduction of the superconducting gap due to overheating of the array in the high-current state. Our work suggests that overheating determines the switching from the high-current state to the low-current state.},
  author       = {Mukhopadhyay, Soham and Lancheros Naranjo, Diego A and Senior, Jorden L and Higginbotham, Andrew P},
  issn         = {2331-7019},
  journal      = {Physical Review Applied},
  publisher    = {American Physical Society},
  title        = {{Dual relaxation oscillations in a Josephson-junction array}},
  doi          = {10.1103/qvls-7s3q},
  volume       = {24},
  year         = {2025},
}

@phdthesis{17881,
  abstract     = {This work can be broadly classified into the study of critical phenomena in a one dimensional
array of Josephson junctions. While we study quantum criticality when the array is in thermal
equilibrium at zero bias, the non-equilibrium study involves understanding the bistability of the
array at a critical non-zero bias. This work furthers our knowledge in understanding quantum
critical behaviour at finite temperatures in a one dimensional Josephson array, while also
establishing relaxation behaviour dual to that observed in a single Josephson junction.
Chapter 1 briefly introduces the model to understand superconductor-insulator phase transition
in a one dimensional Josephson array and points out the state of the field from where we
started our zero-bias experiments. In this context it discusses the phase-charge duality observed
in a Josephson array and its dual hysteretic behaviour to that of a single junction, setting the
ground for our non-equilibrium study of the array.
Chapter 2 shows the experimental setup and the chip layout of the device we measured.
In chapter 3 we show that, unlike the typical quantum-critical broadening scenario, in one dimensional Josephson arrays temperature dramatically shifts the critical region. This shift leads
to a regime of superconductivity at high temperature, arising from the melted zero-temperature
insulator. Our results quantitatively explain the low-temperature onset of superconductivity in
nominally insulating regimes, and the transition to the strongly insulating phase. We further
present, to our knowledge, the first understanding of the onset of anomalous-metallic resistance
saturation [30]. This work demonstrates a non-trivial interplay between thermal effects and
quantum criticality. A practical consequence is that, counterintuitively, the coherence of
high-impedance quantum circuits is expected to be stabilized by thermal fluctuations.
In chapter 4, we show relaxation oscillations in a current-biased one dimensional array of
Josephson junctions. These oscillations are well described by a circuit model, dual to the
ordinary Josephson relaxation oscillations [72]. Injection locking these oscillations results in
current plateaux. The relaxation step is found to obey a characteristic self-consistent relation,
suggesting that it is governed by overheating effects.
Chapter 5 describes the various checks and analysis we performed to support our conclusions
made in chapters 3 and 4.
Finally, chapter 6 describes the nanofabrication steps and the finite element electromagnetic
simulations we performed to fabricate our devices.},
  author       = {Mukhopadhyay, Soham},
  isbn         = {978-3-99078-043-5},
  issn         = {2663-337X},
  pages        = {82},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Thermal effects in one dimensional Josephson chains}},
  doi          = {10.15479/at:ista:17881},
  year         = {2024},
}

@unpublished{18057,
  abstract     = {We report relaxation oscillations in a one-dimensional array of Josephson
junctions. The oscillations are circuit-dual to those ordinarily observed in
single junctions. The dual circuit quantitatively accounts for temporal
dynamics of the array, including the dependence on biasing conditions.
Injection locking the oscillations results in well-developed current plateaux.
A thermal model explains the relaxation step of the oscillations.},
  author       = {Mukhopadhyay, Soham and Lancheros Naranjo, Diego A and Senior, Jorden L and Higginbotham, Andrew P},
  booktitle    = {arXiv},
  title        = {{Dual relaxation oscillations in a Josephson junction array}},
  doi          = {10.48550/arXiv.2408.07829},
  year         = {2024},
}

@article{14032,
  abstract     = {Arrays of Josephson junctions are governed by a competition between superconductivity and repulsive Coulomb interactions, and are expected to exhibit diverging low-temperature resistance when interactions exceed a critical level. Here we report a study of the transport and microwave response of Josephson arrays with interactions exceeding this level. Contrary to expectations, we observe that the array resistance drops dramatically as the temperature is decreased—reminiscent of superconducting behaviour—and then saturates at low temperature. Applying a magnetic field, we eventually observe a transition to a highly resistive regime. These observations can be understood within a theoretical picture that accounts for the effect of thermal fluctuations on the insulating phase. On the basis of the agreement between experiment and theory, we suggest that apparent superconductivity in our Josephson arrays arises from melting the zero-temperature insulator.},
  author       = {Mukhopadhyay, Soham and Senior, Jorden L and Saez Mollejo, Jaime and Puglia, Denise and Zemlicka, Martin and Fink, Johannes M and Higginbotham, Andrew P},
  issn         = {1745-2481},
  journal      = {Nature Physics},
  keywords     = {General Physics and Astronomy},
  pages        = {1630--1635},
  publisher    = {Springer Nature},
  title        = {{Superconductivity from a melted insulator in Josephson junction arrays}},
  doi          = {10.1038/s41567-023-02161-w},
  volume       = {19},
  year         = {2023},
}