In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.
Author indications on fulfilling journal expectations
Provide a novel and synergetic link between different research areas.
Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
Detail a groundbreaking theoretical/experimental/computational discovery
Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We again thank the referees for their comments. We implemented the requests for changes of the manuscript as well as a few additional small improvements. A comprehensive list of changes is given below.
List of changes
-Added clarification of different expectation values where $\langle.\rangle$ denotes averages with respect to thermal fluctuations and $\langle.\rangle_\rho$ denotes the expectation value with regards to the density matrix of the oscillator that is still conditioned on the thermal fluctuations. -Added further comments to clarify the entropy production rate as well as the form of the escapement potential with regards to Ref. [25]. -Included a paragraph on the ansatz for the classical model to build an intuition for the clock dynamics -Included Ref. [36,37] as a study of a similar circuit. -Restructured the Appendices into smaller subsections to allow for a more clear presentation in sections 4 and 5 with references to individual sections. Appendix A now shows the complete derivation of the effective quantum mechanical model of the circuit and Appendix B covers the Adler-type equations in the classical model as well as the influence of thermal noise on the synchronization. -Extended the introductory paragraph of section 4 to briefly outline the use of a Keldysh path integral description -Specified the simulated model as the coupled Lindblad and Langevin equations using the full rotating wave Hamiltonian from Appendix A. -Added interpretation for the increasing size of the synchronization plateau with increasing light-matter coupling $r$. -Added second x-axis to the Figures 2. and 3. to explicitly show the dependence on the bias current. -Included discussion of asymmetric critical currents in section 7. -Added references to path integral literature in Appendix A. -Added Appendix C to further discuss the case of asymmetric critical currents. - Added missing definitions of constants -Corrected typos
