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arXiv:2507.22662 · Physical review. B./Physical review. B

Nonclassical photon-assisted transport in superconducting tunnel junctions

Matthias Hübler, Juan Carlos Cuevas, Wolfgang Belzig

Published Oct 31, 2025• 0 citations
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Abstract

Advances in circuit quantum electrodynamics have enabled the generation of arbitrary nonclassical microwave states, enabling progress in physics. Here, we present a theoretical study of the electrical current in a Josephson tunnel junction interacting with a nonclassical electromagnetic environment. This allows us to generalize classical transport phenomena like photon-assisted tunneling and Shapiro steps to the quantum regime. We predict that the analysis of the supercurrent in such a setup enables the complete reconstruction of quantum states of the electromagnetic environment, something that is not possible with normal tunnel junctions.

DOI
10.1103/64gy-9vnc

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Advances in circuit quantum electrodynamics have enabled the generation of arbitrary nonclassical microwave states, enabling progress in physics. Here, we present a theoretical study of the electrical current in a Josephson tunnel junction interacting with a nonclassical electromagnetic environment. This allows us to generalize classical transport phenomena like photon-assisted tunneling and Shapiro steps to the quantum regime. We predict that the analysis of the supercurrent in such a setup enables the complete reconstruction of quantum states of the electromagnetic environment, something that is not possible with normal tunnel junctions.
Using a perturbation expansion to the fourth order in a junction critical current, the authors study the generation of nonclassical microwave radiation by inelastic Cooper pair tunneling in a small voltage-biased Josephson junction connected to a superconducting transmission line. The second order in the tunneling current only allows consideration of independent events. Pushing the calculation to the fourth order allows capture of the temporal correlations in the charge transport and their connection to the ones in the emitted electromagnetic radiation.
Circular superconducting devices with mesoscopic Josephson junctions are considered in the presence of a dc voltage bias V0{\mathit{V}}_{0}V0​ and of nonclassical electromagnetic fields. It is shown that when the voltage V0{\mathit{V}}_{0}V0​ is an integer multiple of a certain value, the current through the junction has a dc component. This is broadly similar to Shapiro steps in macroscopic Josephson junctions, but the details depend on the nature of the nonclassical electromagnetic field. Coherent states, squeezed states, and number eigenstates are considered and the corresponding Shapiro steps are studied in detail. The presence of thermal noise in the nonclassical fields is also considered and its effect on the results is studied.
Among the most exciting recent advances in the field of superconducting quantum circuits is the ability to coherently couple microwave photons in low-loss cavities to quantum electronic conductors. These hybrid quantum systems hold great promise for quantum information-processing applications; even more strikingly, they enable exploration of new physical regimes. Here we study theoretically the new physics emerging when a quantum electronic conductor is exposed to nonclassical microwaves (for example, squeezed states, Fock states). We study this interplay in the experimentally relevant situation where a superconducting microwave cavity is coupled to a conductor in the tunnelling regime. We find that the conductor acts as a nontrivial probe of the microwave state: the emission and absorption of photons by the conductor is characterized by a nonpositive definite quasi-probability distribution, which is related to the Glauber-Sudarshan P-function of quantum optics. These negative quasi-probabilities have a direct influence on the conductance of the conductor.
This manuscript summarizes my research activities devoted to the study of nonequilibrium phenomena in mesoscopic superconducting and semiconducting circuits. The work develops along two directions: the dynamics of metallic Josephson junctions driven out of equilibrium and the interaction between electrons and microwave photons in mesoscopic quantum circuits.The first part investigates diffusive superconductor–normal metal–superconductor Josephson junctions subjected to strong perturbations such as microwave irradiation or stochastic injection of high-energy quasiparticles. These experiments reveal how nonequilibrium excitations modify the Andreev spectrum and the phase dynamics of the junction. The second part addresses electron–photon coupling in mesoscopic circuits across different interaction regimes. Early work focused on semiconductor double quantum dots coupled to low-impedance microwave cavities in the weak coupling regime. Later work involved the fabrication and characterization of high-kineticinductance superconducting materials, allowing the realization of high-impedance resonators and stronger light-matter coupling. Finally, a superconducting tunnel junction coupled to a high-impedance granular aluminum cavity allowed bath engineering based on photo-assisted quasiparticle tunneling, efficient photon-toelectron conversion, and continuous single microwave photon detection.