Quantumness of Josephson junctions reexamined (original) (raw)

The Josephson junction as a quantum engine

New Journal of Physics, 2023

We treat the Cooper pairs in the superconducting electrodes of a Josephson junction (JJ) as an open system, coupled via Andreev scattering to external baths of electrons. The disequilibrium between the baths generates the direct-current bias applied to the JJ. In the weak-coupling limit we obtain a Markovian master equation that provides a simple dynamical description consistent with the main features of the JJ, including the form of the current-voltage characteristic, its hysteresis, and the appearance under periodic voltage driving of discrete Shapiro steps. For small dissipation, our model also exhibits a self-oscillation of the JJ's electrical dipole with frequency Ω=2eV/ℏ around mean voltage V. This self-oscillation, associated with "hidden attractors" of the nonlinear equations of motion, explains the observed production of monochromatic radiation with frequency Ω and its harmonics. We argue that this picture of the JJ as a quantum engine resolves open questions about the Josephson effect as an irreversible process and could open new perspectives in quantum thermodynamics and in the theory of dynamical systems.

Quantum fluctuations in finite size Josephson junctions

Physics Letters A, 1992

An effective Josephson coupling energy for a one-dimensional Josephson junction is renormalized due to quantum fluctuations of the phase difference. In a longjunction at T-.0 a Kosterlitz-Thouless phase transition takes place. The state with a logarithmically divergent phase-phase correlation function shows a nontrivial combination of phase disorder on a junction surface with phase order in the bulk. For finitesize junctions the renormalized value ofthe Josephson coupling energy turns out to be strongly suppressed for small Josephson-to-charging energy ratio. The implications of this effect for Bloch oscillations are discussed. The prediction [1] of the effect of Bloch oscilla-pacitance Cci.: S should be small enough to allow for tions in ultrasmall superconducting tunnel junctions an experimentally accessible temperature interval. induced substantial theoretical and experimental ac-Typical experimental parameters for "quantum" tivity in the field (see e.g. refs. [2,3] for a review). Josephson junctions are S-S l0~-l0'°cm and Recently reliable experimental evidence of this ef-C-i 10-'~-l0 16 F. Then if we assume the junction fect was reported [4-6].Most of these experimental size in the x-direction Lto be of the order of that results turn out to be in good quantitative agreement in the y-direction L~(x and y are coordinates in the with the theory [7,8]. junction plane) we can estimate L~-~L~- .-' l0~cm.