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The topic of quantum fluctuations in quasi-1D superconductors, also called quantum phase slips (QPS), has attracted a significant attention. It has been shown that the phenomenon is capable to suppress zero resistivity of ultra-narrow…
A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multi-stability emerges associated with…
We study the phase dynamics in coupled Josephson junctions describing by system of nonlinear differential equations. Results of detailed numerical simulations of charge creation in the superconducting layers and the longitudinal plasma wave…
We investigate stationary charge imbalance effect in the system of coupled overdamped Josephson junctions. We show that coupling between junction and nonzero stationary charge imbalance in the resistive state bring to a decrease of the…
The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions…
We analyze the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage biased Josephson junction. When the applied voltage leads to a Josephson frequency across the junction which matches the sum of the two mode…
Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, $i.e.$, amplification of quantum signals while adding the minimum amount of noise allowed by…
This short and opinionated review starts with a concept of quantum signals at microwave frequencies and focuses on the principle of linear parametric amplification. The amplification process arises from the dispersive nonlinearity of…
Schmid predicted that a single Josephson junction coupled to a resistive environment undergoes a quantum phase transition to an insulating phase when the shunt resistance $R$ exceeds the resistance quantum $h/(4 e^ 2)$. Recent measurements…
We present a theoretical study of resonant frequencies and spatial correlations of Josephson phases in frustrated arrays of Josephson junctions. Two types of one-dimensional arrays, namely, the diamond and sawtooth chains, are discussed.…
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or…
Josephson junctions supply the nonlinear inductance element in superconducting qubits. In the widely used transmon configuration, where the junction is shunted by a large capacitor, the low charging energy minimizes the sensitivity of the…
We study transport in an asymmetric SQUID which is composed of a loop with three capacitively and resistively shunted Josephson junctions: two in series in one arm and the remaining one in the other arm. The loop is threaded by an external…
We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The…
With the help of the numerical renormalization group method, we theoretically investigate the Josephson phase transition in a parallel junction with one quantum dot embedded in each arm. It is found that in the cases of uniform dot levels…
Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction…
The Josephson plasma resonance (JPR) provides a sensitive probe of vortex states in layered superconductors. We demonstrate that in the case of weak damping in the liquid phase, broadening of the JPR line is caused mainly by random…
We study theoretically the current-voltage characteristics of intrinsic Josephson junctions in high-$T_c$ superconductors. An oscillation of the breakpoint current on the outermost branch as a function of coupling $\alpha$ and dissipation…
We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular…
We investigate the quantum phase transitions in two capacitively coupled two-dimensional Josephson-junction arrays with charge frustration. The system is mapped onto the S=1 and $S=1/2$ anisotropic Heisenberg antiferromagnets near the…