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Advanced Theory and Simulations

Dynamical Properties of Nanostructured Josephson‐Junction Based on the Schwinger Quantum Action Analysis

Jeong Ryeol Choi

Published Oct 7, 2019• 0 citations

Abstract

Abstract Using the Schwinger action principle, Josephson‐junction dynamics for nanodevices have been investigated with emphasis on characterizing their quantum features. Starting from the time‐ordered Hamiltonian for the phase of the current which flows across the junction, the propagator, the wave functions, and the joint entropy, which are crucial for quantum analyses of the nano systems, are derived. It is shown that while the propagator and the wave functions vary depending on external driving forces, the joint entropy is not affected from such forces. Interestingly, the probability densities oscillate over time on account of the influence of the time‐varying supercurrent in the junction. It is confirmed that if external perturbations on the junction‐current are more complicated, the time behaviors of the probability densities become conspicuously irregular. The properties of the joint entropy are also analyzed in detail. Due to damping of the system, the phase(ϕ) component of the joint entropy decreases linearly over time, whereas the conjugate momentum(q) component exhibits linear increase; however, the corresponding joint entropy consequently does not vary. It is demonstrated that the joint entropy obeys the quantum minimum principle, and that there is a close relationship between the joint entropy and the uncertainty relation.

DOI: 10.1002/adts.201900161

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Abstract Using the Schwinger action principle, Josephson‐junction dynamics for nanodevices have been investigated with emphasis on characterizing their quantum features. Starting from the time‐ordered Hamiltonian for the phase of the current which flows across the junction, the propagator, the wave functions, and the joint entropy, which are crucial for quantum analyses of the nano systems, are derived. It is shown that while the propagator and the wave functions vary depending on external driving forces, the joint entropy is not affected from such forces. Interestingly, the probability densities oscillate over time on account of the influence of the time‐varying supercurrent in the junction. It is confirmed that if external perturbations on the junction‐current are more complicated, the time behaviors of the probability densities become conspicuously irregular. The properties of the joint entropy are also analyzed in detail. Due to damping of the system, the phase(ϕ) component of the joint entropy decreases linearly over time, whereas the conjugate momentum(q) component exhibits linear increase; however, the corresponding joint entropy consequently does not vary. It is demonstrated that the joint entropy obeys the quantum minimum principle, and that there is a close relationship between the joint entropy and the uncertainty relation.

Dynamic evolution of a mesoscopic Josephson junction (MJJ) interacting with quantized electromagnetic fields (QEMF) is investigated. It is shown that the current-voltage steps of the MJJ can reflect quantum coherences of the external QEMF; these characteristics may be used to distinguish different types of quantum electromagnetic fields. It is found that supercurrent fluctuations exhibit periodic oscillations in the time evolution. Supercurrent correlation functions are also studied in some detail. It is shown that the thermal noise in the external electromagnetic field seriously affects the second-order correlation function of the supercurrent. \textcopyright{} 1996 The American Physical Society.

The switching dynamics of a double-barrier Josephson junction is analyzed as a function of the microscopic properties of its electrodes. In particular, it is found that the nonstationary behavior of the Josephson phase difference is very sensitive to dissipation mechanisms acting inside the intrinsic shunt. The leading factor that determines the dissipation is the local electron density of states N(E) inside the electrodes. The roles of junction geometry, electrode purity, and interface quality are discussed and how they affect the details of N(E), hence the resulting phase dynamics. The microscopic analyses allow optimization of the performance of double-barrier Josephson junction-based rapid-single-flux-quantum circuits in two ways: 1) decreasing the switching time of Josephson elements and 2) reducing the excess wiring. Such an analysis is facilitated with the aid of a lumped circuit representation which generalizes the nonlinear resistive-shunted-junction model.

The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.

The dissipative dynamics of a pointlike Josephson junction in binary Bose-Einstein-condensed mixtures is analyzed within the framework of the model of a tunneling Hamiltonian. The transmission of unlike particles across a junction is described by the different transmission amplitudes. The effective action that describes the dynamics of the phase differences across the junction for each of two condensed components is derived by employing the functional integration method. In the low-frequency limit the dynamics of a Josephson junction can be described by two coupled equations in terms of the potential energy and dissipative Rayleigh function using a mechanical analogy. The interplay between mass currents of each mixture component appears in the second-order term in the tunneling amplitudes due to the interspecies hybridizing interaction. The asymmetric case of the binary mixtures with different concentrations and order parameters is considered as well.

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 multistability emerges, associated with dynamical bifurcations so that the often-used modeling as a Duffing oscillator, which can exhibit bistability at most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly nonlinear quasienergy operator in a rotating frame. This allows us to identify in detail parameter regions where simplifications such as the Duffing approximation are valid, to explore classical-quantum correspondences, and to study how quantum fluctuations impact the effective junction parameters as well as the dynamics around higher-amplitude classical fixed points.

Preliminary results are presented concerning static properties of a small Josephson junction under the influence of strong microwave radiation. We discuss the correspondence between a Brownian particle moving in a periodic potential and superconducting phase difference in a small Josephson junction. Next, we describe an experimental method of determining the amplitude of microwave current flowing across the junction. Typical examples of static characteristics of the junction are presented, including its dynamical resistance as a function of microwave power. We discuss also the influence of an external magnetic field on the junction dynamics and show that in this case the one-dimensional Stewart-McCumber model becomes insufficient.