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The Journal of V N Karazin Kharkiv National University Series Physics

Coherent emission from the stack of Josephson junctions with the non-uniform inductive interaction

O. M. Grib, O. L. Samsonik, Р. В. Сухов

Published Jan 1, 2019• 0 citations
Publisher

Abstract

During last decade, considerable efforts were made to achieve coherent emission from stacks of many Josephson junctions. It is known that strong emission from a junction in the presence of external magnetic field appears at the so-called Fiske steps in the IV-characteristic at voltages which correspond to frequencies of geometrical resonances. However, it is possible to obtain resonant steps in long junctions without external magnetic field. The periodical movement of fluxons is excited due to some disorder in the distribution of critical currents along junctions. The so-called zero-field steps are formed in the IV-curve due to the interaction of fluxons with oscillations of voltage at Josephson frequencies. We investigated numerically IV-characteristics and the dependence of the average square of ac voltage at the end of the stack of two long Josephson junctions on the average voltage. Junctions interacted inductively with each other. We introduced not only the Gaussian distribution of critical currents along junctions but also the Gaussian distribution of coefficients of the interaction between junctions (mutual inductances). Zero-field steps in the IV-characteristic were found at voltages which corresponded to frequencies of in-phase collective modes in the stack as well as to frequencies of uncoupled junctions. Zero-field steps appeared in the hysteretic region of the IV-curve. There appeared also jumps of voltage from the resistive branch to the zero-field step. We showed that there existed distributions of mutual inductances along junctions which provided jumps to voltages at which the average square of ac voltage at the end of the stack (which is proportional to power of emission) was larger than that for the stack with the uniform distribution of mutual inductances.

DOI
10.26565/2222-5617-2019-31-9

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During last decade, considerable efforts were made to achieve coherent emission from stacks of many Josephson junctions. It is known that strong emission from a junction in the presence of external magnetic field appears at the so-called Fiske steps in the IV-characteristic at voltages which correspond to frequencies of geometrical resonances. However, it is possible to obtain resonant steps in long junctions without external magnetic field. The periodical movement of fluxons is excited due to some disorder in the distribution of critical currents along junctions. The so-called zero-field steps are formed in the IV-curve due to the interaction of fluxons with oscillations of voltage at Josephson frequencies. We investigated numerically IV-characteristics and the dependence of the average square of ac voltage at the end of the stack of two long Josephson junctions on the average voltage. Junctions interacted inductively with each other. We introduced not only the Gaussian distribution of critical currents along junctions but also the Gaussian distribution of coefficients of the interaction between junctions (mutual inductances). Zero-field steps in the IV-characteristic were found at voltages which corresponded to frequencies of in-phase collective modes in the stack as well as to frequencies of uncoupled junctions. Zero-field steps appeared in the hysteretic region of the IV-curve. There appeared also jumps of voltage from the resistive branch to the zero-field step. We showed that there existed distributions of mutual inductances along junctions which provided jumps to voltages at which the average square of ac voltage at the end of the stack (which is proportional to power of emission) was larger than that for the stack with the uniform distribution of mutual inductances.
We investigated numerically IV-characteristics and power of emission from stacks with various quantities of long Josephson junctions (up to 6 junctions) which interacted inductively with each other. Parameters of junctions were chosen close to those for MoRe-Si(W)-MoRe heterostructures. We set Gaussian spread of about 0.01% of critical currents along junctions. Electrical properties of a stack consisted of three junctions was investigated in details. Zero-fi eld steps at voltages corresponding to frequencies of various modes of electromagnetic waves in the stack were found in the IV-characteristic. We showed that positions of zero-fi eld steps in IV-curves were in good agreement with predictions of the theory. The highest maximum of power of emission corresponded to the so-called in-phase mode at which all voltages over junctions in the stack oscillate in-phase. Considering stacks with many junctions, we showed that power of emission at the voltage of the resonance which corresponds to the in-phase mode is proportional to the square of quantity of long junctions in the stack that is the characteristic of coherent emission.
Flux-flow cavity resonances in intrinsic Josephson junctions (IJJs) with long c-axis periodicity by artificial critical-current (Jc) modulation are studied numerically and theoretically. For an n-1–n-1–n-1–n IJJ system with n-layer high-Jc and one-layer low-Jc alternately stacked, numerical simulation confirms fluxon penetration only in the low-Jc junctions under proper low magnetic fields. The simulation also shows pronounced cavity-resonance steps in the I–V curves of the low-Jc junctions, meaning that fluxon dynamics can be generated under much lower magnetic fields, compared to the fields for usual IJJs with homogeneous Jc. A theoretical method for describing the flux-flow cavity-resonance properties is presented. The general disperse k–ω relationship shows that, at low-k regions, the critical-current-modulated junction system can be regarded as simple homogeneous stacked junctions with a new effective thickness and a new inductive coupling strength. For general-k cases, the cavity-resonant voltage steps on the I–V curves at various magnetic fields can be well indexed by integers, which means excellent agreement between the theoretical analysis and the numerical simulations.
Large constant voltage-current steps were observed in the I-V characteristics of long NbN-MgO-NbN Josephson junctions in the presence of external magnetic fields of a few Gauss. The steps are separated by a voltage corresponding roughly to three to five times the voltage spacing expected between adjacent Fiske steps. Models addressing the origin of such steps are presented. Simultaneous nucleation of fluxons at several sites along the junction with thin electrodes, favored by the large London penetration depth of NbN, would introduce a large amount of magnetic flux into the junction at once, leading to large steps. A model which involves pinning of fluxons in the junction is given. Due to the granularity of NbN and its very small coherence length, there will be pinning sites in the junction preventing single fluxons from moving at low bias currents. At particular junction parameter values the steps become very regular and sharp. The sharp steps can be used as a voltage standard without external RF bias or as a high-power oscillator when the device is suitably biased.>
We describe a variety of models to characterize the behavior of several types of underdamped Josephson systems.We also present numerical results based on these models.We first discuss a stack of small junctions in a single mode resonant cavity.Such a stack is believed to be appropriate to model some high temperature cuprate superconductors such as Bi 2 Sr 2 CaCu 2 O 8+x .Our results show self-induced-resonant-steps in the current voltage (IV) curve.These steps represent a coherent phase locking between the junctions in the stack and the resonant cavity.Next we generalize these results to treat a single long junction coupled to a single mode resonant cavity.We find a number of features not seen in stacks of small junctions.Our numerical results show that if the electromagnetic fields of the cavity mode are spatially periodic, we again see steps in the IV curve and furthermore, for sufficiently large coupling, the cavity frequency is shifted by coupling to the long junction.We also discuss how a stack of long junctions could be used to model a layered high temperature superconductor.We then turn to some properties of single junctions in the "quantum" regime where the phase/number non-commutation is important.This quantum regime is crucial to all proposals to use such junctions as solid state quantum bits (qubits).We show that such qubits, when subjected to external a.c.perturbations, exhibit not only . . . . . . . . . .
A small-area Josephson tunnel junction is pumped by the radiation emitted by a long Josephson junction dc biased on a zero-field singularity. Josephson constant voltage steps are observed in the current-voltage characteristic of the small junction at voltages of ±150 μV corresponding to the fundamental frequency of emission of the oscillator. The radiation also gives rise to quasiparticle steps around the gap-sum voltage of the small junction. From the measured current amplitude of the steps we estimate that the maximum power coupled to the small junction is about 90 nW.
Extensive measurements of radiation emitted from long Josephson junctions d.c.-current biased on zero-field and Fiske-steps are reported. The measurements were made in the band 8-10 GHz on long Nb-Nb oxide-Pb overlap tunnel junctions with the lengths 0.5 mm and 1.0 mm having fundamental frequencies of 10 GHz and 5 GHz, respectively. Depending on the fundamental frequency of the junction 1st or 2nd harmonic detection was employed. In the fundamental scheme the frequency f n vs. the d.c.-voltage V n along the steps follows a modified Josephson voltage/frequency relation f n / V n = 2 e/nh , where n is the step-number n = 1, 2, 3,... for Fiske-steps and n = 2, 4, 6,... for zero-field steps. On a given step the frequency could be tuned (200-500 MHz) by varying the bias point. The linewidth was measured to be less than 5 kHz. All the observed phenomena are consistent with a novel unified dynamic bunched fluxon model applicable to both zero-field and Fiske-steps and are in good agreement with recent numerical solutions of the perturbed sine-Gordon equation with proper boundary conditions. Taking advantage of operation on higher order steps and strong harmonic generation the present upper frequency limit for the Josephson fluxon oscillator is above 200 GHz. The maximum power observed so far is only 5 pW, but the estimated available power is of the order 1 μW, which is quite sufficient to pump other Josephson devices.