Long Josephson junction embedded into a planar resonator at microwave frequencies: Numerical simulation of fluxon dynamics

Goldobin, E.; Клушин, А.М.; Siegel, M.; Klein, N.

doi:10.1063/1.1497466

Cited by 5 publications

(7 citation statements)

References 9 publications

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“…We suppose that in the absence of a ground plane the largest microwave current is induced near the junction edges. That can be described by a distribution of the current γ ac sharply peaked near the junction boundaries [8] or, equivalently, by an oscillating bias component ± h ac at the edges. In the following we show the simulation results obtained for γ ac = 0, so that microwave drive is coupled via the boundary conditions.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The interest to drive vortices in long junctions by microwaves has been also biased by practical applications. Recently, low-frequency microwave properties of long Josephson junctions have been studied in relation to their possible application in tuneable resonators [8]. On the other hand, driving long junctions by microwaves is now successfully used for phase-locking of Josephson flux-flow oscillators in integrated superconducting submillimeter wave receivers [9].…”

Section: Introductionmentioning

confidence: 99%

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Microwave-induced flow of vortices in long Josephson junctions

2004

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We report experimental and numerical study of microwave-induced flow of vortices in long Josephson junctions at zero dc magnetic field. Our intriguing observation is that applying an ac-bias of a small frequency $f \ll f_p $ and sufficiently large amplitude changes the current-voltage characteristics ($I$-$V$ curve) of the junction in a way similar to the effect of dc magnetic field, well known as the flux-flow behavior. The characteristic voltage $V$ of this low voltage branch increases with the power $P$ of microwave radiation as $V_{s}\propto P^{\alpha}$ with the index $\alpha \simeq 0.5 $. Experiments using a low-temperature laser scanning microscope unambiguously indicate the motion of Josephson vortices driven by microwaves. Numerical simulations agree with the experimental data and show strongly {\it irregular} vortex motion. We explain our results by exploiting an analogy between the microwave-induced vortex flow in long Josephson junctions and incoherent multi-photon absorption in small Josephson junctions in the presence of large thermal fluctuations. In the case of long Josephson junctions the spatially-temporal chaos in the vortex motion mimics the thermal fluctuations. In accordance with this analogy, a control of the intensity of chaos in a long junction by changing its damping constant leads to a pronounced change in the shape of the $I$-$V$ curve. Our results provide a possible explanation to previously measured but not yet understood microwave-driven properties of intrinsic Josephson junctions in high-temperature superconductors.Comment: 8 pages, 13 figure

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Microwave-induced flow of vortices in long Josephson junctions

2004

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“…35 Since the distance between the junctions is J λ in the model, the flux between adjacent junctions is determined by…”

Section: Vortex Dynamicsmentioning

confidence: 99%

“…A long Josephson junction can be described by the sine-Gordon equation, 34,35 , t . L J , R J , and C J are all quantities per unit length.…”

Section: Vortex Dynamicsmentioning

confidence: 99%

Microwave nonlinearities of an isolated longYBa2Cu3O7−δbicrystal grain boundary

Lee

Anlage

2005

Phys. Rev. B

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We measure the local harmonic generation from an YBa 2 Cu 3 O 7-δ (YBCO) bi-crystal grain boundary to examine the local Josephson nonlinearities. Spatially resolved images of second and third harmonic signals generated by the grain boundary are shown. The harmonic generation and the vortex dynamics along the grain boundary are modeled with the Extended Resistively Shunted Josephson (ERSJ) array model, which shows reasonable agreement with the experimental data. The model also gives qualitative insight into the vortex dynamics induced in the junction by the probing current distribution. A characteristic nonlinearity scaling current density J NL ~ 5 10 5 . 1 × A/cm 2 for the Josephson nonlinearity is also extracted.

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“…It is then of interest to extend the study to the case of (dc) driven long, but finite Josephson junctions with phase-shifts, as experimentally used in [13,14]. In microwave-driven finite junctions, the boundaries can be a major external drive (see, e.g., [29,30]), which is not present in the study here. A constant (dc) bias current, which is mentioned to play an important role in the measurements reported in [13], is also not included in our current paper, even though the results presented herein should still hold for small enough constant drive.…”

Section: Discussionmentioning

confidence: 99%

Breathing Modes of Long Josephson Junctions with Phase-Shifts

Ali¹,

Susanto²,

Wattis³

2011

SIAM J. Appl. Math.

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Abstract. We consider a spatially inhomogeneous sine-Gordon equation with a time-periodic drive, modeling a microwave driven long Josephson junction with phase-shifts. Under appropriate conditions, Josephson junctions with phase-shifts can have a spatially nonuniform ground state. In recent reports [Phys. Rev. Lett. 98, 117006 (2007), arXiv:0903.1046, it is experimentally shown that a microwave drive can be used to measure the eigenfrequency of a junction's ground state. Such a microwave spectroscopy is based on the observation that when the frequency of the applied microwave is in the vicinity of the natural frequency of the ground state, the junction can switch to a resistive state, characterized by a non-zero junction voltage. It was conjectured that the process is analogous to the resonant phenomenon in a simple pendulum motion driven by a time periodic external force. In the case of long junctions with phase-shifts, it would be a resonance between the internal breathing mode of the ground state and the microwave field. Nonetheless, it was also reported that the microwave power needed to switch the junction into a resistive state depends on the magnitude of the eigenfrequency to be measured. Using multiple scale expansions, we show here that an infinitely long Josephson junction with phase-shifts cannot be switched to a resistive state by microwave field with frequency close to the system's eigenfrequency, provided that the applied microwave amplitude is small enough, which confirms the experimental observations. It is because higher harmonics with frequencies in the continuous spectrum are excited, in the form of continuous wave radiation. The breathing mode thus experiences radiative damping. In the absence of driving, the breathing mode decays at rates of at most O(t −1/4 ) and O(t −1/2 ) for junctions with a uniform and nonuniform ground state, respectively. The presence of applied microwaves balances the nonlinear damping, creating a stable breather mode oscillation. As a particular example, we consider the so-called 0 − π − 0 and 0 − κ Josephson junctions, respectively representing the two cases. We confirm our analytical results numerically. Using our numerical computations, we also show that there is a critical microwave amplitude at which the junction switches to the resistive state. Yet, it appears that the switching process is not necessarily caused by the breathing mode. We show a case where a junction switches to a resistive state due to the continuous wave background becoming modulationally unstable.

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Long Josephson junction embedded into a planar resonator at microwave frequencies: Numerical simulation of fluxon dynamics

Cited by 5 publications

References 9 publications

Microwave-induced flow of vortices in long Josephson junctions

Microwave-induced flow of vortices in long Josephson junctions

Microwave nonlinearities of an isolated longYBa2Cu3O7−δbicrystal grain boundary

Breathing Modes of Long Josephson Junctions with Phase-Shifts

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