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arXiv:0812.2689 · Physical Review Letters

Phase Dynamics of Ferromagnetic Josephson Junctions

Ivana Petković, M. Aprili

Published Apr 16, 2009• 10 citations
arXivHTMLPDF

Abstract

We have investigated the classical phase dynamics of underdamped ferromagnetic Josephson junctions by measuring the switching probability in both the stationary and nonstationary regimes down to 350 mK. We found the escape temperature to be the bath temperature, with no evidence of additional spin noise. In the nonstationary regime, we have performed a pump-probe experiment on the Josephson phase by increasing the frequency of the junction current bias. We show that an incomplete energy relaxation leads to dynamical phase bifurcation. Bifurcation manifests itself as premature switching, resulting in a bimodal switching distribution. We directly measure the phase relaxation time tau_{phi} by following the evolution of the bimodal switching distribution when varying the bias frequency. Numerical simulations account for the experimental values of tau_{phi}.

DOI
10.1103/physrevlett.102.157003

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We have investigated the classical phase dynamics of underdamped ferromagnetic Josephson junctions by measuring the switching probability in both the stationary and nonstationary regimes down to 350 mK. We found the escape temperature to be the bath temperature, with no evidence of additional spin noise. In the nonstationary regime, we have performed a pump-probe experiment on the Josephson phase by increasing the frequency of the junction current bias. We show that an incomplete energy relaxation leads to dynamical phase bifurcation. Bifurcation manifests itself as premature switching, resulting in a bimodal switching distribution. We directly measure the phase relaxation time tau_{phi} by following the evolution of the bimodal switching distribution when varying the bias frequency. Numerical simulations account for the experimental values of tau_{phi}.
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.
A two-step transition model describing phase diffusion and switching process in underdamped Josephson junctions is discussed. The model takes into account the phase particle's escape rate out of the potential well and transition rate from phase diffusion to the running state. Using as examples the experimental switching current distributions of two Nb/AlO x /Nb junctions of different sizes fabricated on the same chip, we extract the transition rate, which turns out to follow the predicted Arrhenius law in the thermal regime but is greatly enhanced when macroscopic quantum tunneling becomes the dominant escape mechanism. Our results show the validity of applying the model to obtain the transition rate out of the phase diffusion state into the running state from measured switching current distribution of underdamped Josephson junctions. The temperature and bias-current dependent data provide strong evidence for phase diffusion in both thermal and quantum regimes.
When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined feature in the escape rate. This feature provides a simple method of determining the junction's energy relaxation time T1{T}_{1}T1​, a key parameter for evaluating its utility for quantum computation. We discuss the temperature regime where this effect is readily observable and describe how the emptying depends directly on the relaxation time. Our model of the junction dynamics agrees well with the measured escape rate of a $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{AlOx}\text{\ensuremath{-}}\mathrm{Nb}$ device in the 25 to 300mK300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}300mK temperature range, yielding ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.
We report on measurements of the switching current probability both in the thermal and quantum regime on moderately damped NbN/MgO/NbN Josephson junctions with very low critical current density (’ 2A/cm2). We observed three distinct regimes: below 90 mK the width of the switching distributions is constant within the experimental error, while from 90 mK to 1.6 K the width increases with temperature, this change of behavior signaling the standard transition from macroscopic quantum tunneling (MQT) to thermal activation (TA) regime respectively. Above 1.6 K we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called Phase Diffusion (PD) are evident, such as the change of the switching distributions symmetry. Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The parameters which completely characterize the dynamics of such moderately damped Josephson junctions have been also extracted.
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
Macroscopic quantum effects in Josephson systems have recently attracted interest in the scientific community both for the physics involved and in view of applications. Here we present experiments on the presence of energy level quantization at temperatures above the classical-quantum regime crossover temperature in different Josephson junctions. This has been possible by extending the measurements of the escape rate out of the zero-voltage state at higher sweeping bias rate (dI/dt up to 100 A/sec) in order to induce nonstationary conditions in the energy potential describing the junction dynamics. Our measurements allow us to obtain as fitting parameter the "effective" resistance to be used in the RSJ model which is compatible with the subgap resistance at very low voltage. The very low dissipation level obtained at low temperatures renders our results quite interesting in view of applications in the quantum limit.