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arXiv:cond-mat/0403245 · Physical Review Letters

Microwave-Induced Thermal Escape in Josephson Junctions

Niels Grønbech‐Jensen, Maria Gabriella Castellano, F. Chiarello, Matteo Cirillo, C. Cosmelli, Lyudmila V. Filippenko, Roberto Russo, G. Torrioli

Published Aug 30, 2004• 55 citations
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Abstract

We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multivalued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.

DOI
10.1103/physrevlett.93.107002

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We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multivalued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.
We perform both theoretical and experimental investigations on the phase escape of a current-biased Josephson tunnel junction under microwave irradiation. The switching current distributions exhibit abundant nonlinear behaviors depending on the power and frequency of the applied microwave. We present a model to describe the behavior of the primary peak in the switching current distribution, which is confirmed by our experimental results. The obtained features can be used to characterize the damping parameter of Josephson junctions.
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.
The escape of a current-biased Josephson tunnel junction from the zero-voltage state in the presence of weak microwave radiation is investigated experimentally at low temperatures. The measurements of the junction switching current distribution indicate the macroscopic quantum tunneling of the phase below a crossover temperature of T small star, filled approximately 280 mK. At temperatures below T small star, filled we observe both single-photon and multiphoton transitions between the junction energy levels by applying microwave radiation in the frequency range between 10 and 38 GHz to the junction. These observations reflect the anharmonicity of the junction potential containing only a small number of levels.
The escape rate of an underdamped ($Q\ensuremath{\approx}30$), current-biased Josephson junction from the zero-voltage state has been measured. The relevant parameters of the junction were determined in situ in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves. At low temperatures, the escape rate became independent of temperature with a value that, with no adjustable parameters, was in excellent agreement with the zero-temperature prediction for macroscopic quantum tunneling.
A quantum-mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e., when the frequency $\ensuremath{\omega}$ of the ac bias matches the Josephson-junction energy-level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current Is{I}_{s}Is​ on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution P(Is).{P(I}_{s}).P(Is​). The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.
The microwave-driven dynamics of the superconducting phase difference across a Josephson junction is now widely employed in superconducting qubits and quantum circuits. With their typical energy level separation frequency being several GHz, cooling these quantum devices to the ground state requires temperatures below 100 mK. Pushing the operation frequency of superconducting qubits up may allow for operation of superconducting qubits at 1 K and even higher temperatures. Here, we present measurements of the switching currents of niobium/aluminum–aluminum oxide/niobium Josephson junctions in the presence of millimeter-wave radiation at frequencies above 100 GHz. The observed switching current distributions display clear double-peak structures, which result from the resonant escape of the Josephson phase from a stationary state. We show that the data can be well explained by the strong-driving model including the irradiation-induced suppression of the potential barrier. While still being measured in the quasi-classical regime, our results point toward a feasibility of operating phase qubits around 100 GHz.