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Physical review. B, Condensed matter

Resonant macroscopic quantum tunneling in SQUID systems

P. Silvestrini, B. Ruggiero, Yuri N. Ovchinnikov

Published Jul 1, 1996• 19 citations
Publisher

Abstract

A detailed theoretical analysis of the resonant macroscopic quantum tunneling in superconducting quantum interference device systems is presented. Our approach allows us to include the effect of both temperature and sweeping rate of the external flux, and to study the phenomenon both in quasistationary and nonstationary conditions, which can be induced by a fast sweep of the external bias. Moreover we compare our theory with the experimental data of Rouse, Han, and Lukens [Phys. Rev. Lett. 75, 1614 (1995)] referring to the quasistationary case, while other observable effects are predicted in the nonstationary case. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.1246

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A detailed theoretical analysis of the resonant macroscopic quantum tunneling in superconducting quantum interference device systems is presented. Our approach allows us to include the effect of both temperature and sweeping rate of the external flux, and to study the phenomenon both in quasistationary and nonstationary conditions, which can be induced by a fast sweep of the external bias. Moreover we compare our theory with the experimental data of Rouse, Han, and Lukens [Phys. Rev. Lett. 75, 1614 (1995)] referring to the quasistationary case, while other observable effects are predicted in the nonstationary case. \textcopyright{} 1996 The American Physical Society.
We consider the theoretical problem of resonant phenomena in the macroscopic quantum tunneling for an rf superconducting quantum interference device in the presence of an external irradiating field. The transition probability between different flux states is studied by varying the external parameters of the double-well potential describing the system in a way that the pumping level in the left potential well is close to one of the levels in the right potential well. The dependence of the transition probability on the external drive of the system shows two resonance peaks, the former connected with the resonant tunneling and the latter with the resonant pumping. The relative position of the peaks depends on the pumping frequency $\ensuremath{\omega}$ and on the system parameters.
We have developed a quantitative theory of resonant tunneling of magnetic flux between discrete macroscopically distinct quantum states in superconducting quantum interference device systems. The theory is based on the standard density-matrix approach. Its elements include the discussion of the two different relaxation mechanisms that exist for the double-well potential, and description of the ``photon-assisted'' tunneling driven by external rf radiation. It is shown that in the case of coherent flux dynamics, rf radiation should lead to splitting of the peaks of resonant flux tunneling, indicating that the resonant tunneling is a convenient tool for studying macroscopic quantum coherence of flux.
We experimentally demonstrate the observation of macroscopic resonant tunneling (MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device (rf-SQUID) under a single-cycle sinusoidal driving. The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells. The dynamics of the qubit depends significantly on the amplitude, frequency, and initial phase of the driving signal. We do the numerical simulations considering the intra-well and inter-well relaxation mechanism, which agree well with the experimental results. This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.
We report experiments on energy level quantization in Nb/AlOx/Nb Josephson junctions while measurements on SQUIDs are in progress. Data on the presence of energy level quantization are shown at temperatures above the classical-quantum regime crossover temperature. This has been possible by extending the measurements of the rate of the escape from the zero-voltage state at higher sweep bias rate in order to induce non-stationary conditions in the energy potential describing the junction dynamics. Data are compatible with extremely low "effective" dissipation in our system. Theoretical predictions on quantum effects related to the presence of non-stationary conditions in the potential associated to a rf SQUID are reported in view of new possible experiments.