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arXiv:cond-mat/0005081 · Physical review. B, Condensed matter

Macroscopic resonant tunneling of magnetic flux

D. V. Averin, Jonathan R. Friedman, James E. Lukens

Published Nov 1, 2000• 35 citations
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Abstract

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.

DOI
10.1103/physrevb.62.11802

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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 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.
The question of whether macroscopic variables obey the laws of quantum mechanics has been debated ever since the earliest days of quantum mechanics.Since early 1980s results from a series of experiments in Josephson junctions and superconducting interference devices(SQUIDs),including macroscopic quantum tunneling,energy level quantization,macroscopic resonant tunneling(MRT),and ac driven coherent dynamics of the phase and flux,strongly support the notion that under proper conditions motions of macroscopic variables are indeed governed by the laws of quantum mechanics.Among many macroscopic quantum phenomena,MRT,which combines two of the most distinctive quantum phenomena-tunneling and energy level-quantization together and does not involve excitation by high frequency fields,is perhaps the strongest evidence demonstrating quantum nature of macroscopic variables.In this article,we review recent development in theory and experiment of MRT.In particular,we show that how dissipation and flux noise affect the rate and line shape of MRT in the double-well of rf SQUID flux qubits and applications of MRT in the ongoing efforts of identifying and understanding mechanisms of decoherence in superconducting qubits for scalable quantum computing.
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 develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with a significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.
We report on measurements of flux and charge noise in an rf-SQUID (superconducting quantum interference device) flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.