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Physical Review Letters

Observation of Resonant Tunneling between Macroscopically Distinct Quantum Levels

R. Rouse, Siyuan Han, James E. Lukens

Published Aug 21, 1995• 206 citations
Publisher

Abstract

We report the first observation of resonant tunneling of a system between two macroscopically distinct states: energy levels in different fluxoid wells of a weakly damped superconducting quantum interference device which differ in mean current by approximately 6 \ensuremath{\mu}A. Near 50 mK, the tunneling rate $\ensuremath{\gamma}({\ensuremath{\Phi}}_{x})$ from the metastable well vs applied flux ${\ensuremath{\Phi}}_{x}$ is found to exhibit a series of local maxima where the levels (spaced by $\ensuremath{\approx}1.9$ K) in the two wells cross. The positions of these maxima agree well with the level crossings calculated using independently determined system parameters.

DOI
10.1103/physrevlett.75.1614

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We report the first observation of resonant tunneling of a system between two macroscopically distinct states: energy levels in different fluxoid wells of a weakly damped superconducting quantum interference device which differ in mean current by approximately 6 \ensuremath{\mu}A. Near 50 mK, the tunneling rate \ensuremathγ(\ensuremathΦx)\ensuremath{\gamma}({\ensuremath{\Phi}}_{x})\ensuremathγ(\ensuremathΦx​) from the metastable well vs applied flux \ensuremathΦx{\ensuremath{\Phi}}_{x}\ensuremathΦx​ is found to exhibit a series of local maxima where the levels (spaced by \ensuremath≈1.9\ensuremath{\approx}1.9\ensuremath≈1.9 K) in the two wells cross. The positions of these maxima agree well with the level crossings calculated using independently determined system parameters.
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.
Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/e2{e}^{2}e2. .AE
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.
dc measurements are made in a superconducting, persistent current qubit structure with a time-ordered meter. The persistent-current qubit has a double-well potential, with the two minima corresponding to magnetization states of opposite sign. Macroscopic resonant tunneling between the two wells is observed at values of energy bias that correspond to the positions of the calculated quantum levels. The magnetometer, a superconducting quantum interference device, detects the state of the qubit in a time-ordered fashion, measuring one state before the other. This results in a different meter output depending on the initial state, providing different signatures of the energy levels for each tunneling direction.
The dynamics of a dissipative, quantized macroscopic two-state system have been experimentally investigated through the measurement of tunneling transitions between the adjacent, equal-energy fluxoid states of a superconducting loop containing Josephson junctions. The tunneling rate \ensuremath{\Gamma} has been observed to approach zero as a power law in the temperature, giving a damping parameter \ensuremath{\alpha}=1.44, in the incoherent relaxation regime. The predicted exponential dependence of \ensuremath{\Gamma} on barrier height has been quantitatively confirmed.