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Physical Review Letters

Influence of Paramagnetic and Kondo Impurities on Macroscopic Quantum Tunneling in SQUID's

Philip C. E. Stamp

Published Dec 26, 1988• 14 citations
Publisher

Abstract

The possibility is investigated that impurity spins in SQUID tunnel junctions might have a strong dissipative effect on macroscopic flux tunneling. A microscopic theory is given which shows that for temperatures lower than the Kondo temperature ${T}_{K}$ of the spins, there is a strong effect if ${T}_{K}\ensuremath{\simeq}{\ensuremath{\omega}}_{J}$, the Josephson plasma frequency. The connection with quantum measurement theory is discussed.

DOI
10.1103/physrevlett.61.2905

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The possibility is investigated that impurity spins in SQUID tunnel junctions might have a strong dissipative effect on macroscopic flux tunneling. A microscopic theory is given which shows that for temperatures lower than the Kondo temperature TK{T}_{K}TK​ of the spins, there is a strong effect if TK\ensuremath≃\ensuremathωJ{T}_{K}\ensuremath{\simeq}{\ensuremath{\omega}}_{J}TK​\ensuremath≃\ensuremathωJ​, the Josephson plasma frequency. The connection with quantum measurement theory is discussed.
Within the well-established quantum picture of Josephson junctions, we study the possibility of resonant macroscopic quantum tunneling. Expressions for the lifetime of metastable states are obtained and the effects of temperature on the main features of the phenomenon are discussed. A "saturation temperature" for the process, below which any temperature effect is negligible, is identified. Quantitative considerations are also given on the actual experimental accessibility to these measurements.
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.
We theoretically investigate the macroscopic quantum dynamics of a $\ensuremath{\pi}$ junction with a superconductor (S) and a multiferroic material or a ferromagnetic insulator (FI). By deriving the effective action from a microscopic Hamiltonian, a $\ensuremath{\pi}$-junction qubit (a S-FI-S superconducting quantum interference device ring) is proposed. In this qubit, a quantum two-level system is spontaneously generated and the effect of the quasiparticle dissipation is found to be very weak. These features make it possible to realize a quiet qubit with high coherency. We also investigate macroscopic quantum tunneling (MQT) in current-biased S-FI-S $\ensuremath{\pi}$ junctions and show that the influence of the quasiparticle dissipation on MQT is negligibly small.
Macroscopic quantum effects in Josephson systems have attracted great interest in the scientific community both for the physics involved and in view of applications. We present data on macroscopic quantum tunneling on Josephson junctions. Actually the most fascinating topic is the observation of macroscopic quantum coherence in rf-SQUID. This effect also has implications for quantum computing, because a quantum two-state system represents a single quantum bit, which is the elementary unit of a quantum computer. In this context, here we present a new method to measure quantum coherence between different fluxoid states of an rf-SQUID by using the procedure of "adiabatic inversion". This method offers the possibility of measuring tunneling and decoherence times in the system.
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 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.