Quantitative Study of Macroscopic Quantum Tunneling in a dc SQUID: A System with Two Degrees of Freedom

Abstract

To test whether the theory of macroscopic quantum tunneling (MQT) is applicable to systems with 2 degrees of freedom, we experimentally investigated the switching current distribution of a dc SQUID. Using sample parameters determined from measurements at T 4:2 K, we are able to make quantitative comparison to the theories from 8 mK to 4.2 K. The excellent agreement between the data and the MQT theory demonstrates that tunneling from the zero-voltage state of the dc SQUID is well described by the quantum mechanics. DOI: 10.1103/PhysRevLett.89.098301 PACS numbers: 85.25.Dq, 03.65.-w, 74.50.+r Whether quantum mechanics is valid for macroscopic variables is one of the most fascinating issues of fundamental physics [1]. The experimental studies, especially quantitative tests of the theory for macroscopic variables in the quantum regime, provide important insights to our understanding of the physical world. In the past few years, devices based on the Josephson effect, such as the Josephson junction (JJ) and the superconducting quantum interference device (SQUID), have been proven effective systems to perform this test. For instance, in a JJ, the phase difference across the junction is a macroscopic variable and the dynamics of the junction is identical to a particle's motion in a one-dimensional (1D) washboard potential. Experiments in 1D systems, such as current biased JJs and rf SQUIDs, have yielded results in very good agreement with the theoretical predictions of macroscopic quantum tunneling (MQT) [2][3][4][5][6]. In contrast, experiments in systems with 2 degrees of freedom (2DF) have produced significant divergences. For example, using a dc SQUID, which contains two JJs and, hence, has two macroscopic degrees of freedom, Sharifi, Gavilano, and Harlingen (SGH) reported the observation of anomalous suppression of thermal activation (TA) from the two-dimensional (2D) potential well of a dc SQUID [7]. SGH suggested that the apparent suppression of TA rate may rise from an enhanced potential barrier caused by interaction between the two macroscopic degrees of freedom in the dc SQUID. On the other hand, experiments by Han, Lapointe, and Lukens (HLL) [8] and Lefevre-Seguin, Turlot, Urbina, Esteve, and Devoret (LTUED) [9] showed that, in the thermal regime, the activation energy of the 2D SQUIDs agreed very well with the potential barrier. More importantly, SGH's result in the quantum regime significantly disagreed with the theoretical prediction as the measured width of switching current distribution-at temperature well below the quantum-classical crossover temperature T co ÿ exceeded the theoretical prediction by more than 40%.Notice that this disagreement could not be accounted for by measurement uncertainties and the barrier enhancement suggested by SGH would actually make the matter much worse. However, the HLL and LTUED's experiments did not address the quantum regime so that the experimental evidence available thus far [7] seems to indicate that, despite its great success in describing 1D systems, MQT theory...

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