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In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.

We report the first observation of resonant tunneling of a system between two macroscopically distinct states: energy levels in different Auxoid wells of a weakly damped superconducting quantum interference device which differ in mean current by approximately 6 p, A. Near 50 mK, the tunneling rate I (4,) from the metastable well vs applied Ilux &9, is found to exhibit a series of local maxima where the levels (spaced by =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. PACS numbers: 74.50.+r, 73.40.Gk Throughout the history of quantum mechanics, there have been a series of paradoxes resulting from attempts to reconcile the description of nature at the microscopic level with everyday observations of macroscopic objects. While many explanations have been proposed, the dilemma remains in the minds of many [1,2]. It is of some interest then to try to observe quantum effects, familiar in the microscopic world, in variables describing macroscopically distinct states. Josephson junctions, along with the superconducting quantum interference device (SQUID), have proven to be excellent systems for such investigations. The IIux 4 linking the SQUID (or the phase difference across a current biased junction) describes the collective motion of a macroscopic number of particles and yet manifests quantum behavior at accessible temperatures. Further, it is possible to characterize these systems very well, permitting quantitative comparison with theory. Tunneling of these macroscopic variables to the continuum (MQT) [3 -7] has been widely studied and generally found to be in excellent agreement with theory. Level quantization within a well has been observed [8], again agreeing with theory [9,10]. However, answers to more fundamental questions (including macroscopic quantum coherence [1]) require measurements of the behavior of systems involving transitions between macroscopically distinct, discrete final and initial states. Extensive theoretical analysis of such transitions has been done using the two state approximation to the SQUID [11,12].These predict that, under conditions of low damping and temperature, 4 should display the quantum interference behavior familiar for microscopic systems. The limited experimental work on such systems has tended to confirm these predictions in the higher damping regime where evidence for discrete final states is indirect [13]. Recently reported results on magnetic systems have been interpreted in terms of macroscopic quantum behavior [14]. However, there is currently substantial controversy as to the interpretation of the results that, it is argued, differ markedly from theory [15]. In this Letter, we report the observation of resonances in the tunneling rate of the fiux between two macroscopically distinct Iluxoid wells of a SQUID when the ground state of the upper well is aligned with an excited state in the lower well. We refer to this phenomenon, in which the quantized final and in...

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We have measured and propose a model for switching rates in hysteretic DC-SQUID in the regime where phase diffusion processes start to occur. We show that the switching rates in this regime are smaller than the rates given by Kramers' formula due to retrapping of Josephson phase. The retrapping process, which is affected by the frequency dependent impedance of the environment of the DC-SQUID, leads to a peaked second moment of the switching distribution as a function of temperature. The temperature where the peaks occur are proportional to the critical current of the DC-SQUID.

low-frequency limit. For frequencies in the neighborhood of the Debye frequency, however, the elastic constants are nearly temperature independent. The elastic constants measured ultrasonically cannot therefore be used to calculate an effective Debye temperature as has traditionally been done. (3) For the same reason the lattice softening will not affect the superconducting transition. 13 (4) The apparent arrest of the structural transition and the anomalies in the elastic constants near the superconducting transition temperature may be explained as characteristic of the structural transition alone which suggests that the superconducting transition may have less influence on the structural transition than has been assumed. (5) The very different behavior of Nb 3 Sn and V 3 Si observed in the distorted structure is found to be due to different relative positions of the band edges and the Fermi level for the two materials. . n For V 3 Si a weak temperature dependence of Cn 0 -c 12° due to anharmonic interactions needs to be included in order that co q 2 remains >0 for T = 0. In this case c n° -c i2° cannot be eliminated in favor of w(0,T m ) as is done to obtain Eq. (19).

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