Macroscopic Quantum Coherence in an Rf-SQUID

We present experimental evidence for a coherent superposition of macroscopically distinct flux states in an rf-SQUID. When the external flux Φ x applied to the SQUID is near 1/2 of a flux quantum Φ o, the SQUID has two nearly degenerate configurations: the zero- and one-fluxoid states, corresponding to a few microamperes of current flowing clockwise or counterclockwise, respectively. The system is modeled as a particle in a double-well potential where each well represents a distinct fluxoid state (0 or 1) and the barrier between the wells can be controlled in situ. For low damping and a sufficiently high barrier, the system has a set of quantized energy levels localized in each well. The relative energies of these levels can be varied with Φ x. External microwaves are used to pump the system from the well-localized ground state of one well into one of a pair of excited states nearer the top of the barrier. We spectroscopically map out the energy of these levels in the neighborhood of their degeneracy point by varying Φ x as well as the barrier height. We find a splitting between the two states at this point, when both states are below the classical energy barrier, indicating that the system attains a coherent superposition of flux basis states that are macroscopically distinct in that their mean fluxes differ by more than 1/4 Φ o and their currents differ by several microamperes.