Abstract. Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantummechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1=2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwavespectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
We present a simple model to describe multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions across the junction when the frequency $\ensuremath{\omega}$ satisfies $n\ensuremath{\hbar}\ensuremath{\omega}=\ensuremath{\Delta}{E}_{10}$, where $\ensuremath{\Delta}{E}_{10}$ is the splitting between the ground and first excited quasi-bound state of the junction. We calculate the matrix elements of the transitions as a function of the dc bias current
I, and the frequency $\ensuremath{\omega}$ and amplitude
Vac of the microwave voltage, for representative junction parameters. We also calculate the frequency-dependent absorption coefficient by solving the relevant Bloch equations when the ac voltage is sufficiently weak. In this regime, the absorption coefficient is a sum of Lorentzian lines centered at the
n-photon absorption frequency, of strength proportional to the squared matrix elements. For fixed
Vac, the transition rate for an
n-photon process usually decreases with increasing
n. We also find a characteristic even-odd effect: The absorption coefficient typically increases with
I for
n even but decreases for
n odd. Our results agree qualitatively with recent experiments.
The escape of a current-biased Josephson tunnel junction from the zero-voltage state in the presence of weak microwave radiation is investigated experimentally at low temperatures. The measurements of the junction switching current distribution indicate the macroscopic quantum tunneling of the phase below a crossover temperature of T small star, filled approximately 280 mK. At temperatures below T small star, filled we observe both single-photon and multiphoton transitions between the junction energy levels by applying microwave radiation in the frequency range between 10 and 38 GHz to the junction. These observations reflect the anharmonicity of the junction potential containing only a small number of levels.
Microwave spectroscopy experiments have been performed on two quantum levels of a macroscopic superconducting loop with three Josephson junctions. Level repulsion of the ground state and first excited state is found where two classical persistent-current states with opposite polarity are degenerate, indicating symmetric and antisymmetric quantum superpositions of macroscopic states. The two classical states have persistent currents of 0.5 microampere and correspond to the center-of-mass motion of millions of Cooper pairs.