We make a detailed theoretical description of the two-dimensional nature of a dc-SQUID, analyzing the coupling between its two orthogonal phase oscillation modes. While it has been shown that the mode defined as longitudinal can be initialized, manip
ulated and measured, so as to encode a quantum bit of information, the mode defined as transverse is usually repelled at high frequency and does not interfere in the dynamics. We show that, using typical parameters of existing devices, the transverse mode energy can be made of the order of the longitudinal one. In this regime, we can observe a strong coupling between these modes, described by an Hamiltonian providing a wide range of interesting effects, such as conditional quantum operations and entanglement. This coupling also creates an atomic-like structure for the combined two mode states, with a V-like scheme.
We have observed Rabi-like oscillations in a current-biased dc SQUID presenting enhanced coherence times compared to our previous realization cite{Claudon_PRL04}. This Josephson device behaves as an anharmonic oscillator which can be driven into a co
herent superposition of quantum states by resonant microwave flux pulses. Increasing the microwave amplitude, we study the evolution of the Rabi frequency from the 2-level regime to the regime of multilevel dynamics. When up to 3 levels are involved, the Rabi frequency is a clear signature of quantum behavior. At higher excitation amplitude, classical and quantum predictions for the Rabi frequency converge. This result is discussed in the light of a calculation of the Wigner function. In particular, our analysis shows that pronounced quantum interferences always appear in the course of the Rabi-like oscillations.
