By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode ({it s}-mode) which g
ives rise to the phase qubit, an anti-symmetric mode ({it a}-mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates $ket{n_{s}}$ and $ket{n_{a}}$ for the {it s} and {it a}-mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$. Finally, coherent frequency conversion is observed via free oscillations between the states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$.
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 present a novel shadow evaporation technique for the realization of junctions and capacitors. The design by E-beam lithography of strongly asymmetric undercuts on a bilayer resist enables in-situ fabrication of junctions and capacitors without the
use of the well-known suspended bridge[1]. The absence of bridges increases the mechanical robustness of the resist mask as well as the accessible range of the junction size, from 0.01 to more than 10000 micron square. We have fabricated Al/AlOx/Al Josephson junctions, phase qubit and capacitors using a 100kV E- beam writer. Although this high voltage enables a precise control of the undercut, implementation using a conventional 20kV E-beam is also discussed. The phase qubit coherence times, extracted from spectroscopy resonance width, Rabi and Ramsey oscillations decay and energy relaxation measurements, are longer than the ones obtained in our previous samples realized by standard techniques. These results demonstrate the high quality of the junction obtained by this controlled undercut technique.
