  Quantum-mechanical systems having two discrete energy levels are ubiquitous
in nature. For crossing energy levels, depending on how fast they approach each
other, there is a possibility of a transition between them. This phenomenon is
known as Landau-Zener tunneling and it forms the physical basis of the Zener
diode, for example. The traditional treatment of the Landau-Zener tunneling,
however, ignores quantum-mechanical interference. Here we report an observation
of phase-sensitive interference between consecutive Landau-Zener tunneling
attempts in an artificial two-level system formed by a Cooper-pair-box qubit.
We interpret the experiment in terms of a multi-pass analog to the well-known
optical Mach-Zehnder interferometer. In our case, the beam splitting occurs by
Landau-Zener tunneling at the charge degeneracy, while the arms of the
Mach-Zehnder interferometer in energy space are represented by the ground and
excited state. Our Landau-Zener interferometer can be used as a high-resolution
detector for phase and charge owing to interferometric sensitivity-enhancement.
The findings also demonstrate new methods for qubit manipulations.
