Landau-Zener interferometry in a Cooper pair box

Quantum-mechanical systems having two crossing energy levels are ubiquitous in nature. The rate $v = d (E_1 - E_0)/dt$ at which such levels in a driven system approach each other determines the probability $P_{LZ}$ of a Landau-Zener (LZ) tunneling between them. The traditional treatment of the LZ process, however, ignores quantum-mechanical interference. Here we report an observation of phase-sensitive interference between consecutive LZ tunneling attempts in an artificial two-state system, a superconducting charge qubit. We interpret the experiment in terms of a multi-pass analog to the optical Mach- Zehnder interferometer: The beam splitting occurs by LZ tunneling at the charge degeneracy, while the arms of the Mach- Zehnder interferometer in energy space are represented by the ground and excited state. In accord with theory, we observe constructive interference when the Stokes phase $\phi_S$ picked up during the LZ interaction, and the dynamical phase of one drive period $\phi = \int (E_1 - E_0) dt$ satisfy the condition: $(\phi - 2 \phi_S) = m \cdot 2\pi$. Our LZ interferometer can be used as a high-resolution detector for phase and charge owing to interferometric sensitivity- enhancement.