  We proposed a scheme to demonstrate macroscopic quantum jumps in a
superconducting phase qubit coupled to a microscopic two-level system in the
Josephson tunnel junction. Irradiated with suitable microwaves, the Rabi
oscillations of the qubit exhibit signatures of quantum jumps: a random
telegraph signal with long intervals of intense macroscopic quantum tunneling
events (bright periods) interrupted by the complete absence of tunneling events
(dark periods). An analytical model was developed to describe the width of the
dark periods quantitatively. The numerical simulations indicate that our
analytical model captured underlying physics of the system. Besides calibrating
the quality of the microscopic two-level system, our results have significance
in quantum information process since dark periods in Rabi oscillations are also
responsible for errors in quantum computing with superconducting qubits.
