Optimal Control of Superconducting N-level quantum systems

Understand

We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux.

• The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic potential, subject to external time-dependent control fields, {\it i.e.} a driven multilevel quantum system.
• The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory.
• Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase.