Optimal control of superconducting N-level quantum systems

¹  LPMMC, CNRS - Université Joseph Fourier - BP 166, 38042 Grenoble-cedex 9, France, EU
²  Institut Néel, CNRS - Université Joseph Fourier - BP 166, 38042 Grenoble-cedex 9, France, EU

Received: 7 April 2009
Accepted: 17 July 2009

Abstract

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 1D anharmonic potential, subject to external time-dependent control fields, 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. The sensitivity of the optimal solution to parameter perturbations is also addressed.