Wave packet control in the Fourier time basis

K. T. Hecht

Antonio S. de Castro

Ashok Muthukrishnan C. R. Stroud

We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an alternative wave-packet basis for quantum information in the atom. A change of basis from energy levels to wave packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces to a series of conditional phase transforms between two entangled atoms in mixed energy and wave-packet bases. We show how to implement such transforms using wave-packet control of the internal states of the ions in the linear ion-trap scheme for quantum computing.

Ashok Muthukrishnan, Stroud, C. R.

We propose a wave packet basis for storing and processing several qubits of quantum information in a single multilevel atom. Using radially localized wave packet states in the Rydberg atom, we construct an orthogonal basis that is related to the usual energy level basis by a quantum Fourier transform. A transform-limited laser pulse that is short compared with the classical Kepler period of the system interacts mainly with the wave packet state localized near the atomic core, allowing selective control in this basis. We argue that wave packet control in this regime is useful for multilevel quantum information processing.

Rajendran Saravanan, Aniruddha Chakraborty