A quantum parametric oscillator in a radiofrequency trap

Abstract

Abstract. An ion confined within a Paul trap can be assimilated, in a good approximation, with a harmonic oscillator. A method which enables constructing of an invariant operator, based on the Lewis and Riesenfeld approach, is reported. The method is then applied to the case of an ion confined in a Paul trap, treated as a quantum harmonic oscillator. An invariant operator is associated to the system. The spectrum of the quasienergy operator finally results. The eigenvectors of the system are found using the Fock state basis. PACS numbers: 03.65, 05.45 Quantum parametric oscillator in a radiofrequency ion trap 2