Transitionless quantum drivings for the harmonic oscillator

J G Muga (1) , X Chen (1, 2) , S Ibáñez (1) , I Lizuain (1) , A Ruschhaupt (3)

1 Departamento de Qumica-Fsica, UPV-EHU
2 Department of Physics
3 ITP - Institut für Theoretische Physik [Hannover]

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

Mots clés: 37.10.De; 42.50.-p; 37.10.Vz

J G Muga, X Chen, S Ibáñez, I Lizuain, A Ruschhaupt. Transitionless quantum drivings for the harmonic oscillator. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010, 43 (8), pp.85509. ⟨10.1088/0953-4075/43/8/085509⟩. ⟨hal-00569912⟩