Double quantum dot as a spin rotator

It is shown that the low-energy spin states of double quantum dots (DQD) with even electron occupation number $N$ possess the symmetry SO(4) similar to that of a rigid rotator familiar in quantum mechanics (rotational spectra of H$_2$ molecule, electron in Coulomb field, etc). The "hidden symmetry" of the rotator manifests itself in the tunneling properties of the DQD. In particular, the Kondo resonance may arise under asymmetric gate voltage in spite of the even electron occupation of the DQD. Various symmetry properties of spin rotator in the context of the Kondo effect are discussed and experimental realization of this unusual scenario is proposed.