We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with $1:1:2$ resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the ${\mathrm{C}\mathrm{O}}_2$ molecule. We uncover quantum monodromy of ${\mathrm{C}\mathrm{O}}_2$ as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.

• Received 15 March 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.024302