  Integrability in quantum theory has been defined in more than one ways.
Recently, Braak suggested a new definition that a quantum system is integrable
if the number of parameters required to specify the eigenstates and the number
degrees of freedom (both discrete and continuous) are equal. It is argued that
the dependence of uncertainty product of suitable operators on the atom-field
interaction strength is distinctly different for the integrable and
nonintegrable cases. These studies indicate that uncertainty product is able to
identify nonintegrable atom-field systems in the context of the new definition.
