The Susskind–Glogower operator, first proposed by Leonard Susskind and J. Glogower, refers to the operator where the phase is introduced as an approximate polar decomposition of the creation and annihilation operators.
It is defined as
and its adjoint
Their commutation relation is
where
They may be regarded as a (exponential of) phase operator because
where
They may be used to solve problems such as atom-field interactions, level-crossings or to define some class of non-linear coherent states, among others.