  Graphene is an atomically thin two-dimensional material demonstrating strong
optical nonlinearities including harmonics generation, four wave mixing, Kerr
and other nonlinear effects. In this paper we theoretically analyze the optical
heterodyne detection (OHD) technique of measuring the optical Kerr effect (OKE)
in two-dimensional crystals and show how to relate the quantities measured in
such experiments with components of the third-order conductivity tensor
$\sigma^{(3)}_{\alpha\beta\gamma\delta}(\omega_1,\omega_2,\omega_3)$ of the
two-dimensional crystal. Using results of a recently developed quantum theory
of the third-order nonlinear electrodynamic response of graphene we analyze the
frequency, charge carrier density, temperature and other dependencies of the
OHD-OKE response of this material. We compare our results with a recent OHD-OKE
experiment in graphene and find good agreement between the theory and
experiment.
