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Slide :: TOP The latter is of the form ${\left|0\right\rangle}_1\otimes\int{\,{\rm d}}\omega_1\,g_{\omega_1}\,g^*_{\omega_1}$, where $g_{\omega_1}$ is the one-photon wave function and $g^*_{\omega_1}$ its complex conjugate. Such states are available through parametric down conversion. The form of this state is the same as for the classical field (cf. ). The description in terms of a classical field is a special case where the three-photon amplitudes are identically zero (as $g_{\omega_1}$ and $g^*_{\omega_1}$). But this is different from the usual argument in quantum optics, where the possible existence of nonclassical states such as Fock states is usually restricted to one- and two-photon level, i.e., the Fock states ${\left|n\right\rangle}_{\omega_1}$.\
These photons are emitted into a solid angle $\Omega$ about the field propagation direction. Integrating the photon flux over the solid angle, we find that each one-photon wave vector is, with the conventions and where the transversal mode numbers are $u_1, u_2=1,2$ and $u_3=3$, subject to the condition $u_1+ u_2+ u_3=0$. As a consequence of unitarity, the one-photon amplitudes are unit vectors and thus the three-photon state that enters the coincidence rate [($eq:coincidence-rate$)]{} is