  Control over the joint spectral amplitude of a photon pair has proved highly
desirable for many quantum applications, since it contains the spectral quantum
correlations, and has crucial effects on the indistinguishability of photons,
as well as promising emerging applications involving complex quantum functions
and frequency encoding of qudits. Until today, this has been achieved by
engineering a single degree of freedom, either by custom poling nonlinear
crystal or by shaping the pump pulse. We present a combined approach where two
degrees of freedom, the phase-matching function, and the pump spectrum, are
controlled. This approach enables the two-dimensional control of the joint
spectral amplitude, generating a variety of spectrally encoded quantum states -
including frequency uncorrelated states, frequency-bin Bell states, and
biphoton qudit states. In addition, the joint spectral amplitude is controlled
by photon bunching and anti-bunching, reflecting the symmetry of the
phase-matching function.
