  We describe the process of parametric amplification in a directional coupler
of quadratically nonlinear and lossy waveguides, which belong to a class of
optical systems with spatial parity-time (PT) symmetry in the linear regime. We
identify a distinct spectral parity-time anti-symmetry associated with optical
parametric interactions, and show that pump-controlled symmetry breaking can
facilitate spectrally selective mode amplification in analogy with PT lasers.
We also establish a connection between breaking of spectral and spatial mode
symmetries, revealing the potential to implement unconventional regimes of
spatial light switching through ultrafast control of PT breaking by pump
pulses.
