  We drastically improve the mode overlap between independently seeded,
gain-switched laser diodes operating at gigahertz repetition rates by
implementing a pulsed light seeding technique. Injecting pulsed light reduces
the emission time jitter and enables frequency chirp synchronization while
maintaining random optical phases of the emitted laser pulses. We measure
interference of these pulsed sources both in the macroscopic regime, where we
demonstrate near perfect mode overlap, and in the single photon regime, where
we achieve a Hong-Ou-Mandel dip visibility of 0.499+/-0.004, thus saturating
the theoretical limit of 0.5. The measurement results are reproduced by
Monte-Carlo simulations with no free parameters. Our light source is an ideal
solution for generation of high rate, indistinguishable coherent pulses for
quantum information applications.
