Photon emission from atoms and free electrons underlie a wealth of
fundamental science and technological innovations. We present a regime where
atom-photon and electron-photon interactions interfere with each other,
resulting in substantial changes in the spontaneous emission rate compared to
the sum of each interaction considered in isolation. We highlight the critical
role played by quantum electron wavepackets, and how the emission can be
tailored via the electron waveshape, as well as the atomic population and
coherence. Our findings reveal that atom-photon and electron-photon
interactions cannot be considered in isolation even when higher-order
contributions involving all three bodies (atom, photon and free electron) are
negligible. Our findings pave the way to more precise control over photon
emission processes and related diagnostics.Comment: 9 pages, 4 figure