Resonant and antiresonant exciton-phonon coupling in quantum dot molecules <jats:p> Spins confined in optically active quantum dot molecules (QDMs) can be used for the deterministic generation of photonic graph states with tailored entanglement structures. Their usefulness for the generation of such nonclassical states of light is determined by orbital and spin decoherence mechanisms, particularly phonon-mediated processes dominant at energy scales up to a few millielectronvolts. Here, we directly measure the spectral function of orbital phonon relaxation between the energy states of the neutral exciton in a QDM and benchmark our findings against microscopic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="bold-italic">k</a:mi> <a:mo>·</a:mo> <a:mi mathvariant="bold-italic">p</a:mi> <a:mspace width="4pt"/> </a:mrow> </a:math> theory. Our results reveal pronounced resonances and antiresonances in the phonon-relaxation rates, ranging from tens of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>µ</e:mi> <e:msup> <e:mrow> <e:mi mathvariant="normal">s</e:mi> </e:mrow> <e:mrow> <e:mo>−</e:mo> <e:mn>1</e:mn> </e:mrow> </e:msup> </e:mrow> </e:math> up to tens of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mrow> <g:mi>ns</g:mi> </g:mrow> <g:mrow> <g:mo>−</g:mo> <g:mn>1</g:mn> </g:mrow> </g:msup> </g:math> . Comparison with a kinetic model reveals the voltage (energy) dependent phonon coupling strength and fully explains the interplay between phonon-assisted relaxation and radiative recombination. The resonances and antiresonances enable further tunability of the exciton lifetime which can be leveraged to increase the lifetime of energetically unfavorable charge configurations needed for realizing efficient spin-photon interfaces and multidimensional cluster states. </jats:p> 112 23 American Physical Society (APS)