Non-Markovian speedup dynamics of a photon induced by gravitational redshift

Gravitational redshift can cause the distortion of photon wave packets; thus, the non-Markovian speedup evolution of a photon system must be controlled by considering gravitational redshift. We analyze the non-Markovian speedup dynamics of a photon system in the amplitude-damping channel or pure-dephasing channel under the effect of gravitational redshift, which is modelled as a beam-splitter operation. We show that the gravitational redshift weakens the non-Markovian dynamical behavior in both channels. For the amplitude-damping channel, the gravitational redshift promotes further speedup evolution of a photon system when the initial coherence of the system is nonzero. A stronger gravitational redshift and larger initial coherence make improving the evolution speed of the photon system easier. For the pure-dephasing channel, the non-Markovian dynamical behavior decreases owing to the gravitational redshift; however, the evolution speed of the photon is not influenced by the gravitational redshift.