Non-Markovian dynamics of a qubit due to accelerated light in a lattice

We study the emission dynamics of a qubit weakly coupled to a one-dimensional coupled-cavity array with a synthetic frequency gradient that mimics a uniform force on photons. This engineered force induces Bloch oscillations, leading to distinct emission regimes. For strong gradients, the qubit exhibits reversible, chiral emission resembling a Jaynes-Cummings model, selectively exciting the array to one side depending on the qubit frequency. For weaker gradients, non-Markovian decay with revivals emerges, analogous to mirror-induced effects in conventional waveguides despite the absence of boundaries. In this regime, the qubit dynamics are captured by a delay differential equation akin to that of an atom in a multi-mode cavity, with Bloch oscillation parameters playing the role of cavity.