Abstract In a recent analysis (Misra et al. in npj Quantum Inf 10:34, 2024. 10.1038/s41534-024-00817-w), it has been shown that Hawking radiation is the main source of energy to empower a coherent signal pulse. In this work, we have explored the same effect for a case where the time derivative of the scalar field mode of the redirected Hawking radiation appears explicitly in the interaction Hamiltonian. We have considered a stream of two-level atoms falling freely towards the event horizon of a black hole. The Hawking radiation redirected from an orbiting mirror interacts with the atoms which make a transition between the ground state and the excited state through the emission of a signal photon. The signal pulse is amplified by the mechanical work done by the redirected Hawking mode. The whole set up works as a black hole powered quantum heat engine. We have shown that this amplification depends on the frequency of both the signal mode and the Hawking mode, the flux of the redirected Hawking mode and the lapse function of the black hole. In contrast to the result obtained in Misra et al. (npj Quantum Inf 10:34, 2024. 10.1038/s41534-024-00817-w), we observe in our analysis, that due to the coupling of the momentum degrees of freedom of the Hawking radiation modes with the freely falling detector, the power output depends inversely with the lapse function of the black hole and is proportional to the frequency of the emitted Hawking radiation. As a result the maximum output power enhances significantly if the atom is very close to the event horizon of the black hole. We have analyzed this effect for two types of detectors attached to the cavity. At first we considered a point-like detector and then we have done the analysis from the perspective of a detector with smearing.
Jana et al. (Wed,) studied this question.