Quantum coherence of continuous variables in the black hole quantum atmosphere

Abstract: Recently, the concept of quantum atmosphere has been introduced as a potential origin of Hawking quanta. This study investigates the properties of quantum fields by exploring the quantum coherence of a two-mode Gaussian state near a black hole, where Hawking quanta originate from the quantum atmosphere region. It is demonstrated that both physically accessible and inaccessible quantum coherence for continuous variable quantum states distinctly exhibit hallmark features of the quantum atmosphere. Specifically, the quantum coherence for these states varies continuously with changes in the normalized distance; it undergoes rapid decreases (or increases) just outside the event horizon before gradually stabilizing through subsequent increases (or decreases). This behavior contrasts with the behaviors of quantum coherence where originates solely from the black hole's event horizon. The quantum features of the fields distinctly reflect characteristics attributable to the quantum atmosphere, thereby deepening our understanding of the origins of Hawking radiation. We also find that the continuous variable coherence is highly dependent on both the squeezing parameter and field frequency of the prepared state; therefore, appropriately adjusting these values can enhance our ability to detect features within the quantum atmosphere. It is noteworthy to observe that quantum features of fields do not entirely dissipate in the quantum atmosphere region, indicating that tasks related to quantum information processing can still be executed there.