Quantum Otto engine with field-decoupled idle levels in a non-Hermitian XY model

We investigated a quantum Otto cycle in a non-Hermitian two-qubit XY model with a staggered imaginary magnetic field. The energy spectrum of this system naturally decomposes into a pair of working levels that depend on the external field and a pair of idle levels that are entirely independent of it. Accordingly, the model represents the first concrete microscopic realization of the idle-level quantum heat engine proposed by de Oliveira and Jonathan [Phys. Rev. E $\mathbf{\text{104}}$, 044133 (2021)] in a physical spin framework. According to our findings, tuning the non-Hermitian parameter ${\eta }_0$ drove a continuous transition from a dissipative regime, characterized by negative net work and net heat absorption from the hot reservoir, to genuine heat-engine operation while enhancing both output work and efficiency. Specifically, as ${\eta }_0$ increased within the stable phase with unbroken parity–time symmetry, the engine efficiency increased considerably and reached a substantial fraction of the Carnot limit. This joint performance enhancement originated from the compression of the idle-level gap, which redistributed the level-occupation weights in the hot and cold equilibrium states and thereby modulated the absorbed heat. Mathematically, the net-work expression had an ${\eta }_0$-independent numerator, but its denominators depended indirectly on ${\eta }_0$ through hyperbolic cosine functions, providing the basis for the idle-level control mechanism. We further thoroughly analyzed the robustness of these findings against parameter variations, critically compared non-Hermitian control with the Hermitian limit, and developed a concrete experimental proposal for trapped-ion quantum simulators. Together, our results demonstrate that non-Hermiticity serves as an indispensable tool for controlling both the operating mode and performance of a quantum engine.