2025/07/30 by Liu, Bing-Bing, Su, Shi-Lei
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2507.22728
For a truly PT-symmetric quantum system, the conventional non-Hermitian Hamiltonian is H = Ωσx -iγ|1⟩⟨1| + iγ|0⟩⟨0|, where Ω and γ are real parameters and σx denotes Pauli X operator. These three terms represent coherent coupling, loss (on state |1⟩), and gain (on state |0⟩), respectively. Although the works in [Phys. Rev. Lett. 101, 230404 (2008); Phys. Rev. Lett. 119, 190401 (2017); Science 364, 878 (2019)] proposed theoretically and/or demonstrate dilation methods for a truly parity-time(PT)-symmetric Hamiltonian by embedding into larger Hermitian space, directly realizing the gain term +iγ|0⟩⟨0| has still remained an outstanding challenge for quantum system. While systems omitting this gain term can exhibit a passively PT-symmetric energy spectrum (featuring a parallel imaginary shift) and display related phenomena, they fail to capture the full physical behavior and unique properties inherent to truly PT-symmetric systems. In this manuscript, we propose a method to achieve effective gain on the ground state |0⟩ (+iγ|0⟩⟨0|) after averaging all trajectories, by integrating the Sørensen-Reiter effective operator method with the Wiseman-Milburn master equation for continuous measurement and instantaneous feedback control after averaging the evolution over all trajectories. This approach provides a possible pathway to efficiently construct truly PT-symmetric quantum devices, offering a powerful platform for engineering quantum resources vital for quantum information technology applications.