Gain on ground state of quantum system for truly $\mathcal{PT}$ symmetry
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918134751952896 |
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| author | Liu, Bing-Bing Su, Shi-Lei |
| author_facet | Liu, Bing-Bing Su, Shi-Lei |
| contents | For a truly $\mathcal{PT}$-symmetric quantum system, the conventional non-Hermitian Hamiltonian is $H = Ωσ_x -iγ|1\rangle\langle1| + iγ|0\rangle\langle0|$, where $Ω$ and $γ$ are real parameters and $σ_x$ denotes Pauli X operator. These three terms represent coherent coupling, loss (on state $|1\rangle$), and gain (on state $|0\rangle$), respectively. Although the works in [Phys. Rev. Lett. \textbf{101}, 230404 (2008); Phys. Rev. Lett. \textbf{119}, 190401 (2017); Science \textbf{364}, 878 (2019)] proposed theoretically and/or demonstrate dilation methods for a truly parity-time($\mathcal{PT}$)-symmetric Hamiltonian by embedding into larger Hermitian space, directly realizing the gain term $+iγ|0\rangle\langle0|$ has still remained an outstanding challenge for quantum system. While systems omitting this gain term can exhibit a passively $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric systems. In this manuscript, we propose a method to achieve effective gain on the ground state $|0\rangle$ ($+iγ|0\rangle\langle0|$) 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 $\mathcal{PT}$-symmetric quantum devices, offering a powerful platform for engineering quantum resources vital for quantum information technology applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gain on ground state of quantum system for truly $\mathcal{PT}$ symmetry Liu, Bing-Bing Su, Shi-Lei Quantum Physics For a truly $\mathcal{PT}$-symmetric quantum system, the conventional non-Hermitian Hamiltonian is $H = Ωσ_x -iγ|1\rangle\langle1| + iγ|0\rangle\langle0|$, where $Ω$ and $γ$ are real parameters and $σ_x$ denotes Pauli X operator. These three terms represent coherent coupling, loss (on state $|1\rangle$), and gain (on state $|0\rangle$), respectively. Although the works in [Phys. Rev. Lett. \textbf{101}, 230404 (2008); Phys. Rev. Lett. \textbf{119}, 190401 (2017); Science \textbf{364}, 878 (2019)] proposed theoretically and/or demonstrate dilation methods for a truly parity-time($\mathcal{PT}$)-symmetric Hamiltonian by embedding into larger Hermitian space, directly realizing the gain term $+iγ|0\rangle\langle0|$ has still remained an outstanding challenge for quantum system. While systems omitting this gain term can exhibit a passively $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric systems. In this manuscript, we propose a method to achieve effective gain on the ground state $|0\rangle$ ($+iγ|0\rangle\langle0|$) 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 $\mathcal{PT}$-symmetric quantum devices, offering a powerful platform for engineering quantum resources vital for quantum information technology applications. |
| title | Gain on ground state of quantum system for truly $\mathcal{PT}$ symmetry |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.22728 |