Gain on ground state of quantum system for truly $\mathcal{P}\mathcal{T}$ symmetry

Bing-Bing Liu, Shi-Lei Su

For a truly $\mathcal{P}\mathcal{T}$-symmetric quantum system, the conventional non-Hermitian Hamiltonian is $H=\Omega {\sigma }_x-i\gamma |1⟩⟨1|+i\gamma |0⟩⟨0|$, where $\Omega$ and $\gamma$ are re…