By no-signaling principle, we showed that parity-time (PT)-symmetric quantum theory as an extension of the quantum theory to non-Hermitian Hamiltonians is either a trivial extension or likely false as a fundamental theory [1]. In addition to the implementation PT-symmetric optical systems by carefully and actively controlling the gain and loss, we show that a 2 2 PT-symmetric Hamiltonian has a unitarily equivalent representation without complex optical potentials in the resulting optical coupler. Through the Naimark dilation in operator algebra, passive PT-symmetric couplers can thus be implemented with a refractive index of real values and asymmetric coupling coefficients [2]. Moreover, with a phase-space representation on the vicinity of an exceptional point, we show that a PT-symmetric phase transition from an unbroken PT-symmetry phase to a broken one is a second-order phase transition [3].

 

References:

[1] Yi-Chan Lee, Min-Hsiu Hsieh, Steven T. Flammia, and Ray-Kuang Lee, Phys. Rev. Lett. 112, 130404 (2014).\\

[2] Yi-Chan Lee, Jibing Liu, You-Lin Chuang, Min-Hsiu Hsieh, and Ray-Kuang Lee, Phys. Rev. A 92, 053815 (2015).\\

[3] Ludmila Praxmeyer, Popo Yang, and Ray-Kuang Lee, Phys. Rev. A 93, 042122 (2016).