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Sinica-NCTS Geometry and Quantum Physics Seminar
11:00 - 12:30, March 20, 2018 (Tuesday)
Room 617, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 617室)
Reflecting on an Alternative (parity-time-symmetric) Quantum Theory, and its Analog in Optics
Ray-Kuang Lee (National Tsing Hua University)


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].
[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).


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