[1] L. Landau, E. Lifshitz. Quantum Mechanics: Non Relativistic Theory, 3(1977).
[2] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243-5246(1998).
[3] Y. N. Joglekar, C. Thompson, D. D. Scott, G. Gautam. Optical waveguide arrays: quantum effects and PT symmetry breaking. Eur. Phys. J., 63, 30001(2013).
[4] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics, 11, 752-762(2017).
[5] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, D. N. Christodoulides. Non-Hermitian physics and PT symmetry. Nat. Phys., 14, 11-19(2018).
[6] M. Mueller, I. Rotter. Exceptional points in open quantum systems. J. Phys. A, 41, 244018(2008).
[7] W. D. Heiss. The physics of exceptional points. J. Phys. A, 45, 444016(2012).
[8] T. Kato. Perturbation Theory for Linear Operators, 132(2013).
[9] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).
[10] K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, C. T. Chan. Emergence, coalescence, and topological properties of multiple exceptional points and their experimental realization. Phys. Rev. X, 6, 021007(2016).
[11] M. Naghiloo, M. Abbasi, Y. N. Joglekar, K. Murch. Quantum state tomography across the exceptional point in a single dissipative qubit(2019).
[12] J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, L. Luo. Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms. Nat. Commun., 10, 855(2019).
[13] Z. Bian, L. Xiao, K. Wang, X. Zhan, F. A. Onanga, F. Ruzicka, W. Yi, Y. N. Joglekar, P. Xue. Time invariants across a fourth-order exceptional point in a parity-time-symmetric qudit(2019).
[14] J. Doppler, A. A. Mailybaev, J. Bohm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, S. Rotter. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016).
[15] H. Xu, D. Mason, L. Jiang, J. G. E. Harris. Topological energy transfer in an optomechanical system with exceptional points. Nature, 537, 80-83(2016).
[16] S. Assawaworrarit, X. Yu, S. Fan. Robust wireless power transfer using a nonlinear parity-time-symmetric circuit. Nature, 546, 387-390(2017).
[17] J. Wiersig. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett., 112, 203901(2014).
[18] J. Wiersig. Sensors operating at exceptional points: general theory. Phys. Rev. A, 93, 033809(2016).
[19] H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017).
[20] W. Chen, S. Kaya Ozdemir, G. Zhao, J. Wiersig, L. Yang. Exceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017).
[21] H. Zhao, Z. Chen, R. Zhao, L. Feng. Exceptional point engineered glass slide for microscopic thermal mapping. Nat. Commun., 9, 1764(2018).
[22] Q. Zhong, D. N. Christodoulides, M. Khajavikhan, K. G. Makris, R. El-Ganainy. Power-law scaling of extreme dynamics near higher-order exceptional points. Phys. Rev. A, 97, 020105(2018).
[23] S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, C. T. Chan. Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators. Nat. Commun., 10, 832(2019).
[24] H.-K. Lau, A. A. Clerk. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun., 9, 4320(2018).
[25] G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, C. Silberhorn. Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics. Phys. Rev. Lett., 116, 143601(2016).
[26] L. Banchi, W. S. Kolthammer, M. S. Kim. Multiphoton tomography with linear optics and photon counting. Phys. Rev. Lett., 121, 250402(2018).
[27] O. S. Magaña-Loaiza, R. de J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, T. Gerrits. Multiphoton quantum-state engineering using conditional measurements(2019).
[28] W. K. Lai, V. Buek, P. L. Knight. Nonclassical fields in a linear directional coupler. Phys. Rev. A, 43, 6323-6336(1991).
[29] K. Tschernig, R. de J. León-Montiel, O. S. Magaña-Loaiza, A. Szameit, K. Busch, A. Perez-Leija. Multiphoton discrete fractional Fourier dynamics in waveguide beam splitters. J. Opt. Soc. Am. B, 35, 1985-1989(2018).
[30] E. M. Graefe, U. Gnther, H. J. Korsch, A. E. Niederle. A non-Hermitian PT symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points. J. Phys. A, 41, 255206(2008).
[31] M. Christandl, N. Datta, A. Ekert, A. J. Landahl. Perfect state transfer in quantum spin networks. Phys. Rev. Lett., 92, 187902(2004).
[32] A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodriguez-Lara, A. Szameit, D. N. Christodoulides. Coherent quantum transport in photonic lattices. Phys. Rev. A, 87, 012309(2013).
[33] A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, D. N. Christodoulides. Perfect transfer of path-entangled photons in Jx photonic lattices. Phys. Rev. A, 87, 022303(2013).
[34] Y. N. Joglekar, A. Saxena. Robust PT-symmetric chain and properties of its Hermitian counterpart. Phys. Rev. A, 83, 050101(2011).
[35] Y. N. Joglekar, C. Thompson, G. Vemuri. Tunable waveguide lattices with nonuniform parity-symmetric tunneling. Phys. Rev. A, 83, 063817(2011).
[36] R. J. Chapman, M. Santandrea, Z. Huang, G. Corrielli, A. Crespi, M.-H. Yung, R. Osellame, A. Peruzzo. Experimental perfect state transfer of an entangled photonic qubit. Nat. Commun., 7, 11339(2016).
[37] R. de J. León-Montiel, M. A. Quiroz-Juárez, J. L. Domínguez-Juárez, R. Quintero-Torres, J. L. Aragón, A. K. Harter, Y. N. Joglekar. Observation of slowly decaying eigenmodes without exceptional points in Floquet dissipative synthetic circuits. Commun. Phys., 1, 88(2018).
[38] N. A. Mortensen, P. A. D. Gonçalves, M. Khajavikhan, D. N. Christodoulides, C. Tserkezis, C. Wolff. Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems. Optica, 5, 1342-1346(2018).
[39] S. Longhi. Loschmidt echo and fidelity decay near an exceptional point(2019).
[40] J. Wei, E. Norman. Lie algebraic solution of linear differential equations. J. Math. Phys., 4, 575-581(1963).
[41] W. H. Louisell. Quantum Statistical Properties of Radiation, 7(1973).
[42] I. Afek, O. Ambar, Y. Silberberg. High-NOON states by mixing quantum and classical light. Science, 328, 879-881(2010).
[43] J. Zhang, M. Um, D. Lv, J.-N. Zhang, L.-M. Duan, K. Kim. NOON states of nine quantized vibrations in two radial modes of a trapped ion. Phys. Rev. Lett., 121, 160502(2018).
[44] M. Teimourpour, Q. Zhong, M. Khajavikhan, R. El-Ganainy. Higher order exceptional points in discrete photonics platforms. Parity-Time Symmetry and Its Applications, 261-275(2018).
[45] A. E. Lita, A. J. Miller, S. W. Nam. Counting near-infrared single-photons with 95% efficiency. Opt. Express, 16, 3032-3040(2008).
