Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators Long Chang 1,2 , Xiaoshun Jiang 1,2 * , Shiyue Hua 1,2 , Chao Yang 1,2 , Jianming Wen 3 * , Liang Jiang 3 , Guanyu Li 1,2 , Guanzhong Wang 1,2 and Min Xiao 1,2,4 * Compound-photonic structures with gain and loss 1 provide a powerful platform for testing various theoretical proposals on non-Hermitian parity–time-symmetric quantum mechanics 2–5 and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Such structures can be designed as optical analogues of complex parity–time- symmetric potentials with real spectra. However, the beam dynamics can exhibit unique features distinct from conserva- tive systems due to non-trivial wave interference and phase-transition effects. Here, we experimentally realize parity– time-symmetric optics on a chip at the 1,550 nm wavelength in two directly coupled high-Q silica-microtoroid resonators with balanced effective gain and loss. With this composite system, we further implement switchable optical isolation with a non-reciprocal isolation ratio from 28 dB to 18 dB, by breaking time-reversal symmetry with gain-saturated nonli- nearity in a large parameter-tunable space. Of importance, our scheme opens a door towards synthesizing novel micro- scale photonic structures for potential applications in optical isolators, on-chip light control and optical communications. One of the most fundamental postulates in canonical quantum mechanics, formulated by Dirac and von Neumann, mandates that the Hermiticity of each operator be directly associated with a physical observable. As such, the spectrum of a self-adjoint operator is ensured to be real and the total probability (or unitary evolution) is conserved. In 1998, however, Bender and colleagues 2 discovered a wide class of complex non-Hermitian Hamiltonians that can possess entirely real spectra below a certain phase-transition point, provided they satisfy combined parity–time (PT) symmetry. This counterintuitive discovery immediately aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators 2–5 . For instance, a PT-symmetric Hamiltonian operator may contain a complex potential V(x) subject to a spatial-symmetry constraint V(x) ¼ V *(2x). One of the most striking properties of a PT-sym- metric operator stems from the appearance of a sharp, symmetry- breaking transition once a non-Hermitian operator crosses a certain critical threshold 2–5 . On crossing that ‘exceptional point’, the spectrum ceases to be real and starts to become complex. This transition signifies the appearance of a spontaneous PT symmetry breaking from the exact- to the broken-PT phase. Despite much fundamental theoretical success in the develop- ment of PT-symmetric quantum mechanics, an experimental obser- vation of pseudo-Hermiticity remains elusive and very challenging in real physical settings. Thanks to the formal equivalence between the quantum-mechanical Schro ¨dinger equation and the paraxial optical diffraction equation, complex PT-symmetric poten- tials can be easily achieved in optics by spatially modulating the refractive index with properly placed gain and loss in a balanced manner 1 . This analogy immediately spurred theoretical and exper- imental efforts in relation to PT symmetry using optics and other suitable physical systems. These include experimental set-ups with one optical component with absorption and another that is either optically pumped (active PT symmetry) 6,7 or lossless (passive PT symmetry) 8 . The PT phase transition has been studied in optical systems both theoretically 9,10 and experimentally 6–8 , and has been observed in non-Hermitian systems either with active PT symmetry composed of one amplifying and one attenuating LRC circuit 11 or in a dissipative microwave billiard 12 . Other suitable systems involving superconductors 13 , atomic gases 14,15 and plasmonics 16 have also been proposed theoretically. Further theoretical studies of PT sym- metry-based effects reveal many interesting optical phenomena, including unconventional beam refraction 17 , conical diffraction 18 , unidirectional invisibility induced by PT-symmetric periodic struc- tures 19–21 and coherent perfect laser absorbtion 22,23 (the latter two have been verified experimentally 7,24,25 ). Achieving rapid progress in integrated photonic circuits demands all-optical elements for high-speed processing of light signals. The optical isolator 26 is one such indispensable element. Similar to electronic diodes, it allows the flow of light to be uni- directional and reduces problems caused by unwanted reflections or interference effects. The successful design of an optical isolator relies on the breaking of time-reversal symmetry, as typically rea- lized in magneto-optical media 27 through the inclusion of anti- symmetric off-diagonal dielectric tensor elements. Recently, uni- directional light reflection has been realized in PT-symmetric systems near the exceptional point, with reflection from one end being diminished, but amplified at the other end 11,19–21,24 . Inspired by these studies, we show another way to obtain tunable optical isolation in two coupled whispering-gallery-mode (WGM) microtoroids with gain and loss functionalities in a large parameter space. In contrast to previous results 27–30 , our system allows variable non-reciprocal transmissions 31 , even at very low light levels, by adjusting the coupling strengths or input laser power. Before illustrating the asymmetric light transport, we begin with PT symmetry in active–passive-coupled microcavities with balanced gain and loss. Remarkably, our scheme explicitly demonstrates itself to be an on-chip ultrasensitive optical isolator 1 National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China, 2 Synergetic Innovation Center in Quantum Information and Quantum Physics, Nanjing University, Nanjing 210093, China, 3 Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA, 4 Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA. *e-mail: jxs@nju.edu.cn; jianming.wen@yale.edu; mxiao@uark.edu LETTERS PUBLISHED ONLINE: 22 JUNE 2014 | DOI: 10.1038/NPHOTON.2014.133 NATURE PHOTONICS | VOL 8 | JULY 2014 | www.nature.com/naturephotonics 524