Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some phase-transition threshold. This stems from the existence of a parameter in the Hamiltonian governing characteristics features of eigenvalues and eigenfunctions. Varying this parameter causes real eigenvalues to coalesce and become complex conjugate pairs, signaling the occurrence of a nontrivial phase transition and the breakdown of PT symmetry. Such an appealing discovery has aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators in the last two decades. Despite much fundamental theoretical success in the development of PT-symmetric quantum mechanics, an experimental observation of pseudo-Hermiticity remains elusive as these systems with complex potential seem absent in Nature. But nevertheless, the notion of PT symmetry has survived in many other branches of physics including optics, photonics, AMO physics, acoustics, electronic circuits, and material science over the past ten years, where a judicious balance of gain and loss constitutes ingeniously a PT-symmetric system. Here, although we concentrate upon reviewing recent progress on PT symmetry in optical microcavity systems, we also wish to present some new results that may help to accelerate the research in the area. These compound photonic structures with gain and loss provide a powerful platform for testing various theoretical proposals on PT symmetry, and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Throughout this article there is an effort to clearly present the physical aspects of PT-symmetry in optical microcavity systems, but mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of PT symmetry using optical microcavities are still expected in the future.
Journal of Physics B: Atomic, Molecular and Optical Physics
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