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Register a new userParity-Time Symmetry in Non-Hermitian Complex Optical Media
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Added by
Samit Kumar Gupta Dr.
Publication date
2018
fields
Physics
and research's language is
English
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The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory, recently ramified into diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant applications prospects and engineering of novel materials. In addition, it has observed increasing research interests in many emerging directions beyond optics and photonics. This Review paper attempts to bring together the state of the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings along with elucidating key concepts and background and a detailed perspective on new emerging directions. It can be anticipated that this trendy field of interest can be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, opto-electronics and beyond, and offer distinctive applications prospects in novel functional materials.
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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. Such a counterintuitive 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 a complex potential seem absent in Nature. But nevertheless, the notion of PT symmetry has highly survived in many other branches of physics including optics, photonics, AMO physics, acoustics, electronic circuits, material science over the past ten years, and others, where a judicious balance of gain and loss constitutes 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. Such 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.
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($mathcal{PT}$) symmetry. The localization transition induced by the non-Hermitian quasiperiodic potential is found to occur at the $mathcal{PT}$-symmetry-breaking point. Our results also demonstrate the existence of energy dependent mobility edges, which separate the extended states from localized states and are only associated with the real part of eigen-energies. The level statistics and Loschmidt echo dynamics are also studied.
Parity-time (PT) symmetry in non-Hermitian optical systems promises distinct optical effects and applications not found in conservative optics. Its counterpart, anti-PT symmetry, subscribes another class of intriguing optical phenomena and implies complementary techniques for exotic light manipulation. Despite exciting progress, so far anti-PT symmetry has only been realized in bulky systems or with optical gain. Here, we report an on-chip realization of non-Hermitian optics with anti-PT symmetry, by using a fully-passive, nanophotonic platform consisting of three evanescently coupled waveguides. By depositing a metal film on the center waveguide to introduce strong loss, an anti-PT system is realized. Using microheaters to tune the waveguides refractive indices, striking behaviors are observed such as equal power splitting, synchronized amplitude modulation, phase-controlled dissipation, and transition from anti-PT symmetry to its broken phase. Our results highlight exotic anti-Hermitian nanophotonics to be consolidated with conventional circuits on the same chip, whereby valuable chip devices can be created for quantum optics studies and scalable information processing.
For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys Theta^2=-1, but no such a degeneracy exists when Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.
The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has drawn a great deal of attention in recent years. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. Among several peculiar phenomena observed at exceptional points, an especially intriguing property, with relevant practical potential, consists in the inherently enhanced sensitivity to small-scale perturbations. So far, however, these principles have been implemented at the expenses of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled distributions of optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of standard single-mode telecommunication fibre, using a setup consisting of entirely of off-the-shelf components. Two propagating signals are amplified and coupled through stimulated Brillouin scattering, which makes the process non-Hermitian and enables exquisite control over gain and loss. Singular response to small variations around the exceptional point and topological features arising around this singularity are experimentally demonstrated with large precision, enabling robustly enhanced spectral response to small-scale changes in the Brillouin frequency shift. Our findings open exciting opportunities for the exploration of non-Hermitian phenomena over a table-top setup, with straightforward extensions to higher-order Hamiltonians and applications in quantum optics, nanophotonics and sensing.
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