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Register a new userOptical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
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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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Exceptional points (EPs) are degeneracies in open wave systems with coalescence of at least two energy levels and their corresponding eigenstates. In higher dimensions, more complex EP physics not found in two-state systems is observed. We consider the emergence and interaction of multiple EPs in a four coupled optical waveguides system by non-Hermitian coupling showing a unique EP formation pattern in a phase diagram. In addition, absolute phase rigidities are computed to show the mixing of the different states in definite parameter regimes. Our results could be potentially important for developing further understanding of EP physics in higher dimensions via generalized paradigm of nonHermitian coupling for a new generation of parity-time (PT) devices.
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Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in presence of either $PT$ symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic $sim k^{1/3}$ dispersion are protected by PT-symmetry, while third-order EPs with a $sim k^{1/2}$ dispersion are protected by the chiral symmetry emerging in non-Hermitian Lieb lattice models. More generally, we identify stable, weak, and fragile aspects of symmetry-protected higher-order EPs, and tease out their concomitant phenomenology.
We propose a scheme to realize parity-time (PT) symmetric photonic Lieb lattices of ribbon shape and complex couplings, thereby demonstrating the higher-order exceptional point (EP) and Landau-Zener Bloch (LZB) oscillations in presence of a refractive index gradient. Quite different from non-Hermitian flatband lattices with on-site gain/loss, which undergo thresholdless PT symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices has completely real values when the index gradient is applied perpendicular to the ribbon, and a triply degenerated (third-order) EP with coalesced eigenvalues and eigenvectors emerges only when the amplitude of gain/loss ratio reaches a certain threshold value. When the index gradient is applied parallel to the ribbon, the LZB oscillations exhibit intriguing characteristics including asymmetric energy transition and pseudo-Hermitian propagation as the flatband is excited. Meanwhile, a secondary emission occurs each time when the oscillatory motion passes through the EP, leading to distinct energy distribution in the flatband when a dispersive band is excited. Such novel phenomena may appear in other non-Hermitian flatband systems. Our work may also bring insight and suggest a photonic platform to study the symmetry and topological characterization of higher-order EPs that may find unique applications in for example enhancing sensitivity.
Topological semimetals feature a diversity of nodal manifolds including nodal points, various nodal lines and surfaces, and recently novel quantum states in non-Hermitian systems have been arousing widespread research interests. In contrast to Hermitian systems whose bulk nodal points must form closed manifolds, it is fascinating to find that for non-Hermitian systems exotic nodal manifolds can be bounded by exceptional points in the bulk band structure. Such exceptional points, at which energy bands coalesce with band conservation violated, are iconic for non-Hermitian systems. In this work, we show that a variety of nodal lines and drumheads with exceptional boundary can be realized on 2D and 3D honeycomb lattices through natural and physically feasible non-Hermitian processes. The bulk nodal Fermi-arc and drumhead states, although is analogous to, but should be essentially distinguished from the surface counterpart of Weyl and nodal-line semimetals, respectively, for which surface nodal-manifold bands eventually sink into bulk bands. Then we rigorously examine the bulk-boundary correspondence of these exotic states with open boundary condition, and find that these exotic bulk states are thereby undermined, showing the essential importance of periodic boundary condition for the existence of these exotic states. As periodic boundary condition is non-realistic for real materials, we furthermore propose a practically feasible electrical-circuit simulation, with non-Hermitian devices implemented by ordinary operational amplifiers, to emulate these extraordinary states.
Engineered non-Hermitian systems featuring exceptional points can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce and present non-Hermitian dynamics of coupled optical parametric oscillators (OPOs) arising from phase-sensitive amplification and de-amplification, and show their distinct advantages over conventional non-Hermitian systems relying on laser gain and loss. OPO-based non-Hermitian systems can benefit from the instantaneous nature of the parametric gain, noiseless phase-sensitive amplification, and rich quantum and classical nonlinear dynamics. We show that two coupled OPOs can exhibit spectral anti-PT symmetry and an exceptional point between its degenerate and non-degenerate operation regimes. To demonstrate the distinct potentials of the coupled OPO system compared to conventional non-Hermitian systems, we present higher-order exceptional points with two OPOs, tunable Floquet exceptional points in a reconfigurable dynamic non-Hermitian system, and generation of squeezed vacuum around exceptional points, all of which are not easy to realize in other non-Hermitian platforms. Our results show that coupled OPOs are an outstanding non-Hermitian setting with unprecedented opportunities in realizing nonlinear dynamical systems for enhanced sensing and quantum information processing.
The finite gain-bandwidth product is a fundamental figure of merit that restricts the operation of standard optical amplifiers. In microcavity setups, this becomes a serious problem due to the narrow bandwidth of the device. Here we introduce a new design paradigm based on exceptional points, that relaxes this limitation and allows for building a new generation of optical amplifiers that exhibits better gain-bandwidth scaling relations. Importantly, our results can be extended to other physical systems such as acoustics and microwaves.
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