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Register a new userChiral modes near exceptional points in symmetry broken H1 photonic crystal cavities
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The H1 photonic crystal cavity supports two degenerate dipole modes of orthogonal linear polarization which could give rise to circularly polarized fields when driven with a $pi$/$2$ phase difference. However, fabrication errors tend to break the symmetry of the cavity which lifts the degeneracy of the modes, rendering the cavity unsuitable for supporting circular polarization. We demonstrate numerically, a scheme that induces chirality in the cavity modes, thereby achieving a cavity that supports intrinsic circular polarization. By selectively modifying two air holes around the cavity, the dipole modes could interact via asymmetric coherent backscattering which is a non-Hermitian process. With suitable air hole parameters, the cavity modes approach the exceptional point, coalescing in frequencies and linewidths as well as giving rise to significant circular polarization close to unity. The handedness of the chirality can be selected depending on the choice of the modified air holes. Our results highlight the prospect of using the H1 photonic crystal cavity for chiral-light matter coupling in applications such as valleytronics, spin-photon interfaces and the generation of single photons with well-defined spins.
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Over the past decade, parity-time ($mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam propagation method analysis. Our results pave a robust way toward studying the interplay between passive $mathcal{PT}$ transitions and quantum effects in dissipative photonic configurations.
We describe the design, fabrication, and spectroscopy of coupled, high Quality (Q) factor silicon nanobeam photonic crystal cavities. We show that the single nanobeam cavity modes are coupled into even and odd superposition modes, and we simulate the frequency and Q factor as a function of nanobeam spacing, demonstrating that a differential wavelength shift of 70 nm between the two modes is possible while maintaining Q factors greater than 10^6. For both on-substrate and free-standing nanobeams, we experimentally monitor the response of the even mode as the gap is varied, and measure Q factors as high as 200,000.
Hybrid quantum information protocols are based on local qubits, such as trapped atoms, NV centers, and quantum dots, coupled to photons. The coupling is achieved through optical cavities. Here we demonstrate far-field optimized H1 photonic crystal membrane cavities combined with an additional back reflection mirror below the membrane that meet the optical requirements for implementing hybrid quantum information protocols. Using numerical optimization we find that 80% of the light can be radiated within an objective numerical aperture of 0.8, and the coupling to a single-mode fiber can be as high as 92%. We experimentally prove the unique external mode matching properties by resonant reflection spectroscopy with a cavity mode visibility above 50%.
We demonstrate the existence of exceptional points of degeneracy (EPD) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show a second-order modal EPD associated with the parity-time ($cal{PT}$) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such degeneracy condition was previously referred to as a degenerate band edge in lossless anisotropic photonic crystals. Here, we rigorously show it under the occurrence of gain and loss balance for a discrete guiding system. We identify a more general regime of gain and loss balance showing that $cal{PT}$-symmetry is not necessary to realize EPDs. Furthermore, we investigate the degree of detuning of the EPD when the geometrical symmetry or balanced condition is broken. These findings open unprecedented avenues toward superior light localization and transport with application to high-Q resonators utilized in sensors, filters, low-threshold switching and lasing.
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.
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