Fermi resonance in optical microcavities

Excited-State Aromatization Drives Nonequilibrium Planarization Dynamics

Excited-state aromaticity is one of the most widely applied concepts in the field of chemistry, often used as a rational guideline for predicting conformational changes of cyclic π-conjugated systems induced by photoexcitation. Yet, the details of the relationship between the corresponding photoinduced electronic and structural dynamics have remained unclear. In this work, we applied femtosecond transient absorption and time-resolved time-domain Raman spectroscopies to track the nonequilibrium planarization dynamics of a cyclooctatetraene (COT) derivative associated with the excited-state aromaticity. In the femtosecond time-resolved Raman data, the bent-to-planar structural change was clearly captured as a continuous peak shift of the marker band, which was unambiguously identified with 13C labeling. Our findings show that the planarization occurs after a significant change in the electronic structure, suggesting that the system first becomes aromatic, followed by a conformational change. This work provides a unique framework for understanding the excited-state aromaticity from a dynamical aspect.

Vibrational Fermi Resonance in Atomically Thin Black Phosphorus

Fermi resonance is a phenomenon involving the hybridization of two coincidentally quasi-degenerate states that is observed in the vibrational or electronic spectra of molecules. Despite numerous examples in molecular systems, vibrational Fermi resonances in dispersive semiconducting systems remain largely unexplored due to the rarity of occurrence. Here we report a vibrational Fermi resonance in atomically thin black phosphorus. The Fermi resonance arises via anharmonic mixing of a fundamental Raman mode and a Davydov component of an infrared mode, leading to a doublet with mixed character. The extent of Fermi coupling can be modulated by the application of external biaxial strain. The consequences of Fermi hybridization are revealed by electronic resonance effects in the thickness-dependent and excitation-wavelength-dependent Raman spectrum, which is predicted by ab initio hybrid functional simulations including excitonic interactions. This work reveals new insight into electron-phonon coupling in black phosphorus and demonstrates a novel method for modulating Fermi resonances in 2D semiconductors.

Observation of electronic modes in open cavity resonator

The resemblance between electrons and optical waves has strongly driven the advancement of mesoscopic physics, evidenced by the widespread use of terms such as fermion or electron optics. However, electron waves have yet to be understood in open cavity structures which have provided contemporary optics with rich insight towards non-Hermitian systems and complex interactions between resonance modes. Here, we report the realization of an open cavity resonator in a two-dimensional electronic system. We studied the resonant electron modes within the cavity and resolved the signatures of longitudinal and transverse quantization, showing that the modes are robust despite the cavity being highly coupled to the open background continuum. The transverse modes were investigated by applying a controlled deformation to the cavity, and their spatial distributions were further analyzed using magnetoconductance measurements and numerical simulation. These results lay the groundwork to exploring matter waves in the context of modern optical frameworks.

Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard

We investigate two types of avoided crossings in a chaotic billiard within the framework of information theory. The Shannon entropy in the phase space for the Landau-Zener interaction increases as the center of the avoided crossing is approached, whereas for the Demkov interaction, the Shannon entropy decreases as the center of avoided crossing is passed by with an increase in the deformation parameter. This feature can provide a new indicator for scar formation. In addition, it is found that the Fisher information of the Landau-Zener interaction is significantly larger than that of the Demkov interaction.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

Rayleigh scatterer-induced steady exceptional points of stable-island modes in a deformed optical microdisk

A formation of second-order non-Hermitian degeneracies, called exceptional points (EPs), in a chaotic oval-shaped dielectric microdisk is studied. Different symmetric optical modes localized on a stable period-3 orbit coalesce to form chiral EPs. Unlike a circular microdisk perturbed by two scatterers (CTS), our proposed system requires only one scatterer to build chiral EPs. The scatterer positions for counterpropagating EP modes are far distant from one another and almost steady against varying scatterer sizes in contrast to the CTS case. Our results can contribute to establishing a more solid platform for EP-based-device applications with flexibility and easy feasibility in obtaining EPs.

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

Extremely high Q and unidirectional laser emission due to combination of the Kolmogorov-Arnold-Moser barrier and the chaotic sea in a dielectric microdisk

Emission characteristics of an oval-shaped microcavity laser are studied. In experiments, modes localized on periodic orbits emit unidirectionally with a narrow in-plane divergence angle of about 12 deg. The origin of high directionality is elucidated by means of classical ray dynamics. Wave calculations show that the Q-factors of the resonances are higher than 10⁸. We explain this extraordinary high Q-factor in relation with a dynamical barrier region where Kolmogorov-Arnold-Moser curves significantly obstruct leakages of resonances.

Shannon entropy and avoided crossings in closed and open quantum billiards

The relation between Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of the probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of the avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system have equivalent effects on the Shannon entropy.

Pair of Exceptional Points in a Microdisk Cavity under an Extremely Weak Deformation

One of the interesting features of open quantum and wave systems is the non-Hermitian degeneracy called an exceptional point, where not only energy levels but also the corresponding eigenstates coalesce. We demonstrate that such a degeneracy can appear in optical microdisk cavities by deforming the boundary extremely weakly. This surprising finding is explained by a semiclassical theory of dynamical tunneling. It is shown that the exceptional points come in nearly degenerated pairs, originating from the different symmetry classes of modes. A spatially local chirality of modes at the exceptional point is related to vortex structures of the Poynting vector.

Avoided level crossings in an elliptic billiard

In an elliptic billiard, we find avoided level crossings taking place over wide ranges, which are of a Demkov type for generations of eigenfunctions localized on an islands chain and its pair unstable periodic orbit. For a proof of the existence of avoided level crossings, first, we show that the quantized eigenvalue of the unstable periodic orbit, obtained by the Einstein-Brillouin-Keller quantization rule, passes the eigenvalues of bouncing-ball modes localized on the unstable periodic orbit after Demkov type avoided level crossings so that pairs of bouncing-ball modes are sequentially generated. Next, by using a perturbed Hamiltonian, we show that off-diagonal elements in Hamiltonian are nonzero, which give rise to an interaction between two eigenfunctions. Last, we verify that the observed phenomenon is Fermi resonance: that is, the quantum number difference of two normal modes equals the periodic orbits, where eigenfunctions are localized after an avoided level crossing.

Separatrix modes in weakly deformed microdisk cavities

Optical modes in deformed dielectric microdisk cavities often show an unexpected localization along unstable periodic ray orbits. We reveal a new mechanism for this kind of localization in weakly deformed cavities. In such systems the ray dynamics is nearly integrable and its phase space contains small island chains. When increasing the deformation the enlarging islands incorporate more and more modes. Each time a mode comes close to the border of an island chain (separatrix) the mode exhibits a strong localization near the corresponding unstable periodic orbit. Using an EBK quantization scheme taking into account the Fresnel coefficients we derive a frequency condition for the localization. Observing far field intensity patterns and tunneling distances, reveals small differences in the emission properties.

Complex-path prediction of resonance-assisted tunneling in mixed systems

We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a prediction based on just a few properties of the classical phase space. For the standard map excellent agreement with numerically determined tunneling rates is observed. The results should similarly apply to ionization rates and quality factors.

Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a nonperturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling. Our approach is based on a new class of integrable approximations which mimic the regular phase-space region and its dominant nonlinear resonance chain in a mixed regular-chaotic system. We illustrate the method for the standard map.

Energy shell structure in a dielectric elliptic microcavity

An energy shell structure depending on eccentricity is analyzed in a dielectric elliptic microcavity. Through the analysis, it is explicated that the energy shell structure is governed by classical constant actions of periodic orbits. For clarification, the relation between dominances of the periodic orbits and bifurcation behaviors are obtained and the length spectra based on eigenvalues computed by a numerical method are compared with the exact lengths of the periodic orbits obtained by analytic calculations. By matching effective wave numbers obtained from the periodic orbit lengths to exact wave numbers of stationary states in closed and open cavities, we find deviations provoked from the openness. We show that these deviations are caused by additional phase factors in the Einstein-Brillouin-Keller quantization.

Resonant torus-assisted tunneling

We report a new type of dynamical tunneling, which is mediated by a resonant torus, i.e., a nonisolated periodic orbit. To elucidate the phenomenon, we take an open elliptic cavity and show that a pair of resonances localized on two classically disconnected tori tunnel through a resonant torus when they interact with each other. This so-called resonant torus-assisted tunneling is verified by using Husimi functions, corresponding actions, Husimi function distributions, and the standard deviations of the actions.

Quantum manifestations of classical nonlinear resonances

When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties.

Fermi resonance in dynamical tunneling in a chaotic billiard

We elucidate that Fermi resonance ever plays a decisive role in dynamical tunneling in a chaotic billiard. Interacting with each other through an avoided crossing, a pair of eigenfunctions are coupled through tunneling channels for dynamical tunneling. In this case, the tunneling channels are an islands chain and its pair unstable periodic orbit, which equals the quantum number difference of the eigenfunctions. This phenomenon of dynamical tunneling is confirmed in a quadrupole billiard in relation with Fermi resonance.