We present spectroscopic observation of an exceptional point or the transition point between mode crossing and avoided mode crossing of neighboring quasieigenmodes in a chaotic optical microcavity of a large size parameter. The transition to the avoided mode crossing was impeded until the degree of deformation exceeded a threshold deformation owing to the system's openness also enhanced by the shape deformation. As a result, a singular topology was observed around the exceptional point on the eigenfrequency surfaces, resulting in fundamental inconsistency in mode labeling.

Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.

A walker is a fluid entity comprising a bouncing droplet coupled to the waves that it generates at the surface of a vibrated bath. Thanks to this coupling, walkers exhibit a series of wave-particle features formerly thought to be exclusive to the quantum realm. In this paper, we derive a model of the Faraday surface waves generated by an impact upon a vertically vibrated liquid surface. We then particularise this theoretical framework to the case of forcing slightly below the Faraday instability threshold. Among others, this theory yields a rationale for the dependence of the wave amplitude to the phase of impact, as well as the characteristic timescale and length scale of viscous damping. The theory is validated with experiments of bead impact on a vibrated bath. We finally discuss implications of these results for the analogy between walkers and quantum particles.

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We investigate lasing and output directionality of limaçon-shaped microdisk lasers of dimensions comparable to the emission wavelength. The far-field patterns are shown to differ between lasing modes, unlike in large cavities where lasing modes exhibit universal emission directionality determined by chaotic ray dynamics. Unidirectional emission is obtained for certain modes in the wavelength-scale cavities. It results from weak coupling of nearly isotropic high-quality resonances to anisotropic low-quality resonances, combined with chiral symmetry breaking of clockwise and counterclockwise propagating waves. The latter is described by an extended ray dynamics which includes the Goos-Hänchen shift and the Fresnel filtering. Mode hybridization and wave effects in open cavities make it possible to control the output properties of individual lasing modes in wavelength-scale lasers.

Experimental investigation of the characteristics of quasi-bound states of a quadrupole deformed microcavity has revealed five distinct mode groups in cavity emission spectra with cavity quality factors different by orders of magnitude and consistently with much different intracavity mode distributions but with almost universal far-field emission patterns. These universal directionality of high Q modes are explained by a subtle manifestation of unstable manifolds of classical chaos in the formation of quasi-bound states.

We experimentally studied evolution of quasi-eigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity we traced all high-Q cavity modes in a wide range of frequency as the cavity deformation increased. By employing an internal parameter we were able to obtain a mode-dynamics diagram at a given deformation, showing avoided crossings between different mode groups, and could directly observe the coupling strengths induced by ray chaos among encountering modes. We also show that the observed mode-dynamics diagrams reflect the underlying classical ray dynamics in the phase space. PACS numbers: 42.55.Sa,42.65.Sf, 05.45.Mt Quantum manifestation in a classically chaotic system has become an important issue in atomic, nano, mesoscopic physics, etc., due to its fundamental importance in quantum mechanics and applications to practical quantum/wave systems [1]. Most of early works have focused on statistical analysis of eigenvalues and eigenfunctions and comparison with the random matrix theory, e.g., the transition from Poisson to Wigner distribution of level spacings during a transition to chaos, providing an averaged view on mode dynamics [1]. Experimental verifications of the statistics have been performed mainly in closed microwave cavities [2]. Dynamical tunneling or coupling between regular and chaotic modes has recently been observed for a mixed phase space specially tailored for this purpose [3].In open quantum systems, each quasi-eigenmode has a linewidth, and thereby changes the mode dynamics significantly. Trapped modes were observed showing high Q even with increasing coupling strength to open channels in microwave cavities [4], and crossing and avoided crossing (AC) of cavity modes were reported near an exceptional point formed by two coupled microwave cavities [5]. We note, however, that the previous experimental works in microwave cavities and other systems neither realized an optimal system showing a continuous chaotic transition from being regular to chaotic nor provide observations direct enough to tell the variation of statistics.In this paper, we have experimentally observed, for the first time, the evolution of quasi-eigenmode dynamics in a generic open nonintegrable system when classical dynamics undergoes a transition from being regular to fully chaotic. In a dielectric deformation-variable chaotic optical microcavity (COM) we traced all high-Q cavity modes in a wide range of frequency as the cavity deformation increases. By introducing an additional parameter orthogonal to the cavity deformation, we could explicitly observe mode-mode dynamics under the chaotic transi-tion and measure various mode-mode coupling constants which can be associated with the underlying classical ray dynamics in phase space. We believe our data would be a valuable asset for future formulation of a currentlynonexisting semiclassical theory for coupling strengths between modes in a mixed phase space.Our experiment was performed i...

We present both experimental and theoretical evidences for uncertainty-limited turnstile transport in deformed microcavities. As the degree of cavity deformation was increased, a secondary peak gradually emerged in the far-field emission patterns to form a double-peak structure. Our observation can be explained in terms of the interplay between turnstile transport and its suppression by the quantum mechanical uncertainty principle.PACS numbers: 05.45. Mt, 42.55.Sa, In the studies of quantum counterparts of classical chaotic systems, we often encounter a situation in which classical diffusion is suppressed in quantum mechanics by the intrinsic limitation of the resolvable action quantity [1] due to the Heisenberg uncertainty principle. Partial barrier localization [2][3][4][5] and the suppression of multiphoton ionization [6] are well-known examples. This suppression phenomenon would become more conspicuous when a Hamiltonian system takes a gradual transition to chaos so that the action transport by chaotic dynamics also increases along the chaotic transition [7,8].Recently, many works have converged to a consensus that the emission directionality in chaotic deformed microcavities is well explained by classical ray dynamics in phase space [9][10][11][12][13][14][15][16]. However, the evanescent leakage from a symmetric or slightly deformed microcavity is inexplicable by the classical dynamics [17], and thus it is of considerable interest to understand how emission mechanism changes along the chaotic transition. In this context we can expect that the resolvability of action quantity would also play an important role in light transport and thus emission directionality in deformed microcavities. Such understanding is important not only for theoretical interests, but also for the practical purpose of optimizing the directional emission with a high cavity quality factor Q for various photonics applications.In this letter, we elucidate the effect of action resolvability on the light transport in a deformed microcavity with continuously variable shape deformation. We observed in both experiment and theory that output emission is characterized by the emergence of a sharp secondary peak as the degree of cavity deformation is increased. These double peaks originate from two separate phase-space lobes in the so-called turnstile transport [18,19] for whispering-gallery-mode-like quasieigenmodes. Moreover, the gradual emergence of the secondary peak is a direct evidence for suppression of chaotic diffusion due to the quantum mechanical uncertainty principle.Our deformed microcavity is realized by optically ex- citing a thin cross-sectional volume across a liquid jet column of ethanol (refractive index m=1.361) doped with Rhodamine B dye at a concentration of 10 −7 mol/cm 3 . The details of our liquid-jet apparatus is described elsewhere [20]. Surface profiling measurement based on forward shadow diffraction shows that the shape of our cavity is described by r(φ) = a(1 + η 0 cos 2φ + ǫη 2 0 cos 4φ) in the polar coordinate with...