Uncertainty-Limited Turnstile Transport in Deformed Microcavities

Abstract

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...

Whispering gallery modes formed by partial barriers in ultrasmall deformed microdisks

“…Accordingly, deformed microcavities are realized in such a ultrasmall regime where the vacuum wavelength λ is of the order of the length scale of the cavity size R, i.e., R/λ ∼ 1 [8,9]. In this regime, high-Q WGMs still exist, but the emission from them is not as directional as from larger cavities, and the ray dynamical prediction of emission directionality is not valid anymore, because the resolutions of the modes are not enough to follow the fine structures in chaotic phase space [17,18]. So far, only the possibility of accidental coupling with low-Q modes is known to lead to directional emission [9].…”

“…The deformed microcavities have been experimentally realized with several different cross-sectional shapes and various materials [6-10]. Also, they become important models in the field of quantum chaos [11,12] for the study of ray-wave correspondence in open systems [13][14][15][16][17].Nonetheless, it is not easy to understand and predict the spectrum and emission directionality because the internal ray dynamics is chaotic due to the broken rotational symmetry. Therefore, many studies have concentrated on the properties of the spectrum and the role of the chaotic dynamics to generate directional light emission from high-Q WGMs.…”

“…The deformed microcavities have been experimentally realized with several different cross-sectional shapes and various materials [6-10]. Also, they become important models in the field of quantum chaos [11,12] for the study of ray-wave correspondence in open systems [13][14][15][16][17].…”

High-Q and Unidirectional Emission Whispering Gallery Modes: Principles and Design

“…Based on the necessary condition of a continuous and single-line symmetric boundary shape, we can well control the directional emission from an ARC by setting boundary shape to adjust the stable islands and fixed points of unstable orbits in phase space. Actually, to some extent, the design of the dielectric ARC for directional emission is the control of chaotic transport in phase space [42]. Thanks to the ray-wave correspondence, the cavity for high-Q and unidirectional emission can be obtained by simple ray simulations.…”

Ultrahigh-Q, largely deformed microcavities coupled by a free-space laser beam

“…25 It has been revealed that larger deformation breaks more KAM tori, enables more excitation light localized in the cavity, and leads to a higher probability of coupling into regular high-Q modes. 26 In addition, larger deformation has more potential for better unidirectionality, since controlling the chaotic behavior of rays in the cavity by unstable manifolds is fairly promising.…”