Frequency splittings in deformed optical microdisk cavities

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

“…Recent experiments, however, have impressively demonstrated the effect also in microwave resonators [13] and in two-dimensional optical microcavities [20]. While the latter qualitatively follows the theoretical description of resonance-assisted tunneling obtained in quantum maps a quantitative description of resonance assisted tunneling in optical microcavities has been given only recently for systems with near-integrable ray dynamics [24,25]. For this, the classical ray dynamics has been approximated by a pendulum-like Hamiltonian, which subsequently allows for the perturbative expansion of optical modes and their quality factors as predicted by resonance-assisted tunneling.…”

“…Note, that for the elliptic cavity the imaginary parts of the wave numbers do not show a pure exponential decay as there are deviations around Re k m,l R = 13. This is expected to be due to the open boundary condition of optical cavities [25]. However, for both the near-integrable and the mixed system, at some point the imaginary parts of the wave numbers deviate from the integrable case due to resonance-assisted tunneling induced by the 4 : 1 resonance.…”

“…Specifically, in the circular case one has p(s, P m,l ) = P m,l = m/(nRe k m,l ), which allows to fix α in Eq. (25). We further assume, that α remains constant under deformation of the boundary.…”

“…One major mechanism causing this enhanced decay is the wave effect of dynamical tunneling which was first observed and extensively studied in quantum systems [8,9]. More recently it has been studied both theoretically and experimentally in microwave resonators [10][11][12][13] and optical microcavities [14][15][16][17][18][19][20][21][22][23][24][25]. Dynamical tunneling allows for coupling of optical modes associated with dynamically separated classical phase-space regions.…”

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

“…In addition, it should be noticed that the Resonance-Assisted-Tunneing (RAT) partly can explain the results above. RAT induces an enhanced interaction of unperturbed modes (WGM) that live along nearby invariant tori, owing to nonlinear resonance chains located between unperturbed modes when quantum number of unperturbed modes differ in a multiple of the order of the resonance chain (selection rule) [35][36][37], and the selection rule are associated with Fermi resonance [11,38]. Hence, RAT implies a leading to the wavefunction localization on the periodic orbits associated with nonlinear resonance chain [39,40].…”