Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets shows a bistable transition in its transmission curve as the Kerr-nonlinearity in the cavity is increased. At the same time, one rotational mode gets dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled mode theory, the underlying mode dynamics of the phenomena is theoretically modelled and clarified.Comment: 7 pages, 5 figure

Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers

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

Bohmian trajectories for the half-line barrier

Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields one of the simplest cases of diffraction. Using the exact time-dependent propagator found by Schulman, the trajectories are computed numerically for different initial Gaussian wave packets. In particular, it is found that different boundary conditions may lead to qualitatively different sets of trajectories. In the Dirichlet case, the particles tend to be more strongly repelled. The case of an incoming plane wave is also considered. The corresponding Bohmian trajectories are compared with the trajectories of an oil drop hopping on the surface of a vibrating bath

Quasi-Eigenstate Evolution in Open Chaotic Billiards

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.Comment: 4 pages, 4 figure

Development of deformation-tunable quadrupolar microcavity

We have developed a technique for realizing a two-dimensional quadrupolar microcavity with its deformation variable from 0% to 20% continuously. We employed a microjet ejected from a noncircular orifice in order to generate a stationary column with modulated quadrupolar deformation in its cross section. Wavelength red shifts of low-order cavity modes due to shape deformation were measured and were found to be in good agreement with the wave calculation for the same deformation, indicating the observed deformation is quadrupolar in nature.Comment: 7 pages, 6 figures, intended for Rev. Sci. Instu

Chaos-assisted nonresonant optical pumping of quadrupole-deformed microlasers

Efficient nonresonant optical pumping of a high-Q scar mode in a two-dimensional quadrupole-deformed microlaser has been demonstrated based on ray and wave chaos. Three-fold enhancement in the lasing power was achieved at a properly chosen pumping angle. The experimental result is consistent with ray tracing and wave overlap integral calculations.Comment: 3 pages, 5 figure

Theoretical Estimation of Cannulation Methods for Left Ventricular Assist Device Support as a Bridge to Recovery

Left ventricular assist device (LVAD) support under cannulation connected from the left atrium to the aorta (LA-AA) is used as a bridge to recovery in heart failure patients because it is non-invasive to ventricular muscle. However, it has serious problems, such as valve stenosis and blood thrombosis due to the low ejection fraction of the ventricle. We theoretically estimated the effect of the in-series cannulation, connected from ascending aorta to descending aorta (AA-DA), on ventricular unloading as an alternative to the LA-AA method. We developed a theoretical model of a LVAD-implanted cardiovascular system that included coronary circulation. Using this model, we compared hemodynamic responses according to various cannulation methods such as LA-AA, AA-DA, and a cannulation connected from the left ventricle to ascending aorta (LV-AA), under continuous and pulsatile LVAD supports. The AA-DA method provided 14% and 18% less left ventricular peak pressure than the LA-AA method under continuous and pulsatile LVAD conditions, respectively. The LA-AA method demonstrated higher coronary flow than AA-DA method. Therefore, the LA-AA method is more advantageous in increasing ventricular unloading whereas the AA-DA method is a better choice to increase coronary perfusion

Numerical Test of Born-Oppenheimer Approximation in Chaotic Systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space.Comment: 5 pages, 5 figures, accepted for publication in Phys. Lett.