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Nonlinear resonance-assisted tunneling induced by microcavity deformation.

Kwak H, Shin Y, Moon S, Lee SB, Yang J, An K - Sci Rep (2015)

Bottom Line: It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics.A selection rule for strong interactions is also found in terms of angular quantum numbers.Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea.

ABSTRACT
Noncircular two-dimensional microcavities support directional output and strong confinement of light, making them suitable for various photonics applications. It is now of primary interest to control the interactions among the cavity modes since novel functionality and enhanced light-matter coupling can be realized through intermode interactions. However, the interaction Hamiltonian induced by cavity deformation is basically unknown, limiting practical utilization of intermode interactions. Here we present the first experimental observation of resonance-assisted tunneling in a deformed two-dimensional microcavity. It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics. A selection rule for strong interactions is also found in terms of angular quantum numbers. Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

No MeSH data available.


Related in: MedlinePlus

Nonlinear resonance chains in the phase space.For our 2D-ADM to be discussed below, PSOS is constructed in terms of action angle variables s and sin χ, where a ray is reflected off the cavity boundary with an incidence angle χ at the normalized arc-length coordinate s (0 ≤ s ≤ 1) along the boundary from the major axis. Cavity deformation is given by a parameter η = 0.1. Nonlinear resonance chains with p = 6 and 8 are easily noticed. The separatrix of the p = 6 resonance chain is illustrated. KAM tori 1 and 2 associated with two UBM's are indicated around p = 6 resonance chain. RAT can then occur between these UBM's mediated by the p = 6 resonance chain.
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f1: Nonlinear resonance chains in the phase space.For our 2D-ADM to be discussed below, PSOS is constructed in terms of action angle variables s and sin χ, where a ray is reflected off the cavity boundary with an incidence angle χ at the normalized arc-length coordinate s (0 ≤ s ≤ 1) along the boundary from the major axis. Cavity deformation is given by a parameter η = 0.1. Nonlinear resonance chains with p = 6 and 8 are easily noticed. The separatrix of the p = 6 resonance chain is illustrated. KAM tori 1 and 2 associated with two UBM's are indicated around p = 6 resonance chain. RAT can then occur between these UBM's mediated by the p = 6 resonance chain.

Mentions: In order to understand how RAT comes about in ADM's, let us briefly recapitulate the RAT theory. In an integrable multi-dimensional system, classical trajectories appear as invariant tori on the Poincarè surface of section (PSOS), a phase-space representation of classical motion. The Husimi functions, the phase-space projections of quantum eigenstates, are then localized along these tori. In the presence of perturbation, invariant tori are deformed following the Kolmogorov-Arnold-Moser (KAM) scenario and some orbits evolve into a chain-like nonlinear resonance structure. According to the RAT theory, a nonlinear resonance structure can then strongly enhance a tunneling process between the UBM's localized along nearby invariant tori when specific conditions are satisfied (see Fig. 1 for illustration). This type of enhanced dynamical tunneling is called RAT202140.


Nonlinear resonance-assisted tunneling induced by microcavity deformation.

Kwak H, Shin Y, Moon S, Lee SB, Yang J, An K - Sci Rep (2015)

Nonlinear resonance chains in the phase space.For our 2D-ADM to be discussed below, PSOS is constructed in terms of action angle variables s and sin χ, where a ray is reflected off the cavity boundary with an incidence angle χ at the normalized arc-length coordinate s (0 ≤ s ≤ 1) along the boundary from the major axis. Cavity deformation is given by a parameter η = 0.1. Nonlinear resonance chains with p = 6 and 8 are easily noticed. The separatrix of the p = 6 resonance chain is illustrated. KAM tori 1 and 2 associated with two UBM's are indicated around p = 6 resonance chain. RAT can then occur between these UBM's mediated by the p = 6 resonance chain.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4355734&req=5

f1: Nonlinear resonance chains in the phase space.For our 2D-ADM to be discussed below, PSOS is constructed in terms of action angle variables s and sin χ, where a ray is reflected off the cavity boundary with an incidence angle χ at the normalized arc-length coordinate s (0 ≤ s ≤ 1) along the boundary from the major axis. Cavity deformation is given by a parameter η = 0.1. Nonlinear resonance chains with p = 6 and 8 are easily noticed. The separatrix of the p = 6 resonance chain is illustrated. KAM tori 1 and 2 associated with two UBM's are indicated around p = 6 resonance chain. RAT can then occur between these UBM's mediated by the p = 6 resonance chain.
Mentions: In order to understand how RAT comes about in ADM's, let us briefly recapitulate the RAT theory. In an integrable multi-dimensional system, classical trajectories appear as invariant tori on the Poincarè surface of section (PSOS), a phase-space representation of classical motion. The Husimi functions, the phase-space projections of quantum eigenstates, are then localized along these tori. In the presence of perturbation, invariant tori are deformed following the Kolmogorov-Arnold-Moser (KAM) scenario and some orbits evolve into a chain-like nonlinear resonance structure. According to the RAT theory, a nonlinear resonance structure can then strongly enhance a tunneling process between the UBM's localized along nearby invariant tori when specific conditions are satisfied (see Fig. 1 for illustration). This type of enhanced dynamical tunneling is called RAT202140.

Bottom Line: It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics.A selection rule for strong interactions is also found in terms of angular quantum numbers.Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea.

ABSTRACT
Noncircular two-dimensional microcavities support directional output and strong confinement of light, making them suitable for various photonics applications. It is now of primary interest to control the interactions among the cavity modes since novel functionality and enhanced light-matter coupling can be realized through intermode interactions. However, the interaction Hamiltonian induced by cavity deformation is basically unknown, limiting practical utilization of intermode interactions. Here we present the first experimental observation of resonance-assisted tunneling in a deformed two-dimensional microcavity. It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics. A selection rule for strong interactions is also found in terms of angular quantum numbers. Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

No MeSH data available.


Related in: MedlinePlus