Research

Transformation Cavity: deformed gradient index microcavities designed by transformation optics.

• Deformed gradient index microcavities designed by transformation optics, which are named transformation cavity, have been proposed to obtain directional light emission while simultaneously maintaining the nature of high-Q WGMs [Nature Photonics 10, 647 (2016)]. The cavity boundary shapes and corresponding refractive index profiles of the transformation cavities were designed utilizing conformal transformation optics. Transformation cavities have attracted considerable attention not only in resonator optics as they combine optical microcavities with transformation optics, but also in applications requiring high-Q modes with unidirectional light emission. The transformation cavity with deformed boundary shape and inhomogeneous refractive index profile can be implemented effectively by drilling subwavelength-scale air holes in a dielectric slab or by arranging dielectric posts with high refractive indices. The optimal system parameters for the coexistence of strong bidirectionality and a high Q-factor was also obtained for anisotropic whispering gallery modes supported by total internal reflection [Scientific Reports 9, 8506 (2019)]. We developed a boundary element method using Green’s function to analyse the resonant mode for the transformation cavities [Scientific Reports 9, 19684 (2019)].

Non-Hermitian physics: emergent phenomena originated from openness.

• Non-Hermiticity has attracted great interest, both theoretical and experimental, in open systems with energy gain and loss. We demonstrated a reconfiguration of quantum states in PT-symmetric quasi-one-dimensional lattices, where the quantum states can be controlled by balanced gain and loss. We explored how the variations of quantum states originate in the transition from the unbroken to broken PT-symmetric phase, via exceptional point [Scientific Reports 7, 8746 (2017)].We also considered the role of non-triviality resulting from a non-Hermitian Hamiltonian that conserves twofold PT-symmetry assembled by interconnections between a PT-symmetric lattice and its time reversal partner. We reported two pairs of interface states that decay exponentially in the space distinguished by the bulk states [Phys. Rev. Research 2, 033149 (2020)].

Complex collective behaviors such as synchronization and amplitude death in coupled dynamical systems.

• • Cooperative behaviors in coupled dynamical systems are of significant interest in the field of physics, biology, and engineering. The prominent cooperative behaviors that occur in periodic and chaotic oscillating systems are synchronization and amplitude death. We studied the amplitude death which is complete cessation of oscillations in chaotic oscillators with coupling or delayed feedback [PRE 70, 036220 (2004); JKPS 55, 395 (2009)]. We also studied the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way [Chaos 27, 083119 (2017)]. Recently, we studied the non-Hermitian effect in coupled nonlinear dynamical systems. We studied the exceptional point, non-Hermitian degenerate point, in dynamical systems and investigated the role of the exceptional point in the transient behaviors of amplitude death in coupled limit cycle oscillators [PRE 91, 052910 (2015)]. We studied oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. In the systems, we discussed the robust neutral stability of the oscillation death in non-conservative systems via the anti-parity-time-symmetric phase transitions at exceptional points in terms of non-Hermitian systems [PRE 100, 022209 (2019)].

Classical-quantum (ray-wave) correspondence in quantum (optical) systems with classically chaotic dynamics.

• • Quantum chaos describes and tries to understand the nature of the wave-like motions for the electrons in atoms and molecules as well as electromagnetic waves in classically chaotic systems. Quantum chaos provides an intriguing arena for the discussion of the quantum-classical correspondence, e.g., decoherence appears to be very effective in restoring correspondence.

  • We have studied the classical-quantum and ray-wave correspondence in open quantum maps and optical microcavities, respectively [PRE 86, 066213 (2012); Chaos 29, 043123 (2019)]. In particular, the optical microcavities can serve as a useful platform for investigating the correspondence between quasi-bound states and associated chaotic classical dynamics due to well-known one-to-one correspondence between Schroedinger equation and the Maxwell equation in dynamical billiard problem. We have introduced a ray model for coupled optical microdisks in which we select coupling-efficient rays among the splitting rays [PRA 82, 033824 (2010); PRE 85, 056213 (2012)]. Some resonance modes of the coupled microcavities can be explained by the classical phase space structure emerging from this model which does not exist in a single microcavity [OL 39, 4196 (2014)].

Quantum mechanical description of open chaotic and disorder systems in terms of non-Hermitian formalism.

• • Every real quantum system is coupled to the environment since no information can be extracted from completely closed systems. Thus it is natural to ask how the coupling of the quantum system to the environment modifies genuine quantum effects such as the quantum localization. It is known that open quantum systems are very different from closed ones. In the mathematical viewpoint, the closed quantum systems are described by usual Hermitian formalism, while the open ones by non-Hermitian formalism.

  • We studied the exceptional points, one of important features of non-Hermitian systems, and the related phenomena in practical systems such as chaotic-shaped and coupled optical microcavities [PRA 78, 015805 (2008); PRA 79, 053858 (2009)]. These works was the first reports showing existence of the exceptional points in chaotic-shaped and coupled optical microcavities, respectively. The effect of multiple exceptional points has been investigated in non-Hermitian Hamiltonian and coupled microcavities [PRA 85, 042101 (2012); PRA 85, 064103 (2012)]. These works opened up the possibility for a systematic description of the complex eigenvalue structure near multiple exceptional points using simple mathematical formula. Recently, We also proposed a plausible explanation on a long-lasting question, why most modes are found to be localized in open quantum systems with classically chaotic dynamics in terms of non-Hermitian matrix model [Chaos 29, 043123 (2019)].

  • We also studied a quasi-bound state of a delta-kicked rotor with absorbing boundaries and figured out the nature of a dynamical localization in open quantum systems. The localization lengths of lossy quasi-bound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates are dramatically enhanced [PRE 78, 037201 (2008)].

Applications of optical microcavities.

• • Another focus of my research is on the application of open quantum mechanics to optical microcavity systems. An optical microcavity is an interesting system where one can verify rather mathematical features of non-Hermitian quantum mechanics. Besides theoretical study of optical microcavities, We made several useful proposals for practical applications of optical microcavities, e.g., designing coupled microcavity lasers for high-Q modes with unidirectional light emission and terahertz beat frequency generation from two-mode lasing operation of coupled microdisk laser. [OL 36, 1116 (2011); OL 37, 3210 (2012)].

Energy spectrum and quantum transport in Quasi-1D lattices.

• • Quasi-1D lattices exhibit various interesting phenomena in contrast to 1D and 2D lattices. We have demonstrated mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss [Scientific Reports 7, 8746 (2017)]. We have reported the effect of symmetry-broken contacts on quantum transport in quasi-1D lattices. In contrast to 1D chains, transport in quasi-one-dimensional lattices, which are made up of a finite number of 1D chain layers, is strongly influenced by contacts [PRB 96, 125421 (2017)]. We have studied how the non-orientability of a Moebius strip affects the eigenenergies and eigenstates of tight-binding models by comparing circular and Moebius ladder lattices as the simplest models in real space. We have demonstrated avoided crossings and PT phase transitions in terms of Hermitian and non-Hermitian perturbations, respectively. Additionally, corresponding resonances and antiresonances appearing in quantum transport have been also studied [arXiv:2001.10221].