Quantum-Field Laser Laboratory, KW An's Group

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02 Research

Quantum chaos

in asymmetric dielectric microcavity systems

in asymmetric dielectric microcavity systems

Dynamical tunneling is a quantum mechanical tunneling phenomenon which occurs between dynamically separated classical trajectories. We directly observed the dynamical tunneling effect in a dye-doped liquid-jet microcavity system. In our experiment, pump beam was injected into chaotic region below the critical line in phase space. Therefore, the only route of the pump light into a mode in the regular region is the dynamical tunneling process. By utilizing the dynamical tunneling between the chaotic and the regular region, we enhanced the laser pumping efficiency by 100 times compared to the previous studies. Recently, we experimentally observed another kind of dynamical tunneling in a slightly deformed microcavity system, namely Resonance Assisted Tunneling (RAT), which is mediated by classical resonances. RAT has been actively studied in abstract objects like quantum maps. But there have been no experiments to confirm the RAT theory. We have established that, as predicted by the RAT theory, the strength of the intermode interaction is proportional to the square of the area of the interaction-mediating resonance-chain structure. Our semi-classical study suggests a new way to predict the quantum mechanical intermode interaction in real non-integrable system.

(a) Spectrum of our asymmetric microcavity. (b) Spectrum of the pumped region around 600nm. (c) Pumping efficiency versus pump wavelength. Plots are from J. Yang et. al., Phys. Rev. Lett. **104**, 243601 (2010). (d) Relation between the strength of RAT-mediated intermode interaction and the area S of the resonance-chain structure (unpublished). The classical rays totally reflecting off the cavity boundary are represented as the trajectories in the position (s) - incident angle (χ) phase space (inset). The area of the resonance chainS corresponds to the shaded region in the inset.

It is known that in a non-Hermitian system, there exist the points of a parametric space where its interacting eigenstates coalesce. These points are called Exceptional Points (EPs). Asymmetric microcavities are non-Hermitian systems, due to a cavity loss which causes damping of their resonant states. We confirmed the existence of an EP in a deformation-tunable liquid jet microcavity by observing its resonant states. Atom-cavity systems are non-Hermitian systems as well, due to their cavity losses and a decay of excitations. In this case, we observed the EP by changing the atom-cavity coupling constant [Y. Choi et al., Phys. Rev. Lett. **104**, 153601 (2010)]. This is the first experimental confirmation of an EP in a full quantum system. Many theoretical studies show that the Petermann factor, which is related to the fundamental laser linewidth broadening, diverges at EPs. We verified this phenomenon theoretically for a stadium-type deformed microcavity [S.-Y. Lee et al., Phys. Rev. A **78**, 015805 (2008)]. Experimental study is now ongoing in our laboratory to observe changes of Petermann factor near EPs by using the liquid microjet cavity system.

Quasi-eigenstates around an EP, which is observed experimentally in a deformed quadrupolar microcavity, are illustrated in parameter – frequency space. Interacting modes are represented by different colors according to their properties. When one parameter is fixed and the other parameter is changed, the shortest path connecting modes (example: E→F→G→H→A→B→C→D) has form of a Möbius strip. From S.-B. Lee et al., Phys. Rev. Lett. **103**, 134101 (2009).

The excess noise is another interesting property of non-Hermitian systems. It originates from the bi-orthogonality of eigenfunctions of a non-Hermitian system. It is now understood that the excess noise is physically equivalent to enhancement of spontaneous emission addressed by the Petermann factor. Therefore, the divergence of the Petermann factor near an EP suggests a possibility of realizing a thresholdless laser operating near the EP. This is a totally different approach for thresholdless lasing, which have been usually based on the Purcell effect. If the disappearance of lasing threshold based on the Petermann effect is realized, it would have an enormous impact in the photonics field.

An increase in the number of cavity photons with the relative intensity of pumping. A ratio A/κ of an emission linewidth of a gain medium to a laser emission coefficient is assumed to be 100,000. Here R is the pumping rate and γ is the damping rate of the cavity. The figure shows that a lasing threshold vanishes as Petermann factor K gets close to A/κ. This phenomenon is already suggested theoretically by Eijkelenborg et al. [M. A. van Eijkelenborg et al., Phys. Rev. A **57**, 571 (1998)]

In the previous studies of quantum chaos, interaction between the particles has been neglected. However, there exists interaction between particles in real physical systems. Bose-Einstein Condensate (BEC) is a state of matter occupying the lowest quantum state. In the BEC system, the interaction between particles is very important. Atoms in a BEC have phase coherence and they are described by a single quantum wave function. It is an advantage of the BEC of ultra-cold atoms that its potential and the particle interaction can be controlled precisely. We are working toward realization of a quantum chaotic system based on the BEC. By controlling the interaction between atoms, it is expected that new quantum chaotic phenomena that has not been observed in previous systems would be discovered.

Last updated: February 25, 2014