# Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions

## Abstract

We investigate the quantum signatures of classical nonlinear resonances by making the analytic connection between the quantum wave functions and the classical periodic orbits for the uncoupled systems. It is found that the highly efficient extension of the localized coherent states within the classical caustics is an intriguing phenomenon in mesoscopic systems with nonlinear resonances. With the theoretical analysis, we experimentally demonstrate that the laser resonator with an intracavity saturable absorber can be employed to visualize the wave patterns analogous to the quantum wave functions associated with Fermi resonance.

- Authors:

- Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan (China)

- Publication Date:

- OSTI Identifier:
- 20709842

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.72.056210; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION; ANNIHILATION OPERATORS; CHAOS THEORY; EIGENSTATES; FERMI RESONANCE; LASER CAVITIES; LASERS; NONLINEAR PROBLEMS; ORBITS; PERIODICITY; RESONATORS; WAVE FUNCTIONS

### Citation Formats

```
Chen, Y.F., Lu, T.H., Su, K.W., and Huang, K.F.
```*Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevE.72.056210.

```
Chen, Y.F., Lu, T.H., Su, K.W., & Huang, K.F.
```*Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions*. United States. doi:10.1103/PhysRevE.72.056210.

```
Chen, Y.F., Lu, T.H., Su, K.W., and Huang, K.F. Tue .
"Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions". United States.
doi:10.1103/PhysRevE.72.056210.
```

```
@article{osti_20709842,
```

title = {Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions},

author = {Chen, Y.F. and Lu, T.H. and Su, K.W. and Huang, K.F.},

abstractNote = {We investigate the quantum signatures of classical nonlinear resonances by making the analytic connection between the quantum wave functions and the classical periodic orbits for the uncoupled systems. It is found that the highly efficient extension of the localized coherent states within the classical caustics is an intriguing phenomenon in mesoscopic systems with nonlinear resonances. With the theoretical analysis, we experimentally demonstrate that the laser resonator with an intracavity saturable absorber can be employed to visualize the wave patterns analogous to the quantum wave functions associated with Fermi resonance.},

doi = {10.1103/PhysRevE.72.056210},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}

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