# Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit

## Abstract

Coherent properties of a two-dimensional spatially periodic structure, polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function overlapping for both photonic and atomic states, a cubic-quintic complex nonlinear Schroedinger equation is derived for the dynamics of coupled atom-light states, wave function of low-branch polaritons, associated with PolC in the continuous limit. A variational approach predicts that a stable ground-state wave function of PolC exists but is accompanied by an oscillating width. For a negative scattering length, the wave function collapses in the presence of a small quintic nonlinearity appearing due to a three-body polariton interaction. By studying the nonequilibrium (dissipative) dynamics of polaritons with adiabatic approximation, we have shown that the collapse of PolC wave function can be prevented even in the presence of small decaying of a number of polariton particles.

- Authors:

- Department of Physics and Applied Mathematics, Vladimir State University, Gorky Street 87, RU-600000 Vladimir (Russian Federation)
- (China)

- Publication Date:

- OSTI Identifier:
- 22058772

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ADIABATIC APPROXIMATION; ATOMS; CRYSTALS; GROUND STATES; NONLINEAR PROBLEMS; POLARONS; SCATTERING LENGTHS; SCHROEDINGER EQUATION; THREE-BODY PROBLEM; TWO-DIMENSIONAL CALCULATIONS; VARIATIONAL METHODS; VISIBLE RADIATION; WAVE FUNCTIONS

### Citation Formats

```
Sedov, E. S., Alodjants, A. P., Arakelian, S. M., Lin, Y. Y., Lee, R.-K., and Institute of Photonics Technologies, National Tsing-Hua University, Hsinchu 300, Taiwan.
```*Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.013813.

```
Sedov, E. S., Alodjants, A. P., Arakelian, S. M., Lin, Y. Y., Lee, R.-K., & Institute of Photonics Technologies, National Tsing-Hua University, Hsinchu 300, Taiwan.
```*Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit*. United States. doi:10.1103/PHYSREVA.84.013813.

```
Sedov, E. S., Alodjants, A. P., Arakelian, S. M., Lin, Y. Y., Lee, R.-K., and Institute of Photonics Technologies, National Tsing-Hua University, Hsinchu 300, Taiwan. Fri .
"Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit". United States. doi:10.1103/PHYSREVA.84.013813.
```

```
@article{osti_22058772,
```

title = {Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit},

author = {Sedov, E. S. and Alodjants, A. P. and Arakelian, S. M. and Lin, Y. Y. and Lee, R.-K. and Institute of Photonics Technologies, National Tsing-Hua University, Hsinchu 300, Taiwan},

abstractNote = {Coherent properties of a two-dimensional spatially periodic structure, polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function overlapping for both photonic and atomic states, a cubic-quintic complex nonlinear Schroedinger equation is derived for the dynamics of coupled atom-light states, wave function of low-branch polaritons, associated with PolC in the continuous limit. A variational approach predicts that a stable ground-state wave function of PolC exists but is accompanied by an oscillating width. For a negative scattering length, the wave function collapses in the presence of a small quintic nonlinearity appearing due to a three-body polariton interaction. By studying the nonequilibrium (dissipative) dynamics of polaritons with adiabatic approximation, we have shown that the collapse of PolC wave function can be prevented even in the presence of small decaying of a number of polariton particles.},

doi = {10.1103/PHYSREVA.84.013813},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}