# Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices

## Abstract

Highlights: > Dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in optical lattices. > Regime of very strong interactions between atoms, the so-called hard core bosons regime. > Character of soliton excitations is dramatically different from the usual Gross-Pitaevskii regime. - Abstract: We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg-de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability of one dimensional solutions to transverse fluctuations. Our results are also relevant for understanding nonequilibrium dynamics of lattice spin models.

- Authors:

- Department of Physics, Harvard University, Cambridge, MA 02138 (United States)
- L.D. Landau Institute for Theoretical Physics, Chernogolovka, Moscow Reg. 142432 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21583309

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 326; Journal Issue: 7; Other Information: DOI: 10.1016/j.aop.2011.04.001; PII: S0003-4916(11)00046-7; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; DECAY; DENSITY; EXCITATION; FLUCTUATIONS; HYDRODYNAMICS; KORTEWEG-DE VRIES EQUATION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; SEMICLASSICAL APPROXIMATION; SOLITONS; SPIN; STABILITY; STRONG INTERACTIONS; THREE-DIMENSIONAL CALCULATIONS; ANGULAR MOMENTUM; APPROXIMATIONS; BASIC INTERACTIONS; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; ENERGY-LEVEL TRANSITIONS; EQUATIONS; FLUID MECHANICS; INTERACTIONS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE PROPERTIES; PHYSICAL PROPERTIES; QUASI PARTICLES; VARIATIONS

### Citation Formats

```
Demler, Eugene, E-mail: demler@physics.harvard.edu, and Maltsev, Andrei.
```*Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices*. United States: N. p., 2011.
Web. doi:10.1016/j.aop.2011.04.001.

```
Demler, Eugene, E-mail: demler@physics.harvard.edu, & Maltsev, Andrei.
```*Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices*. United States. doi:10.1016/j.aop.2011.04.001.

```
Demler, Eugene, E-mail: demler@physics.harvard.edu, and Maltsev, Andrei. Fri .
"Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices". United States. doi:10.1016/j.aop.2011.04.001.
```

```
@article{osti_21583309,
```

title = {Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices},

author = {Demler, Eugene, E-mail: demler@physics.harvard.edu and Maltsev, Andrei},

abstractNote = {Highlights: > Dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in optical lattices. > Regime of very strong interactions between atoms, the so-called hard core bosons regime. > Character of soliton excitations is dramatically different from the usual Gross-Pitaevskii regime. - Abstract: We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg-de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability of one dimensional solutions to transverse fluctuations. Our results are also relevant for understanding nonequilibrium dynamics of lattice spin models.},

doi = {10.1016/j.aop.2011.04.001},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = 7,

volume = 326,

place = {United States},

year = {2011},

month = {7}

}