# Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate

## Abstract

We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of themmore »

- Authors:

- Department of Physics, Bilkent University, 06800 Ankara (Turkey)

- Publication Date:

- OSTI Identifier:
- 20974627

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.023611; (c) 2006 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; BOSE-EINSTEIN CONDENSATION; DENSITY; DISPERSION RELATIONS; EXCITATION; INTERACTIONS; MEAN-FIELD THEORY; OPTICAL MODES; OSCILLATIONS; PHASE TRANSFORMATIONS; SYMMETRY; WAVELENGTHS

### Citation Formats

```
Keceli, M., and Oktel, M. Oe.
```*Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.023611.

```
Keceli, M., & Oktel, M. Oe.
```*Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate*. United States. doi:10.1103/PHYSREVA.73.023611.

```
Keceli, M., and Oktel, M. Oe. Wed .
"Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate". United States.
doi:10.1103/PHYSREVA.73.023611.
```

```
@article{osti_20974627,
```

title = {Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate},

author = {Keceli, M. and Oktel, M. Oe.},

abstractNote = {We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.},

doi = {10.1103/PHYSREVA.73.023611},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}