# Stability of Bose-Einstein condensates in a Kronig-Penney potential

## Abstract

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small q and the dynamical instability is caused by the excitations with q={pi}/a at their onsets, where q is the quasimomentum of excitation and a is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.

- Authors:

- National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)
- (Japan)
- Dipartimento di Fisica, Universita di Trento and CNR-INFM BEC Center, I-38050 Povo, Trento (Italy)

- Publication Date:

- OSTI Identifier:
- 20982381

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.033612; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOGOLYUBOV METHOD; BOSE-EINSTEIN CONDENSATION; EFFECTIVE MASS; EXCITATION; INSTABILITY; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; PHONONS; POTENTIALS; SIMULATION; SPECTRA; STABILITY; SUPERFLUIDITY; TRANSMISSION

### Citation Formats

```
Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, and Tsuchiya, Shunji.
```*Stability of Bose-Einstein condensates in a Kronig-Penney potential*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.033612.

```
Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, & Tsuchiya, Shunji.
```*Stability of Bose-Einstein condensates in a Kronig-Penney potential*. United States. doi:10.1103/PHYSREVA.75.033612.

```
Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, and Tsuchiya, Shunji. Thu .
"Stability of Bose-Einstein condensates in a Kronig-Penney potential". United States.
doi:10.1103/PHYSREVA.75.033612.
```

```
@article{osti_20982381,
```

title = {Stability of Bose-Einstein condensates in a Kronig-Penney potential},

author = {Danshita, Ippei and Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555 and Tsuchiya, Shunji},

abstractNote = {We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small q and the dynamical instability is caused by the excitations with q={pi}/a at their onsets, where q is the quasimomentum of excitation and a is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.},

doi = {10.1103/PHYSREVA.75.033612},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}