# Mode locking of a driven Bose-Einstein condensate

## Abstract

We consider the dynamics of a driven Bose-Einstein condensate with positive scattering length. Employing an accustomed variational treatment we show that when the scattering length is time modulated as a(1+{epsilon} sin[{omega}(t)t]), where {omega}(t) increases linearly in time, i.e., {omega}(t)={gamma}t, the response frequency of the condensate locks to the eigenfrequency for small values of {epsilon} and {gamma}. A simple analytical model is presented which explains this phenomenon by mapping it to an auto-resonance, i.e., close to resonance the reduced equations describing the collective behavior of the condensate are equivalent to those of a virtual particle trapped in a finite-depth energy minimum of an effective potential.

- Authors:

- Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100 (Denmark) and Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- (Denmark)
- (United States)

- Publication Date:

- OSTI Identifier:
- 21072402

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.75.036208; (c) 2007 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; EIGENFREQUENCY; MODE LOCKING; POTENTIALS; RESONANCE; SCATTERING LENGTHS; SOLITONS; TRAPPING; VARIATIONAL METHODS; VIRTUAL PARTICLES

### Citation Formats

```
Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720.
```*Mode locking of a driven Bose-Einstein condensate*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.036208.

```
Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, & Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720.
```*Mode locking of a driven Bose-Einstein condensate*. United States. doi:10.1103/PHYSREVE.75.036208.

```
Nicolin, Alexandru I., Jensen, Mogens H., Carretero-Gonzalez, R., Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100, and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720. Thu .
"Mode locking of a driven Bose-Einstein condensate". United States.
doi:10.1103/PHYSREVE.75.036208.
```

```
@article{osti_21072402,
```

title = {Mode locking of a driven Bose-Einstein condensate},

author = {Nicolin, Alexandru I. and Jensen, Mogens H. and Carretero-Gonzalez, R. and Niels Bohr Institute, Blegdamsvej 17, Copenhagen O, DK-2100 and Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720},

abstractNote = {We consider the dynamics of a driven Bose-Einstein condensate with positive scattering length. Employing an accustomed variational treatment we show that when the scattering length is time modulated as a(1+{epsilon} sin[{omega}(t)t]), where {omega}(t) increases linearly in time, i.e., {omega}(t)={gamma}t, the response frequency of the condensate locks to the eigenfrequency for small values of {epsilon} and {gamma}. A simple analytical model is presented which explains this phenomenon by mapping it to an auto-resonance, i.e., close to resonance the reduced equations describing the collective behavior of the condensate are equivalent to those of a virtual particle trapped in a finite-depth energy minimum of an effective potential.},

doi = {10.1103/PHYSREVE.75.036208},

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

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}

}