# Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates

## Abstract

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency using the two-mode approach. Starting from Bloch states, we succeed in obtaining analytical solutions for the TD Schroedinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differ by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one-species condensate in a double-well potential (external Josephson effect)

- Authors:

- Departamento de Fisica, Universidade Federal de Sao Carlos, 13565-905, Sao Carlos, SP (Brazil)
- (Brazil)
- Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-970, Sao Carlos, Sao Paulo (Brazil)

- Publication Date:

- OSTI Identifier:
- 20982244

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032113; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ANALYTICAL SOLUTION; BOSE-EINSTEIN CONDENSATION; CONDENSATES; DEGREES OF FREEDOM; HYPERFINE STRUCTURE; JOSEPHSON EFFECT; PHOTON-ATOM COLLISIONS; POTENTIALS; SCHROEDINGER EQUATION; TIME DEPENDENCE; TRAPS; TUNNEL EFFECT; WAVE FUNCTIONS

### Citation Formats

```
Duzzioni, E. I., Mizrahi, S. S., Sanz, L., Instituto de Fisica, Universidade Federal de Uberlandia, Caixa Postal 593, 38400-902, Uberlandia, Minas Gerais, and Moussa, M. H. Y.
```*Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032113.

```
Duzzioni, E. I., Mizrahi, S. S., Sanz, L., Instituto de Fisica, Universidade Federal de Uberlandia, Caixa Postal 593, 38400-902, Uberlandia, Minas Gerais, & Moussa, M. H. Y.
```*Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates*. United States. doi:10.1103/PHYSREVA.75.032113.

```
Duzzioni, E. I., Mizrahi, S. S., Sanz, L., Instituto de Fisica, Universidade Federal de Uberlandia, Caixa Postal 593, 38400-902, Uberlandia, Minas Gerais, and Moussa, M. H. Y. Thu .
"Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates". United States.
doi:10.1103/PHYSREVA.75.032113.
```

```
@article{osti_20982244,
```

title = {Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates},

author = {Duzzioni, E. I. and Mizrahi, S. S. and Sanz, L. and Instituto de Fisica, Universidade Federal de Uberlandia, Caixa Postal 593, 38400-902, Uberlandia, Minas Gerais and Moussa, M. H. Y.},

abstractNote = {We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency using the two-mode approach. Starting from Bloch states, we succeed in obtaining analytical solutions for the TD Schroedinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differ by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one-species condensate in a double-well potential (external Josephson effect)},

doi = {10.1103/PHYSREVA.75.032113},

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}

}