# Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit

## Abstract

Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.

- Authors:

- Faculty of Science, Assiut University, Assiut (Egypt)
- Faculty of Science, Al-Azhar University, Nasr City, Cairo (Egypt)

- Publication Date:

- OSTI Identifier:
- 21583330

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 326; Journal Issue: 9; Other Information: DOI: 10.1016/j.aop.2011.06.005; PII: S0003-4916(11)00106-0; 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; ASYMPTOTIC SOLUTIONS; CURRENTS; DAMPING; ELECTRONIC CIRCUITS; GEOMETRY; GLOBAL POSITIONING SYSTEM; PARTURITION; RESONATORS; ELECTRONIC EQUIPMENT; EQUIPMENT; MATHEMATICAL SOLUTIONS; MATHEMATICS

### Citation Formats

```
Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com, and Obada, A.-S.F.
```*Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit*. United States: N. p., 2011.
Web. doi:10.1016/j.aop.2011.06.005.

```
Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com, & Obada, A.-S.F.
```*Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit*. United States. doi:10.1016/j.aop.2011.06.005.

```
Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com, and Obada, A.-S.F. Thu .
"Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit". United States. doi:10.1016/j.aop.2011.06.005.
```

```
@article{osti_21583330,
```

title = {Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit},

author = {Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com and Obada, A.-S.F.},

abstractNote = {Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.},

doi = {10.1016/j.aop.2011.06.005},

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

issn = {0003-4916},

number = 9,

volume = 326,

place = {United States},

year = {2011},

month = {9}

}