# Numerical Modeling of the Central Spin Problem Using the Spin-Coherent-State P Representation

## Abstract

In this work, we consider decoherence of a central spin by a spin bath. In order to study the nonperturbative decoherence regimes, we develop an efficient mean-field-based method for modeling the spin-bath decoherence, based on the P representation of the central spin density matrix. The method can be applied to longitudinal and transverse relaxation at different external fields. In particular, by modeling large-size quantum systems (up to 16 000 bath spins), we make controlled predictions for the slow long-time decoherence of the central spin.

- Authors:

- ORNL
- Ames Laboratory

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1003653

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 3

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; RELAXATION; SIMULATION; SPIN; numerical modeling; central spin; spin coherent state p

### Citation Formats

```
Al Hassanieh, Khaled A, Dobrovitski, V. V., Dagotto, Elbio R, and Harmon, B. N.
```*Numerical Modeling of the Central Spin Problem Using the Spin-Coherent-State P Representation*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevLett.97.037204.

```
Al Hassanieh, Khaled A, Dobrovitski, V. V., Dagotto, Elbio R, & Harmon, B. N.
```*Numerical Modeling of the Central Spin Problem Using the Spin-Coherent-State P Representation*. United States. doi:10.1103/PhysRevLett.97.037204.

```
Al Hassanieh, Khaled A, Dobrovitski, V. V., Dagotto, Elbio R, and Harmon, B. N. Sun .
"Numerical Modeling of the Central Spin Problem Using the Spin-Coherent-State P Representation". United States.
doi:10.1103/PhysRevLett.97.037204.
```

```
@article{osti_1003653,
```

title = {Numerical Modeling of the Central Spin Problem Using the Spin-Coherent-State P Representation},

author = {Al Hassanieh, Khaled A and Dobrovitski, V. V. and Dagotto, Elbio R and Harmon, B. N.},

abstractNote = {In this work, we consider decoherence of a central spin by a spin bath. In order to study the nonperturbative decoherence regimes, we develop an efficient mean-field-based method for modeling the spin-bath decoherence, based on the P representation of the central spin density matrix. The method can be applied to longitudinal and transverse relaxation at different external fields. In particular, by modeling large-size quantum systems (up to 16 000 bath spins), we make controlled predictions for the slow long-time decoherence of the central spin.},

doi = {10.1103/PhysRevLett.97.037204},

journal = {Physical Review Letters},

number = 3,

volume = 97,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}

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