### Abstract

Thermal fluctuations generate magnetic noise in the vicinity of any conductive and/or magnetically permeable solid. This magnetic noise plays a fundamental role in the design of spintronic devices: namely, it sets the time scale during which electron spins retain their coherence. This paper presents a rigorous classical and quantum analysis of thermal magnetic noise, together with practical engineering examples. Starting with the fluctuation-dissipation theorem and Maxwell's equations, a closed-form expression for the spectral density of thermal magnetic noise is derived. Quantum decoherence, as induced by thermal magnetic noise, is analyzed via the independent oscillator heat bath model of Ford et al. The resulting quantum Langevin equations yield closed-form expressions for the spin relaxation times. For realistic experiments in spintronics, magnetic resonance force microscopy, Bose-Einstein condensates, atomic physics, and solid-state quantum computing, the predicted relaxation rates are rapid enough that substantial experimental care must be taken to minimize them. At zero temperature, the quantum entanglement between a spin state and a thermal reservoir is computed. The same Hamiltonian matrix elements that govern fluctuation and dissipation are shown to also govern entanglement and renonnalization, and a specific example of a fluctuation-dissipation- entanglement theorem is constructed. We postulate that this theorem is independent of the detailed structure of thermal resenvirs, and therefore expresses a general thermodynamic principle.

Original language | English (US) |
---|---|

Pages (from-to) | 799-816 |

Number of pages | 18 |

Journal | Proceedings of the IEEE |

Volume | 91 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 2003 |

Externally published | Yes |

### Fingerprint

### Keywords

- Decoherence
- Magnetic noise
- Magnetic resonance force microscopy (MRFM)
- Quantum computation
- Spintronics
- Thermal noise

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the IEEE*,

*91*(5), 799-816. https://doi.org/10.1109/JPROC.2003.811796

**The classical and quantum theory of thermal magnetic noise, with applications in spintronics and quantum microscopy.** / Sidles, John A.; Garbini, Joseph L.; Dougherty, William M.; Chao, Shih-Hui.

Research output: Contribution to journal › Review article

*Proceedings of the IEEE*, vol. 91, no. 5, pp. 799-816. https://doi.org/10.1109/JPROC.2003.811796

}

TY - JOUR

T1 - The classical and quantum theory of thermal magnetic noise, with applications in spintronics and quantum microscopy

AU - Sidles, John A.

AU - Garbini, Joseph L.

AU - Dougherty, William M.

AU - Chao, Shih-Hui

PY - 2003/12/1

Y1 - 2003/12/1

N2 - Thermal fluctuations generate magnetic noise in the vicinity of any conductive and/or magnetically permeable solid. This magnetic noise plays a fundamental role in the design of spintronic devices: namely, it sets the time scale during which electron spins retain their coherence. This paper presents a rigorous classical and quantum analysis of thermal magnetic noise, together with practical engineering examples. Starting with the fluctuation-dissipation theorem and Maxwell's equations, a closed-form expression for the spectral density of thermal magnetic noise is derived. Quantum decoherence, as induced by thermal magnetic noise, is analyzed via the independent oscillator heat bath model of Ford et al. The resulting quantum Langevin equations yield closed-form expressions for the spin relaxation times. For realistic experiments in spintronics, magnetic resonance force microscopy, Bose-Einstein condensates, atomic physics, and solid-state quantum computing, the predicted relaxation rates are rapid enough that substantial experimental care must be taken to minimize them. At zero temperature, the quantum entanglement between a spin state and a thermal reservoir is computed. The same Hamiltonian matrix elements that govern fluctuation and dissipation are shown to also govern entanglement and renonnalization, and a specific example of a fluctuation-dissipation- entanglement theorem is constructed. We postulate that this theorem is independent of the detailed structure of thermal resenvirs, and therefore expresses a general thermodynamic principle.

AB - Thermal fluctuations generate magnetic noise in the vicinity of any conductive and/or magnetically permeable solid. This magnetic noise plays a fundamental role in the design of spintronic devices: namely, it sets the time scale during which electron spins retain their coherence. This paper presents a rigorous classical and quantum analysis of thermal magnetic noise, together with practical engineering examples. Starting with the fluctuation-dissipation theorem and Maxwell's equations, a closed-form expression for the spectral density of thermal magnetic noise is derived. Quantum decoherence, as induced by thermal magnetic noise, is analyzed via the independent oscillator heat bath model of Ford et al. The resulting quantum Langevin equations yield closed-form expressions for the spin relaxation times. For realistic experiments in spintronics, magnetic resonance force microscopy, Bose-Einstein condensates, atomic physics, and solid-state quantum computing, the predicted relaxation rates are rapid enough that substantial experimental care must be taken to minimize them. At zero temperature, the quantum entanglement between a spin state and a thermal reservoir is computed. The same Hamiltonian matrix elements that govern fluctuation and dissipation are shown to also govern entanglement and renonnalization, and a specific example of a fluctuation-dissipation- entanglement theorem is constructed. We postulate that this theorem is independent of the detailed structure of thermal resenvirs, and therefore expresses a general thermodynamic principle.

KW - Decoherence

KW - Magnetic noise

KW - Magnetic resonance force microscopy (MRFM)

KW - Quantum computation

KW - Spintronics

KW - Thermal noise

UR - http://www.scopus.com/inward/record.url?scp=33646794968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646794968&partnerID=8YFLogxK

U2 - 10.1109/JPROC.2003.811796

DO - 10.1109/JPROC.2003.811796

M3 - Review article

AN - SCOPUS:33646794968

VL - 91

SP - 799

EP - 816

JO - Proceedings of the IEEE

JF - Proceedings of the IEEE

SN - 0018-9219

IS - 5

ER -