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 |
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Keywords
- Decoherence
- Magnetic noise
- Magnetic resonance force microscopy (MRFM)
- Quantum computation
- Spintronics
- Thermal noise
ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
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.
In: Proceedings of the IEEE, Vol. 91, No. 5, 01.12.2003, p. 799-816.Research output: Contribution to journal › Review article
}
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 -