The Classical and Quantum Theory of Thermal Magnetic Noise

A general theory of thermal magnetic fluctuations near the surface of conductive and/or magnetically permeable slabs is developed; such fluctuations are the magnetic analog of Johnson voltage noise. Starting with the fluctuation-dissipation theorem and Maxwell’s equations, a closed-form expression for the magnetic noise spectral density is derived. Quantum decoherence, as induced by thermal magnetic noise, is analyzed via the independent oscillator heat bath model of Ford, Lewis, and O’Connell. The resulting quantum Langevin equations yield closedform expressions for the spin relaxation times T1, T2, and T1ρ. For realistic experiments in atomic physics, quantum computing, and magnetic resonance force microcopy (MRFM), 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 renormalization, 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 reservoirs, and therefore expresses a general thermodynamic principle. Date: February 1, 2008. Supported by the NIH Biomedical Research Technology Program (BRTP), the NSF Major Research Instrumentation Program (MRI), the U.S. Army Research Office (ARO), and the University of Washington Department of Orthopædics. 1 FLUCTUATION, DISSIPATION, AND ENTANGLEMENT 2