Geometric Quantum Noise of Spin

Abstract

The presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nano-magnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön (AES) effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

8 pages including Supplemental Material

References in corpus (6)

• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Bang-bang control of fullerene qubits using ultra-fast phase gates
• Spin-torque shot noise in magnetic tunnel junctions
• Transient fluctuation relations for time-dependent particle transport
• The Interplay of Spin and Charge Channels in Zero Dimensional Systems
• Stochastic dynamics of magnetization in a ferromagnetic nanoparticle out of equilibrium

Cited by in corpus (3)

• Strong non-equilibrium effects in spin torque systems
• Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles
• Coulomb blockade of chiral Majorana and complex fermions far from equilibrium