Persisting correlations of a central spin coupled to large spin baths

Abstract

The decohering environment of a quantum bit is often described by the coupling to a large bath of spins. The quantum bit itself can be seen as a spin $S=1/2$ which is commonly called the central spin. The resulting central spin model describes an important mechanism of decoherence. We provide mathematically rigorous bounds for a persisting magnetization of the central spin in this model with and without magnetic field. In particular, we show that there is a well defined limit of infinite number of bath spins. Only if the fraction of very weakly coupled bath spins tends to 100\% does no magnetization persist.

19 pages, 15 figures, rigorous bounds for the central spin model

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Cited by in corpus (12)

• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
• Measurement Induced Continuous Time Crystals
• Quantum model for mode locking in pulsed semiconductor quantum dots
• Non-equilibrium nuclear spin distribution function in quantum dots subject to periodic pulses
• Efficient algorithms for the dynamics of large and infinite classical central spin models
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots
• Quantum mechanical treatment of large spin baths
• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• Influence of quadrupolar interaction on NMR spectroscopy
• Truncated Wigner approximation for the bosonic model of large spin baths