Royal Society of Chemistry eBooks

Workshop 4: The Dynamics of an Ensemble of Spin-1/2 Pairs and Spin Relaxation

Giuseppe Pileio

Published Jun 13, 2022• 0 citations

Abstract

In this workshop, the reader can practice with calculating the dynamics of an ensemble of spin-1/2 pairs, calculating the evolution of the state of the ensemble across a pulse sequence, calculating the dynamics due to spin relaxation and deriving spin relaxation rates.

DOI: 10.1039/9781837670871-00188

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Workshop 3: The Dynamics of Single Spin-1/2 Systems

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Royal Society of Chemistry eBooks

Workshop 4: The Dynamics of an Ensemble of Spin-1/2 Pairs and Spin Relaxation

Giuseppe Pileio

Published Jun 13, 2022• 0 citations

Publisher

Abstract

DOI: 10.1039/9781837670871-00188

Related papers

Workshop 3: The Dynamics of Single Spin-1/2 Systems

Giuseppe Pileio

Royal Society of Chemistry eBooksJun 13, 20220 citations

A geometric framework for spin relaxation

Sophia N. Fricke, Kieren A. Harkins, Ashok Ajoy +1 more

Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal ( $R_1$ ) and transverse ( $R_2$ ) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which $R_1$ and $R_2$ emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized $^{13}C$ spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal ($R_1$) and transverse ($R_2$) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which $R_1$ and $R_2$ emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized $^{13}C$ spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.

quant-pharXiv:2607.21569Jul 24, 2026

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Giuseppe Pileio

Royal Society of Chemistry eBooksJun 13, 20220 citations

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Mitsuhiro Arikawa

素粒子論研究Apr 20, 20060 citations

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G. A. Bochkin, Edward B. Fel’dman, S. G. Vasil’ev

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Liu Shao-Ding, Mu-Tian Cheng, Xia Wang +2 more

The second-order cross correlation function of the photon emission and the polarization density matrix of the photon pairs emitted from the biexciton system of single semiconductor quantum dots under pulsed excitation were calculated using the dynamical population density matrix equations and quantum regression theorem. The entanglement of the photon pairs emitted from the single quantum dot with degenerate exciton states were investigated, and the relationship between the entanglement and the spin relaxation rate was also discussed. The simulations revealed that the spin relaxation destroys the entanglement of the photon pairs emitted from this system.The second-order cross correlation function of the photon emission and the polarization density matrix of the photon pairs emitted from the biexciton system of single semiconductor quantum dots under pulsed excitation were calculated using the dynamical population density matrix equations and quantum regression theorem. The entanglement of the photon pairs emitted from the single quantum dot with degenerate exciton states were investigated, and the relationship between the entanglement and the spin relaxation rate was also discussed. The simulations revealed that the spin relaxation destroys the entanglement of the photon pairs emitted from this system.

Acta Physica SinicaJan 1, 20072 citations

Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal (

R_1

) and transverse (

R_2

) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which

R_1

and

R_2

emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized

^{13}C

spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.