Diamond Spins Show Relaxation Varies With Pulse Sequence Order

Researchers have demonstrated that the order of pulses in a quantum control sequence directly influences how spin relaxation occurs, challenging the long-standing view that relaxation can be fully described by only two independent rates. Sophia N. Fricke and colleagues from University of California used hyperpolarized carbon-13 (^13C) spins in diamond containing nitrogen-vacancy (NV) centers to show that pulse sequences applied in noncommuting directions generate off-diagonal relaxation components that vary with transmitter frequency. Their findings indicate that spin relaxation is more accurately described by a single, experimentally measurable relaxation tensor in Liouville space rather than by separate longitudinal and transverse relaxation rates. The researchers argue that this tensor is not merely a mathematical construct but a physical quantity that can be directly probed through carefully designed pulse sequences.

Spin relaxation is a fundamental process in magnetic resonance and quantum technologies, describing how quantum spins lose coherence and return to equilibrium after being disturbed. Traditionally, this behavior has been characterized using two phenomenological parameters known as longitudinal (T1) and transverse (T2) relaxation times. While this framework has successfully explained many experimental observations, it assumes that relaxation occurs independently along different directions and does not fully capture the complexity of spin dynamics under more sophisticated quantum control protocols.

To investigate these effects, the researchers performed experiments on hyperpolarized ^13C spins in diamond with nitrogen-vacancy centers, a platform widely used for quantum sensing and quantum information research because of its exceptional spin coherence and precise optical control. By applying pulse sequences in different orders, they compared commuting and noncommuting operations. Commuting pulse sequences produced the expected diagonal relaxation matrices, whereas noncommuting sequences generated frequency-dependent off-diagonal elements. These results demonstrate that the observed relaxation depends not only on the properties of the material but also on the geometry and ordering of the applied control operations.

The study also examined the geometric phase accumulated during spin evolution, providing additional evidence that relaxation is closely connected to the geometry of quantum state evolution rather than representing only a simple dissipative loss of energy. This perspective suggests that relaxation should be viewed as motion across the quantum state manifold, where both geometric and dissipative effects contribute to the observed dynamics. The experimentally measured relaxation tensor therefore offers a unified description capable of capturing these directional and geometric features.

By replacing the traditional two-rate model with an experimentally accessible tensor framework, the research provides a more comprehensive picture of spin relaxation in quantum systems. The findings could improve the interpretation of magnetic resonance experiments, enhance quantum sensing techniques based on diamond NV centers, and support the development of more accurate methods for controlling quantum information. More broadly, the work establishes a new framework for understanding relaxation as a geometric property of quantum dynamics, opening opportunities for future advances in quantum computing, precision measurement, and spin-based quantum technologies.