Direct Measurement of the Flip-Flop Rate of Electron Spins in the Solid State

Electron spins in solids have a central role in many current and future spin-based devices, ranging from sensitive sensors to quantum computers. Many of these apparatuses rely on the formation of well-defined spin structures (e.g., a 2D array) with controlled and well-characterized spin-spin interactions. While being essential for device operation, these interactions can also result in undesirable effects, such as decoherence. Arguably, the most important pure quantum interaction that causes decoherence is known as the flip-flop process, where two interacting spins interchange their quantum state. Currently, for electron spins, the rate of this process can only be estimated theoretically, or measured indirectly, under limiting assumptions and approximations, via spin-relaxation data. This work experimentally demonstrates how the flip-flop rate can be directly and accurately measured by examining spin-diffusion processes in the solid state for physically fixed spins. Under such terms, diffusion can occur only through this flip-flop-mediated quantum-state exchange and not via actual spatial motion. Our approach is implemented on two types of samples, phosphorus-doped Si-28 and nitrogen vacancies in diamond, both of which are significantly relevant to quantum sensors and information processing. However, while the results for the former sample are conclusive and reveal a flip-flop rate of approximately 12.3 Hz, for the latter sample only an upper limit of approximately 0.2 Hz for this rate can be estimated.