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

Abstract

Electron spins in solids have a central role in many current and future spinbased devices, ranging from sensitive sensors to quantum computers (QC). 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 for the first time 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 was implemented on two types of samples, phosphorus-doped 28 Si and nitrogen vacancies (NV) 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 ~12.3 Hz, for the latter sample only an upper limit of ~0.2 Hz for this rate could be estimated.

Emergent hydrodynamics in a strongly interacting dipolar spin ensemble

“…On the experimental front, tremendous progress in time-resolved measurement techniques has enabled the direct observation of emergent classical diffusion in several classes of quantum systems (3,4,(34)(35)(36)(37)(38)(39)(40)(41).…”

Sensing Coherent Dynamics of Electronic Spin Clusters in Solids

“…Additionally, electronic spin dynamics external to an NV could enable a range of potential sensing applications. For example, it can be employed following a recent proposal to measure the spin diffusion rate between intra-molecular spin labels in biomolecules [13,14], to obtain improved distance measurements beyond the standard DEER protocol [38,39].…”

“…For example, a quantum register consisting of several coherently coupled electronic spins could serve as the basic building block of quantum information processors and quantum networks [6][7][8]. Additionally, recent proposals indicate that dynamics between many unpolarized electronic spins can mediate fully coherent coupling between distant qubits to be used for quantum state transfer [9][10][11][12]; measuring the coherent flip-flop rate between a pair of electronic spins could allow for sensitive distance measurements in individual molecules in nanoscale magnetic resonance imaging [13,14].…”

“…However, such an interaction is a challenge to observe [13,14]. In particular, the identical spins need to be close enough to interact strongly, such that the spins cannot be spatially or spectrally resolved, to allow for polarization exchange.…”

Measuring electron spin flip-flops through nuclear spin echo decays

“…idealized scenarios, 4,5 but in practice inhomogeneous broadening from other mechanisms can obscure their calculation or measurement. 1,[5][6][7] For flip-flops of 31 P donor electron spins in silicon, measurements of their rates have previously required the use of magnetic field gradients 1,7 in combination with multiple sets of Hahn echo decays. Here we demonstrate how Electron-Nuclear Double Resonance (ENDOR) experiments may be used to determine electron spin flip-flop rates without the use of such gradients.…”