Shaped Pulses for Energy-Efficient High-Field NMR at the Nanoscale

Abstract

The realisation of optically detected magnetic resonance via nitrogen vacancy centers in diamond faces challenges at high magnetic fields which include growing energy consumption of control pulses as well as decreasing sensitivities. Here we address these challenges with the design of shaped pulses in microwave control sequences that achieve orders magnitude reductions in energy consumption and concomitant increases in sensitivity when compared to standard top-hat microwave pulses. The method proposed here is general and can be applied to any quantum sensor subjected to pulsed control sequences.We consider the detection of nuclear spins at a strong magnetic field B z 1 T. If the Rabi frequency of the MW driving field is limited, then, for sufficiently high B z , nuclear spins complete several oscillations during a π-pulse. Now we analyse the reduction in sensitivity due to this effect. The Hamiltonian of an NV-nucleus system isHere, S z = |1 1|−|−1 −1|, S x = 1/ √ 2(|1 0|+|−1 0|+H.c.), D = (2π) × 2.87 GHz, γ e ≈ −(2π) × 28.024 GHz/T and A is the hyperfine vector of the NV-nucleus interaction [36]. For B z 1 T, the NV energy splitting between the |0 ↔ | ± 1 arXiv:1805.01741v2 [quant-ph] 31 Oct 2018Here F z (t) is the modulation function that appears as a consequence of the MW pulse sequence, ω n is the nuclear resonance frequency, and A ⊥ x,y are electron-nucleus coupling constants (see Appendix A). We consider periodic pulse sequences of period T such that F z (t) = l f l cos (lω m t) where ω m = 2π T and f l = 2 T T 0 F z (s) cos (lω m s) ds. Examples of these sequences are those of the XY family [37,38] or more sophisticated schemes [17,[39][40][41][42][43][44][45]. For kω m = ω n (resonance condition with the kth harmonic, i.e. for l = k ) Eq. (2) is

Selective hybrid spin interactions with low radiation power

“…However, in real cases we deal with finite-width pulses such that, e.g., when caused by a H c with constant Ω, a time t π = π Ω is needed to produce a π pulse. This has adverse consequences on the NV-nuclei dynamics such as the appearance of spurious resonances [32][33][34] , or the drastic reduction of the NMR sensitivity at large B z 35 . Note that, in Ref.…”

“…Note that, in Ref. 35 a strategy to signal recovery is also presented, while that approach does not lead to selective nuclear interactions. However, we will demonstrate that the introduction of extended pulses with tailored Ω leads to tunable NV-nuclei interactions with low power MW radiation.…”

“…Unfortunately, to consider π pulses as instantaneous in situations with large B z is not correct, since nuclei have time to evolve during π pulse execution leading to signal drop 35 . Hence, if one cannot deliver a huge MW power to the sample, the results in Fig.…”

Modulated Continuous Wave Control for Energy-Efficient Electron-Nuclear Spin Coupling

“…These power requirements also imply significant challenges for their use in biological samples, because a strong microwave heats the organic matter, perturbing its dynamics or even destroying it. In recent work this challenge was identified and addressed [50]. However, in microwave power sensitive applications continuous wave may offer advantages as their average energy consumption at the same decoupling and sensing efficiency can be lower than for pulsed schemes [36].…”

Modulated Continuous Wave Control for Energy-efficient Electron-nuclear Spin Coupling

“…These power requirements also imply significant challenges for their use in biological samples, because a strong microwave heats the organic matter, perturbing its dynamics or even destroying it. In recent work this challenge was identified and addressed [50]. However, in microwave power sensitive applications continuous wave may offer advantages as their average energy consumption at the same decoupling and sensing efficiency can be lower than for pulsed schemes [36].…”