Scalable Spin Amplification with a Gain Over a Hundred

We propose a scalable and practical implementation of spin amplification which does not require individual addressing nor a specially tailored spin network. We have demonstrated a gain of 140 in a solid-state nuclear spin system of which the spin polarization has been increased to 0.12 using dynamic nuclear polarization with photoexcited triplet electron spins. Spin amplification scalable to a higher gain opens the door to the single spin measurement for a readout of quantum computers as well as practical applications of nuclear magnetic resonance spectroscopy to infinitesimal samples which have been concealed by thermal noise.

Figure 1

(a) Spin amplification referred to by DiVincenzo [1]. (b) Spin amplification of the $S$ spin response signal using selective SWAP gates and (c) that using the hetero-SD process. (d) Scalable version of (a). The $I$ spins are initialized to $|0⟩$ for simplicity, although they do not have to be in practice.

Figure 2

The top dashed line shows the gain $G$ of the SNR of ideal spin amplification [Figs. 1a, 1b] with respect to the number of SWAP gates $N$. The solid lines show the expected gain [Eq. (2)] of the proposed one [Fig. 1c] with respect to the number of the hetero-SD process gates $N$ for different system sizes. The bottom dashed line shows the gain of the direct simple repetitive detection with respect to the number of repetitions $N$.

Figure 3

(a) An experimental procedure of spin amplification using the hetero-SD process [15]. (b) A DNP sequence with integrated solid effect [16]. (c) A schematic diagram of an experimental setup where the sample position at each stage is indicated.

Figure 4

(a) The behaviors of the ${}^1\mathrm{H}$ spin polarization with respect to the number of steps $N$ of spin amplification without rf pulse ($U=\mathit{I}$) and with on-resonance $\pi$ pulses ($U=\mathrm{NOT}$). The dashed line is the theoretical decay. (b) The circles show the spin-amplified frequency response spectra obtained for $N=40$ and 200. They were obtained with the rf pulse with a peak amplitude of 45 kHz (the pulse length is $\sim 3$ times as long as that of 140 kHz). The squares show the spin-amplified frequency response spectra obtained for $N=200$ with the rf pulse with a peak amplitude of 140 kHz. Directly detected ${}^{19}\mathrm{F}$ spectrum vertically magnified is also shown for comparison.