核磁共振力显微术中玻尔兹曼极化成像的可行性
Feasibility of imaging using Boltzmann polarization in nuclear Magnetic Resonance Force Microscopy
摘要：
我们报告了磁共振力显微镜测量的玻尔兹曼极化的核自旋在铜通过检测软悬臂梁的频率偏移。我们使用的布洛赫方程的时间相关的解决方案，推导出一个简洁的方程描述的效果，射频磁场上的和非共振自旋在高磁场梯度。然后，我们将此理论应用于饱和实验上进行的100 nm厚的铜层，在那里我们使用的更高的模式的悬臂作为源的射频场。我们证明了检测体积的灵敏度只有（40 nm）$^3$，对应于约1.6 $\cdot 10^4$极化铜核自旋。我们提出了一个实验的质子，在适当的技术改进，基于频移的磁共振成像的分辨率优于（10 nm）$^3$可能。实现这种分辨率将使基于玻尔兹曼偏振的成像与更传统的基于随机自旋波动的成像竞争，并有可能在毫开尔文温度下工作。
英文摘要：
We report on Magnetic Resonance Force Microscopy measurements of the Boltzmann polarization of the nuclear spins in copper by detecting the frequency shift of a soft cantilever. We use the time-dependent solution of the Bloch equations to derive a concise equation describing the effect of rf magnetic fields on both on- and off-resonant spins in high magnetic field gradients. We then apply this theory to saturation experiments performed on a 100 nm thick layer of copper, where we use the higher modes of the cantilever as source of the rf field. We demonstrate a detection volume sensitivity of only (40 nm)$^3$, corresponding to about 1.6$\cdot 10^4$ polarized copper nuclear spins. We propose an experiment on protons where, with the appropriate technical improvements, frequency-shift based magnetic resonance imaging with a resolution better than (10 nm)$^3$ could be possible. Achieving this resolution would make imaging based on the Boltzmann polarization competitive with the more traditional stochastic spin-fluctuation based imaging, with the possibility to work at milliKelvin temperatures.
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