Feasibility of imaging in nuclear magnetic resonance force microscopy using Boltzmann polarization

Abstract

We report on magnetic resonance force microscopy measurements of the Boltzmann polarization of 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 radio-frequent (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 a source of the RF field. We demonstrate a detection volume sensitivity of only (40nm)3, corresponding to about 1.6×104 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 (10nm)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.

Spin Detection via Parametric Frequency Conversion in a Membrane Resonator

“…This facilitates the integration of our proposed scanning force setup into a high-finesse optical cavity, which allows very sensitive readout of the membrane vibrations and enables a host of optomechanical control techniques [32]. From our analysis with realistic experimental parameters, we currently predict a sensitivity competitive with that of contemporary cantilever-based MRFM [10,11,29,33], while harnessing the advantages of the membrane platform (these we discuss in more detail in Sec. VII B).…”

“…Let us now evaluate the SNR of the feedback-damped system [Eq. (33)]. Driving the pump mode X S stronger boosts the SNR via the parametric conversion into the force F spin [cf.…”

Spin detection via parametric frequency conversion in a membrane resonator

“…This facilitates the integration of our proposed scanning force setup into a high-finesse optical cavity, which allows very sensitive readout and enables a host of optomechanical control techniques [32]. From our analysis with realistic experimental parameters, we predict a sensitivity competitive with that of contemporary cantilever-based MRFM [10,11,29,33] while harnessing the advantages of the new platform. Furthermore, we pinpoint the critical properties of the transducer to achieve an improved performance in the future.…”

“…We proceed to calculate the expected SNR [Eq. (33)] for values motivated by recent experiments [24]. The filtering constant C n [Eq.…”