Magnetometry: Toward single-molecule NMR and single-nucleus sensing

Nuclear magnetic resonance (NMR) has numerous applications in medicine (such as in the well-known magnetic resonance imagining technology), biology, chemistry, materials science, physics, etc. This technology is still undergoing fast development. The most important perspective is to push the sensitivity to the single-molecule level to realize imaging resolution to the nanometer or even atomic scale. Moreover, in the recent 15 years, scientists are considering nuclear magnetic resonance for quantum computing. However, magnetic dipoles of nuclear spins are extremely weak, and only a large amount of molecules can produce detectable signals. This difficulty limits the imaging resolution and makes large-scale nuclear spin quantum computing an impossible mission.

General idea

Detection of single nuclear spin clusters and single-molecule NMR are possible by cascade amplification of the weak signals/noises from the clusters/molecules

Key points:

  1. Detection of single photons is matured technology. A photon has energy much higher than room temperature and therefore the signal-to-noise ratio is large.

  2. ODMR (optically detected magnetic resonance) can measure spin coherence of a single electron, if the optical transitions distinguish the spin states (by selection rules).

  3.  ODMR therefore measures a single nuclear spin if it is strongly coupled to the electron spin (> MHz coupling).

  4. Distant nuclear spins or single molecules (with kHz coupling to the electron spin), however, usually cause a broaden noise spectrum and induce decoherence of the electron spin.

  5. If two or more nuclear spins are strongly coupled to each other (with coupling ~ kHz, e.g.) to form a cluster, they have chracteristic flip-flops between themselves. This may cause fingerprint oscillations onto the decoherence profile of the electron spin, which can be used to identify the nuclear spin cluster.

  6. The weak noises due to nuclear spin transitions in single molecules can be greatly enhanced by many-pulse dynamical decoupling (see details below). If the transitions have frequencies higher than the noise spectrum due to the background nuclear spins, the electron spin coherence will present fingerprint dips corresponding to NMR of the molecules.

Nitrogen-vacancy center in diamond

Features of negatively charged NV centers in diamond:

  1. Deep level with chemical and thermal stabilities
  2. Optical polarization & detection are allowed (ODMR)
  3. Spin-orbit coupling is weak (for C-atoms are light) and phonon scattering is weak even at room temperature
  4. Small abundance of C-13 (1.1%) and other isotopes of C have no nuclear spin: Weak Overhauser field noises
  5. Ion-implantation of N with nanometer resolution

The electron spin of NV centers in high-purity (Type IIa) diamond has long coherence time (~millisecond), and there is very sensitive to weak magnetic noises. Good candidate for nano-magnetometry.

 

Figure: Structure (top) and optical and spin transitions of an NV center in diamond 

Atomic-scale magnetometry of distant C-13 dimers

Among the background of C-13 nuclear spins in diamond, the nuclear spin fluctuations are mostly featureless. But if two or more c-13 are closely located to each other (not necessary close to the NV center), like the dimer shown in the right figure, the interaction within the C-13 cluster can be comparable to the hyperfine interaction with the NV center, and the characteristic transitions of the cluster can induce  coherent oscillations on the NV center spin decoherence profile . Such characteristic oscillations are sensitive to the location and orientation of the cluster.

The dependence of the coherent oscillations on the external field and the dynamical decoupling control constitutes the fingerprint of a nuclear spin cluster, by which a cluster can be identified with atomic scale resolution and single-nucleus sensitivity. Right figure (bottom) shows the fingerprint oscillation induced by a dimer as the field direction [Zhao et al, Nature Nanotech. (2011)]. When the dimer is shifted by one atom site (along [110] direction), the coherent oscillations are significantly different.

Figure: Top-left, a C-13 dimer; top-right, coherent oscillation due to a C-13 dimer onto the NV center spin coherence; bottom, NV center spin coherence versus time and external field direction, in which (a) contains both background and the dimer contribution, (b) contains only dimer contribution and (c) is the cross-section plot. 
  1.    

Single-molecule NMR by many-pulse dynamical decoupling

By dynamical decoupling (DD), the NV center spins is flipped repeatedly by microwave pulses. Effectively, the field felt by the electron spin is inversed repeatedly. This tends to cancel the noises  (by a modulation function alternating between 1 and -1) and prolongs the NV center spin coherence time. But when a noise has the same frequency as the modulation (or an integer multiple), the noise is amplified instead.  Thus, a relatively high-frequency noise (10~100 kHz) from NMR transitions of single molecules, though extremely weak, can induce sharp dips in the NV center spin coherence under protection of many-pulse DD.  

Figure [from Zhao et al, Nature Nanotech. (2011)]:  Coherence of an NV center spin under 100-pulse periodic DD control. 5 water or methane molecules are on the diamond surface. The center is 10 nm below the surface. No external magnetic field is applied.

ODMR of NV center spin coherence under many-pulse DD can detect NMR of single molecules (e.g., 5 water or methane molecules in the above figure).

Features:

  • Full information about nuclear spin interaction within molecules (c.f.
    liquid-state NMR: nuclear spin interactions within molecules are averaged out due to fast rotation of the molecules    )

  • High-resolution (c.f., solid-state NMR: interactions between molecules cause large broadening of the transitions within a molecule).

 

Last update: 12th Mar 2011

 

© R. B. Liu, Department of Physics, The Chinese University of Hong Kong. All rights reserved.