## Optical NMR detection

### The principle of Nuclear Spin-induced Optical Rotation(NSOR)

Optical NMR detection in our experiment is based on Nuclear Spin-induced Optical Rotation(NSOR), which is the polarization rotation of a laser beam induced by the nuclear spins in a liquid sample. Many people expected that laser can aid NMR detection by shifting NMR frequencies, but the effect is too small to be observed as far. On the contrast, NSOR is actually the complementary effect — the laser polarization will be rotated slightly by polarized nuclear spin. NSOR is readily measurable, especially for heavy nuclei, thus providing a new way to detect nuclear spin information.

NSOR is essentially one type of Faraday rotation, but its magneto-optics effects arise from internal hyperfine interactions between nuclear spins and electrons. In the sample that contains magnetic nuclei(e.g. 1H, 19F), there will have nuclear spin polarization in a magnetic field. Due to the hyperfine interaction between nuclear spins and electrons, this sample will have circular dichroism. Hence, when a linearly polarized laser beam passes through this sample, the light polarization will be rotated due to the circular dichroism of the sample. In current experiment, the measurement of NSOR is practically carried out in liquid samples, since the spin density is high in liquids.

For atoms with a nuclear spin $$\small{\mathbf{I}}$$ and a 1S0 electronic ground state, the vector polarizability as a function of laser frequency $$\small{\omega}$$ and the nuclear spin-induced optical rotation angle along the $$z$$ direction are written as: $${\mathbf{\alpha}\equiv\alpha_{v}{\textstyle \mathbf{I}}=\frac{2\omega r_{e}c^{2}}{\hbar}{\displaystyle \sum_{k}\frac{f_{k}\alpha_{k}}{(\omega_{k}^{2}-\omega^{2})^{2}}\mathbf{I}}}$$ $${\phi=-{\displaystyle \frac{2\pi\omega lN}{nc}}\alpha_{v}\left\langle I_{z}\right\rangle }$$ where, in the first formula, the sum is taken over dipole-transition-allowed excited states with resonance frequencies $$\small{\omega_k}$$, oscillator strengths $$\small{f_k}$$ and hyperfine coupling constants given by $$\small{H_k^{hf}}=a_k\small{\mathbf{L}{\cdot}\mathbf{I}}$$, and $$\small{r_e}$$ is the classical electron radius. In the second formula, $$\small{l}$$ is the sample length, $$\small{N}$$ is the nuclear spin density, $$\small{n}$$ is the refraction index in the liquid and $$\small{c}$$ is the light speed. From the above formulas, the optical rotation angle is proportional to the sample length $$\small{l}$$, nuclear spin density $$\small{N}$$, nuclear spin $$\small{I_z}$$ and hyperfine coupling constant $$\small{a_k}$$. The most remarkable thing is that the optical rotation could be dramatically enhanced at resonance condition $$\small{\omega\sim\omega_k}$$. In addition, when at far-off-resonant condition, $$\small{\phi\propto\omega^2}$$, which means optical rotation is generally larger for the laser with shorter wavelength.

Comparing with traditional NMR detection method that is based on the induction coil, NSOR have several new points:

1. The optical rotation will be enhanced dramatically when the laser is on resonance with atoms or molecules.
2. NSOR signal will be much larger for heavier nuclei. Although the NSOR signal for Hydrogen is small from the measurement, NSOR is more effective to investigate heavy-nuclear NMR, which is quite different from traditional NMR.
3. Since NSOR arises from the hyperfine interaction between nuclei and electrons, which is sensitive to the electronic configuration in different molecules and chemical environment, hence NSOR provides a new potential method to distinguish molecules. This effect could be termed as chemical enhancement.
4. Laser beam could achieve high spatial resolution, that is only limited by diffraction. Therefore, NSOR could bring the advantage of optical detection to the multi-dimensional NMR imaging in future.

### Optical NMR detection of 129Xe and 1H in Water

The first measurement of NSOR was done in liquid 129Xe(LXe) and water. In the experiment of liquid 129Xe, liquid 129Xe in natural abundance is pre-polarized in a separate apparatus before introducing into a rectangular glass cell inside magnetic shields and maintained at -90℃ by flowing cold N2. The laser bean is linearly polarized before passing through LXe and the polarization rotation caused by the LXe is measured by being converted to a change in intensity with a λ/4 waveplate, a photoelastic modulator(PEM) operating at 50 kHz and a linear polarizer(LP2). The light intensity is detected by a photodiode and demodulated with a lock-in amplifier. Magnetic fields B0 and B1 are applied with field coils inside magnetic shields. A separate SQUID magnetometer is used to measure LXe polarization. Data obtained with 770 nm laser for this set-up is shown as the amplitude of the optical rotation as a function of LXe polarization.

In the experiment of water, Water is spin-polarized by flowing through a superconducting (SC) magnet and is adiabatically spin-locked to a field B1 oscillating at 21 kHz in the y direction as it flows into a cylindrical glass tube placed in a uniform field B0 in the x direction. The polarization rotation of laser light polarized with a linear polarizer is measured with a balanced polarimeter consisting of a polarizing beam splitter cube and two photodiodes(PD1 and PD2) and a lock-in amplifier referenced to the NMR frequency. The NMR signal is also independently measured with a pick-up coil wound around the glass tube. A current source modulates the B0 field on and off resonance at 8 Hz to avoid cross-talk. Data collected at 770 nm is displayed as the Fourier spectral density of the optical rotation lock-in amplifier output for water with effective proton polarization $$\small{P=5.3\times10^{-6}}$$. The signal-to-noise ratio after 1000s of averaging is about 4.5. The dashed line is the shot noise level for 2.9 mW detected laser power, calculated from the photocurrent in the photodetectors.

### Optical NMR detection in organic liquids

Nuclear spin-induced optical rotation is sensitive to the chemical environment in molecules, due to the fact that hyperfine interaction varies with different nuclear-electronic configurations. In a recent paper(Ikäläinen etc, PRL 105, 153001 (2010)), efficient first-principles calculations for 1 in different pure chemicals (water, Ethanol, etc.) reveal optical chemical shift, which supports NSOR as a new method to distinguish chemicals. Currently, we are doing relevant experiments at both low field and high field set-up, in order to explore the potential capability of NSOR spectroscopy for analytical chemistry.

### Pictures

 The low-field set-up of pyrex cell with liquid sample inside and B0 and B1 coil Multi-pass optical pattern.