The energetic disorder induced by fluctuating liquid environments acts in opposition to the precise control required for coherence-based sensing. Overcoming fluctuations requires a protected quantum subspace that only weakly interacts with the local environment. We reported a ytterbium complex that exhibited an ultra-narrow absorption linewidth in solution at room temperature with a full-width at half-maximum of 0.625 meV. Using spectral hole-burning, we measured an even narrower linewidth of 410 peV at 77 K. Narrow linewidths allowed low-field magnetic circular dichroism at room temperature, used to sense Earth-scale magnetic fields. These results demonstrated that ligand protection in lanthanide complexes could significantly diminish electronic state fluctuations. We termed this system an ‘atom-like molecular sensor’ (ALMS) and proposed approaches to improve its performance.

Absorption/Transmission Spectroscopy

The broad band absorption spectra reported in the manuscript were collected using the Shimadzu UV-3101PC UV-VIS-NIR scanning spectrophotometer. A high-resolution transmission/absorption spectrum of the sample was measured with a tunable narrow band CW laser (M Squared SolsTis Ti:Sapph laser). The laser beam is split into two paths by a polarizing beam splitter (PBS). One beam measures the absorption of the solvent and the other measures the absorption of the sample. The quarter waveplate is used to change the polarization of the laser beam so that we can measure the absorption of circlarly polaried light. The two permanent magnets create a strong static magnetic field to induce Zeeman splitting. The translational stage allows us to control the distance between the magnet and the sample and to vary the strength of the magnetic field at the sample’s location. The setup is shown in fig. S37.

Fluorescence Spectroscopy

The fluorescence spectra of the room-temperature solution sample was taken using a home-built Fourier spectrometer, as described in [1]. The sample is excited in the ligand absorption band with 420nm excitation. The fluorescence at longer wavelengths are collected past longpass filters via single photon counting detectors. We used a Mach-Zhender interferometer with TCSPC using mltiple detectors to interferometrically sort and time-resolve the emission. This setup is also used for lifetime measurements. 

Cryogenic Transmission Spectroscopy

A JANIS ST-100 cryostat with LakeShore 321 Autotuning Temperature Controller was used for cooling down the sample. This cryostat was inserted into the absorption/transmission setup as described above.

Spectral Hole Burning Spectroscopy

The laser was split into two paths using a polarizing beam spliiter, with an AOM on each leg. The AOM would modulate the pump and probe beams to control the detuning, as shown in Fig. S39. 

Imaging

We use a home-made external cavity diode laser (ECDL) for imaging (fig. S49). The laser is set at the half max of the absorption peak of the sample. We use two lenses to expend the laser beam size to cover the whole cuvette. A permanent magnet is mounted onto a rotating motor beneath the sample. We image the sample with a webcam. Under circularly polarized light, the sample’s absorption depends on the strength of the magnetic field, so as we rotate the magnet, the image blink.

The video showing the change in intensity of the transmission image can be found in movie S1.

Magnetic Circular Dichroism Spectorscopy

An M Squared SolsTis Ti:Sapph laser with a Lighthouse Sprout pump laser system was used to generate 304 THz to 307 THz light. The laser power needed in this measurement is under 30 mW. The beam is split into two paths, each going through an acousto-optic modulator (AOM; Gooch & Housego 2308-1-1.06 and Isomet SR48607) set at f and f+df, and brought together at another polarizing beam splitter (PBS). The resulting beam is oscillating between right- and left-hand circular polarizations at df=100kHz. The amplitude of the transmitted light was collected with Thorlabs PDA8A. The setup is shown in fig. S50.

The measurement of an AC field was achieved by taking the setup above and adding a Helmholtz coil around the sample holder. This gives rise to two more sidebands at frequency df+/-f{AC}, and their amplitude is tracked by a spectrum analyzer (Agilent Technologies N9010A). The optical setup is shown in fig. S51, and the collected data is shown in fig. S52, which shows the change in signal as the magnitude of the AC field is brought down below 1G (the values reported in the manuscript accounted for background noise of the gaussmeter, which are slightly lower than what is shown here). The AC magnetic field was generated by taking the output of an arbitrary waveform generator (Agilent 33220A) to run an oscillating current onto the coil. The field was then measured by a gaussmeter (Lakeshore 410) to confirm its magnitude as well as mathematically confirmed by checking the AC current magnitude.

A frequency analyzer was used to track the transmission intensity at the sideband frequency (df+f{AC}) composed of the frequency at which the polarization of the light is oscillating (df=100 kHz) and the frequency of the AC field generated by helmholtz coils (f{AC}=1 kHz). The  reading was converted to change in power (, where  is the measured power), and the power value was then converted to volts by accounting for the equipment resistance (P=V^2/R, where R=50 Ohms). Voltage noise has units of VHz^(-1/2), which was converted to magnetic noise in units of THz^(-1/2) by measuring the relationship between our voltage reading and the gaussmeter reading that we conducted separately (fig. S53).

References

1. T. L. Atallah, A. V. Sica, A. J. Shin, H. C. Friedman, Y. K. Kahrobai, J. R. Caram, Decay-Associated Fourier Spectroscopy: Visible to Shortwave Infrared Time-Resolved Photoluminescence Spectra. Journal of Physical Chemistry A 123, 6792–6798 (2019).