DOI: 10.5061/dryad.tht76hf6x
title: Toward liquid cell quantum sensing: Ytterbium complexes with ultra-narrow absorption

description: 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.
description: <strong>Absorption/Transmission
 Spectroscopy</strong> 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.
 <strong>Fluorescence Spectroscopy</strong>
 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.  <strong>Cryogenic Transmission
 Spectroscopy</strong> 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.
 <strong>Spectral Hole Burning
 Spectroscopy</strong> 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. 
 <strong>Imaging</strong> 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. <strong>Magnetic Circular Dichroism
 Spectorscopy</strong> 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). <strong>References</strong>
 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. <em>Journal of Physical Chemistry
 A</em> <strong>123</strong>, 6792–6798
 (2019).
description: # Toward liquid cell quantum sensing: Ytterbium complexes with
 ultra-narrow absorption
 [https://doi.org/10.5061/dryad.tht76hf6x](https://doi.org/10.5061/dryad.tht76hf6x) All the spectral data behind the main text figures in the manuscript is provided here. The raw data are provided with their units noted, and manual fitting of those data as described in the main text leads to the reported spectral properties. The fitting is done either by Gaussian, Lorentzian, or linear functions, depending on the data. Combined with descriptions in the manuscript, details provided in the supplemental material, and the data provided here - all figures and conclusions are reproducible.  ## Description of the data and file structure Data for every plot in each main text figure are provided here. The tabulated data can be found in "AllFigures.xlsx". However, we recommend using the provided MATLAB script to visualize the data. The script output is also included under "AllFigures.pdf". The tabulated data in "**AllFigures.xlsx**" have sheets named *fig1*, *fig2*, *fig3*, and *fig5*. The descriptions of the variables, units, and the data are provided here. *fig1.* *Broad absorption spectra and laser transmission.* x1c_1: energy eV. y1c_1: UV-VIS absorption normalized to transition IV. y2c_2: UV-VIS absorption normalized to ligand absorption. x1c_2: energy eV. y1c_3: laser transmission converted to absorption of IV. *Ensemble emission spectra.* x1d: energy eV. y1d: emission.  *fig2.* *Temperature-dependent absorption* *data.* x2a_{temp}: frequency THz, y2a_{temp}: transmission mV. For example, x2a_320 and y2a_320 are the variables needed to plot the absorption spectrum of the sample at 320 K. *Spectral hole burning data.* x2e: frequency kHz. y2e: probe transmission mV. *fig3.* *Absorption data of various Yb transitions from literature are traced from the papers and data of our samples are experimentally obtained.* x3a_1: energy eV. y3a_1: absorption. x3a_2: wavelength nm. y3a_2: traced absorption of (3), ref. 26. x3a_3: energy eV. y3a_3: traced absorption of (4), ref. 27. x3a_4: energy eV. y3a_4: traced absorption of (5), ref. 28. x3a_5: energy eV. y3a_5: traced absorption of (6), ref. 29.  *fig5.* *Magnetic circular dichroism (MCD) data obtained by subtracting differential absorption via circularly polarized light (sigma +/-) under a magnetic field. *x5a_1: frequency THz. x5a_2: frequency THz. y5a_1: sigma - absorption. y5a_2: sigma + absorption. x5b_1 energy eV. x5b_2 energy eV. x5b_3 energy eV. y5b_1: differential absorption under 0T. y5b_2: differential absorption under 0.16T. y5b_3: differential absorption under 0.38T. MCD with static field of varying strengths. x5d: B field (T). y5d: spectrum analyzer amplitude in V. *MCD with dynamic field.* x5f_1 time (s). y5f_1 spectrum analyzer amplitude (dBm) of sample. x5f_2 time (s). y5f_2 spectrum analyzer amplitude (dBm) of air. x5f_3 time (s). y5f_3 spectrum analyzer amplitude (dBm) of THF solvent. The MATLAB script "**AllFigures.mlx**" can also be run to look at the same data, as provided above in the tabulated form. The script itself contains the same annotations and should run with the provided **fig1.mat, fig2.mat, fig3.mat, and fig5.mat** files in the same directory as the .mlx script. The expected output of this script is provided in "**AllFigures.pdf**" ## Code/Software A MATLAB code to visualize all the data is included. It can be run with the script "AllFigures.mlx" and provided data files: fig1.mat, fig2.mat, fig3.mat, and fig5.mat. For other analysis softwares, the tabulated data is provided in "AllFigures.xlsx".