Supplementary Material
To reach the sensitivity necessary to observe nuclear-spin-induced Faraday rotation we
used the setup sketched in Fig. S1. The light source is a linearly-polarized, diode-pumped laser
operating at 532 nm (Coherent Compass 315). The beam propagates along a ~2.5 cm cylindrical
container with glass windows on each end. An 8-turn, ~1.5-cm-long solenoid wound on the
container surface was integrated to a homemade NMR probe and used alternatively to generate
Fig. S1: (Left) Schematics of the experimental setup. F1 to F4 denote fiber couplers and LP indicates a
linear polarizer. Experiments where carried out both with and without a dc field B0=9.4 T (see text). The
laser beam propagates along an axis parallel to the rf field B1 (coincident with the x-axis in the chosen
reference frame) and perpendicular to B0. (Upper right corner) Photograph of our homemade probe head
during initial tests at high-frequency in the absence of dc field. A metal shield with two small input/output
apertures (not shown) was added during measurements to reduce rf emission. (Lower right corner) Sample
OFR signal of water at rf=400 MHz with no dc magnetic field; the rf amplitude was Brf=0.5 gauss. The
insert shows the corresponding Fourier transform after averaging 100 1-s-long scans (note that the chosen
1 s duration of the scan facilitates the determination of the system sensitivity). The peak pattern reflects
the amplitude modulation of the beam at 200 Hz (an arbitrary but fixed value chosen with the only
purpose of separating ligh-encoded signal from inadvertent rf pick-up) . Note the absence of the central
peak (corresponding to a dc-offset and eliminated during processing).
1
cw or pulsed rf fields over the sample volume (see below). To observe Faraday rotation we used
a ‘bridge configuration’1 comprising a half-wave plate, a Glan-Laser polarizer, and a dual, 600
MHz-bandwidth photoreceiver (New Focus 1607-AC). The 50-Ohm-matched rf output of the
latter was connected to the preamp of a NMR spectrometer for final demodulation and
processing. To distinguish the optical signal from spurious rf pick-up, we used a mechanical
chopper to modulate the laser amplitude at a predetermined frequency. The TTL ‘monitor’ signal
from the chopper was used to trigger acquisition and thus allow for coherent averaging of
successive scans.
It is not difficult to show2 that, for the detector configuration used in the present
experiment, the rf signal S is given by
S t  ~ f I 0 , rf I 0 F , N  g c sin rf t 
(S1)
where F (or N in the case of nuclear-spin-induced signal) is the observed Faraday rotation
as defined by Formula (1) (or (5)) of the main text, Io is the laser intensity, and rf (c) is the rf
(chopper) frequency; f(Io, is a function that takes into account potentially non-linear responses
of the photodetector and pre-amplifier at a given rf frequency and laser intensity whereas
g(c) represents the square-wave amplitude modulation due to the chopper. For reference, Fig.
S1 shows the Faraday rotation signal of water after 100 scans in a cw rf field of 0.5 gauss at
rf=400 MHz: After Fourier transform, the corresponding spectrum displays the pattern of
satellites expected for a square modulation at the preset frequency c=200 Hz. (Note the virtual
absence of a central peak, eliminated during processing after dc offset correction).
Prior to detecting nuclear spins via Faraday rotation, we conducted an exhaustive series
of experiments aimed at determining detection sensitivity and minimizing potential sources of
systematic error. We distinguish two categories of tests, depending on whether the sample was or
2
not within the bore of our NMR magnet: Initial work was carried out on an optical table, in the
absence of a dc magnetic field. A 1-Ohm resistance in series with the excitation coil was used to
monitor the current (and thus the rf magnetic field) on the sample volume. Fig. S2 shows a
summary of our observations using a water sample under different conditions, while Fig. S3
presents the response of our system as a function of rf amplitude, light intensity and number of
scans. Measurements at 400 MHz, 80 MHz and 3 MHz (not shown) indicate a minor increase of
the observed signal with increasing frequency (approximately a factor 1.5 over the tested range).
It is presently unclear whether this change is the manifestation of a physical process or an artifact
caused by a frequency-dependent receiver stage. Not withstanding this observation, we use the
dc Verdet constant of water3 (VH2O=5.24 rad T-1m-1 at 514 nm), the calibration curves in Fig. S3
Fig. S2: (a) Fourier transform of the OFR
signal of water. The rf frequency is 400
MHz, the rf amplitude is 0.5 gauss and no
dc field is present. Amplitude modulation
of the beam was carried out via a
synchronous mechanical chopper at 200
Hz. The light intensity at the photoreceivers was 1.2 mW; the duration of each
scan was 1 s and the total number of
repeats was 50. (b) Same as in (a) but in
the absence of illumination. With the
exception of a small central peak (resulting
from imperfect dc offset correction, see
Fig. S1), no signal is present. (c) In this
case the laser light is on but the fluid has
been removed from the cell. The glass
windows at the ends of the sample tube
experience a weak (yet non-negligible) rf
field yielding an observable signal. That
this is indeed the case is shown in (d)
where the same ‘empty-tube’ experiment
was carried out but with the glass windows
removed.
and Formula (1) in the main text to calculate a system sensitivity of 300 nrad/Hz1/2.
To meet the constraints imposed by the NMR magnet, our second set of experiments used
a platform — rigidly connected to the bottom plate of the magnet, see Fig. S4 — to
accommodate all optical components in a vicinity of the bore. Exceptions were the mechanical
3
Fig. S3: (Left) Calibration as a function of the rf amplitude for the conditions of Fig. S2. To
determine the rotation angle we used the Verdet constant of water at 514 nm, VH2O =5.24 rad T-1 m-1.
(Upper right corner) Signal-to-noise ratio (SNR) as a function of the number of one-second scans.
The solid curve is a linear fit whose slope is equal to 0.53±0.02 demonstrating that the SNR grows
steadily (over the time interval of the experiment) with the square root of the number of scans.
(Lower right corner) SNR vs. laser intensity. The slope of the solid curve is 0.97±0.02 implying that
the SNR grows linearly with the beam intensity. Because the signal amplitude also grows linearly
with light intensity (insert), we surmise that we have not yet reached the shot-noise-limited regime
(where the SNR grows with the square root of the number of photons).
chopper and the laser, which remained on the optical table, far removed (~10 m) from the
magnet. We used a 20 m long fiber, optical couplers on each end and a collimator to steer the
beam into the magnet platform without sacrificing much light intensity or introducing noticeable
divergence. This array proved convenient because it circumvented complications derived, for
example, from the effect of the stray field (reaching ~200 to 500 gauss underneath the magnet)
on the mechanical chopper. By the same token, and because the magnet sits on vibrationisolation legs, the system exhibited good stability over long measurement times (see Fig. S4).
Finally, the long distance separating the magnet from the optical table contributes to avoid
crosstalk between the optical and rf sources: In particular, we note that while the diode laser used
here proved immune to the location and amplitude of the rf generator and coil (see Figs. S2 and
S4), artifacts in the form of spurious OFR signal can be detected if the rf wavelength is resonant
with the cavity length of the source laser. (In preliminary tests at ~400 MHz, we did observe
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Fig. S4: High-field OFR measurements. Given the stronger hyperfine coupling in 19F we focused this
time on a sample of perfluorohexane (see text). (Left panel) (a) Fourier transform of the OFR signal of
perfluorohexane at 376 MHz within the bore of our 9.4 T magnet. The signal corresponds to a 1 s scan
with mechanical modulation of the beam at 200 Hz. The rf field amplitude was 0.4 gauss and the
number of repeats was 50. (b) Same as in (a) but after emptying the sample container; the residual
signal is caused by Faraday rotation at the end windows of the tube (see Fig. S3). (c) Same as in (a) but
with the beam blocked just before reaching the photoreceivers. (Right panel) (Upper left corner) Signal
amplitude as a function of the rf field for both water and perfluorohexane for the conditions listed in (a).
Comparison of the slopes allowed us to determine the Verdet constant of perfluorohexane relative to
that of water. The rotation angle on the left axis was calculated by comparison with the water OFR
signal in the absence of a dc field. (Lower left corner) Signal-to-noise ratio (SNR) as a function of light
intensity in perfluorohexane. Similar to Fig. S3, the linear growth (slope equal to 0.96±0.07) reveals
that we are yet to reach the shot-noise limited regime. (Upper right corner) Photograph of the
experimental setup underneath the bottom plate of our NMR magnet. (Lower right corner) SNR as a
function of the number of acquisitions. The growth is proportional to the square root of the number of
repeats demonstrating the time stability of our system (slope equal to 0.50±0.01).
non-negligible crosstalk while experimenting with a commercial HeNe laser proximate to our rf
signal generator.)
To first observe nuclear spin OFR we implemented a CPMG train with stroboscopic
acquisition at the midpoint of the interpulse intervals. We used a sample of commercial
perfluorohexane (CF3(CF2)4CF3, Aldrich, 95% purity) knowing that, while the 19F magnetization
(and spin density) is comparable to that found in protonated solvents, the hyperfine interaction is
two to six times stronger4-6. In our CPMG experiment the rf frequency was 376.364 MHz and the
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Fig. S5: (Main) Reference CPMG signal of
perfluorohexane (inductive detection). Each
point in the curve represents the signal
amplitude at the echo center (stroboscopic
acquisition). (Right insert) Fourier transform of
this signal. (Left insert) Sample echoes forming
during part of the CPMG train. In this case, the
acquisition is enabled during a 2 ms interval
around each echo center.
duration of the /2-pulse (-pulses) was 23 s (56 s). Inversion pulses were separated by 8 ms
and the total number of echoes was set at 200; the time delay between successive scans was 6 s
and the total number of scans was 5x104. The light intensity on each branch of the photoreceiver
reached 1.2 mW (below the allowed maximum of 2 mW). Relying on the calibration of Fig. S4
and using the signal amplitude in Fig. 1 of the main text, we estimate an effective
19
F-induced
rotation '  N  of ~4 nrad. This value must be multiplied by a factor  that takes into account the
transverse relaxation time of the
19
F signal (~1 s) and the
modified detection protocol (CPMG vs. cw excitation).
After comparing with (stroboscopically-detected) OFR
signal induced by a train of rf pulses — that somewhat
emulates the train of echoes during the CPMG sequence —
we
find
~4
and
the
corrected
rotation
  N   k' N   16 nrad . Using Formula (5) in the main text
Fig. S6: Fourier transform of the
'regular' OFR signal of water. The
experimental conditions are those listed
in Fig. S2. The application of a strong
dc magnetic field perpendicular to the
direction of propagation of the beam
results in a reduction of the system’s
Verdet constant.
and the observed rotation   F  =500 nrad for B1  0.1 gauss
(see Fig. S4), we estimate a nuclear field of order BN~300
nT. Similarly, we can use the
6
19
F spin polarization
<Ix>=2.8x10-5 to calculate the hyperfine constant a H 2  ~ ~ e B N
I x ~300 MHz, with
~  g *  2  denoting the electron gyromagnetic ratio over 2. We emphasize that the
e
B
above value only holds as a crude estimate. Further, we note that our formal description is
strictly incomplete because the presence of the dc magnetic field perpendicular to the direction of
light propagation is not taken into account. That this assumption is only a coarse approximation
can be seen in Fig. S6.
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