jump after the push pulse exhibited oscilla-
tory behavior—i.e., spin quantum beats. The
observed pump-push signals of the triplet
product and their magnetic field dependence
were simulated quantum theoretically as men-
tioned above (Fig. 4C). To obtain a realistic
representation of the observed signals, the
finite width [full width at half maximum
(FWHM); 9.5 ns total extension with fringes up
to 40 ns; fig. S11] of the laser pulses has been
considered. The width of the pump pulse was
considered as well. In the region of overlap of
pump and push pulse, the initial bleaching by
the pump pulse and the rise partially com-
pensated each other, making it difficult to
separate the contribution of the positive jump
because of the push pulse within the first
~20 ns. However, this situation can be treated
with a theoretical simulation of the pump-push
signals, such as shown in Fig. 4C (for more
examples at higher fields, see fig. S17).
Electron spin motion is determined by in-
ternal and external magnetic fields. To extract
the essential information about the spin quan-
tum beats, we plotted the signal intensities
at the end of each push pulse as a function of
the delay time in Fig. 4B. In addition to zero
field, the behavior at fields of 1, 7, and 500 mT—
representing the cases of level crossing, middle
field, and high field—has also been determined
(see fig. S17 for the signal representations). The
pump-push time profiles obtained, although
somewhat noisy, directly revealed the oscilla-
torystructureofspinmotioninthefirst~50ns.
In Fig. 4D, the theoretically simulated pump-
push time profiles are shown. The positions of
the oscillation maxima and minima as well
as the general absolute scaling of the effects
were well reproduced, although for 1 mT, the
amplitude of the first maximum is obtained
higher than in experiments. In fitting the
theoretical results, it was found that the sign
of the exchange interactionJcaused a sig-
nificant difference in the field-dependent
pump-push profiles at low fields. Without
carrying out the fitting of all parameters in the
quantum calculation to a final optimum—
becauseinthisworkwewantedtofocusona
proof of principle of the pump-push spectros-
copy—it can be concluded that only a positive
exchange interaction (i.e.,^3 CSS below^1 CSS)
led to satisfactory results (figs. S18 to S20). For
small absolute values of the exchange energy
parameterJon the order of the intrinsic
hyperfine couplings of the system, the usual
rule of a magnetic field effect resonance at
a field ofBmax= |2J| is no longer valid. A
diagram of the resonance fieldBresversus the
value ofJfor positive and negative values is
not symmetric aroundJ=0,wheretheso-
called low-field effect is dominated by the
hyperfine coupling constants. So far, the sign ofJ
could only be determined for spin-correlated
RPs by EPR ( 38 – 41 ) or by field-dependent
CIDNP experiments ( 42 ). The pump-push
spectroscopic method, which has also been
exploited for the fluorescence signal yielding
complementary results (figs. S13 to S16), of-
fers a new approach with a much better time
resolution.Discussion and conclusions
In this paper, we have established pump-push
spectroscopy as an optical technique for real-
time observation of electron spin motion in
CSSs. Although the spin motion in such states
is usually hidden for optical probing absorp-
tion techniques, the proposed method allows
us to look behind the scenes. This realization
was achieved through push pulses triggering
quasi-instantaneous spin measurements by
two spin-selective CR channels exhibiting
drastically enhanced rates in the electronically
excited CSS. This method has the potential
to fully map the coherent and incoherent spin
dynamics in a CSS, including eventual quan-
tum beats, as in the present case.
As has been shown in the work of Molin and
co-workers ( 16 ), the best conditions for quan-
tum beats prevail if radicals have either (i)
simple hyperfine structure (i.e., small numbers
of preferably equivalent nuclear spins, as is the
case for the TAA-An-PDI dyad studied here) or
(ii) small hyperfine coupling (e.g., because of
perdeuteration) and largeDgin combinationwith strong external magnetic fields. These
rules apply for any method of observation.
However, Molin’s method requires nonpolar
solvents, high energy excitation, and efficient
fluorophores with short fluorescence lifetimes.
The pump-push method with absorption detec-
tion introduced here requires neither of these
conditions and therefore is more generally ap-
plicable. However, our method is best suited
for RPs with fixed distance. In flexibly linked
or freely diffusing RPs, the fluctuating dis-
tance modulates the recombination efficiency
after the push pulse to a large extent, which
will probably attenuate the push pulse effect
substantially.
Compared with the detection of quantum
beats by transient EPR, our method provides
the advantage that it can be applied at any
magnetic field, including the notableJ-resonant
fields. The EPR technique requires microwaves
and a magnetic field resonant with the micro-
waves, so only a discrete set of fields is acces-
sible for which microwave frequency bands
are available.
As far as the time resolution of the pump-
push method is concerned, the laser pulse
length and the recombination time in the
CSS* state could be limiting. In the present
case, the recombination time is much shorter
than the laser pulse because the time deriva-
tive of the signal jumps induced by the pushSCIENCEscience.org 17 DECEMBER 2021•VOL 374 ISSUE 6574 1473
Fig. 4. Measured and simulated spin quantum beats.(A) Experimental pump-push TA signals taken at
19,600 cm−^1 for the formation of^3 PDI* product at 0 mT. (B) Experimental postpush signal profiles at
magnetic fields of 0, 1, 7, and 500 mT. (C) Theoretical pump-push signals at zero field, calculated
withJ= 0.35 mT. (D) Theoretical results simulating the curves in (B); for details, see the text. The vertical
line in (A) marks the position of the maximum of the pump pulse. The black dots in (A) and (C) represent the
positions of the maxima of the push pulses for the pertinent signals, and the red points represent the
positions of the ends of the push pulses, taken 17 ns later. The end of that push pulse with the same
maximum as the pump pulse is taken as time zero in (B) and (D).RESEARCH | RESEARCH ARTICLES