Thus, so far, the S/T composition of the CSS
at any instant of time has not been easily ac-
cessed experimentally.
Inthiswork,wehaveappliedasecond
strong laser pulse of 14,300 cm−^1 , time-delayed
relative to the pump laser pulse of 18,800 cm−^1.
This, so-called push pulse excited^1 CSS and
(^3) CSS with equal probability, creating a CSS
state with a^1 CSS/^3 CSS ratio exactly reproduc-
ing their ratio in the CSS. Excited doublet states
of radical ions are known to be much stronger
electron donors and acceptors than their
ground states and exhibit typical lifetimes
of a few hundred picoseconds ( 30 ). Thus, CR
from the excited CSS state is extremely fast—
i.e., essentially immediate on the time scale
of normal CSS recombination. Recombina-
tion of^3 CSS, just like the unexcited^3 CSS,
yielded the locally excited^3 PDI; whereas re-
combination of^1 CSS, unlike^1 CSS, which is
too low in energy, mainly yielded the excited
(^1) PDI state. The excited (^1) PDI formed this
way decayed nonradiatively, by fluorescence,
and by renewed charge separation to CSS.
Thus, a push pulse induced three immedi-
ate responses: a jump in CSS population, a
jump in^3 PDI population, and a delayed flu-
orescence signal. This situation is exemplified
experimentally in Fig. 2A for a push pulse at
90-ns delay time.
Quantum dynamical simulation
In Fig. 2B, we show a simulation based on a
quantum theoretical kinetic model. For dyads
of the present type, involving the TAA donor
and PDI acceptor, the push-free kinetics of
CR comprising the channels to singlet ground
state from^1 CSS and to^3 PDI from^3 CSS has
been successfully simulated in our previous
work ( 29 , 31 – 33 ). Briefly, the reaction kinetics
involving quantum mechanical spin motion
was treated by a stochastic Liouville equa-
tion for the CSS electron–nuclear spin density
matrixr(t) of the general form
r
ðÞ¼t iH½þ;r K^rþ^Rr ð 1 Þ
whereHrepresents the spin Hamiltonian ac-
counting for Zeeman interaction, exchange
interaction, and isotropic hyperfine interac-
tion;K^represents the spin-selective reaction
superoperator; andR^represents the relaxation
superoperator ( 34 ), accounting for the effect of
rotational modulation of anisotropic hyper-
fine interaction. For the details of parame-
trization, refer to supplementary text, section
IV, and ( 29 ). Specific parameter values in the
present case refer to the reaction rate con-
stants of singlet recombination (kS=9.5×10^6 s−^1 )
and triplet recombination (kT=0.35×10^6 s−^1 ).
Inmodelingthepushprocess,itwasas-
sumed that the push laser pulse excited all CSS
population to CSS, keeping the ratio of S/T
unchanged. Recombination from^1 CSS oc-
curred promptly with a probability ofpSSof
fluorescence plus nonradiative decay to the
ground state and a probability ofpTTfor
recombining from^3 CSS to^3 PDI. The com-
plementary parts, namely (1−pSS) of^1 CSS
and (1−pTT) of^3 CSS, were assumed to return
to the CSS with no other decoherence than
that induced by the spin-selective recombina-
tions in CSS, as described by the Haberkorn
( 35 ) type of reaction operator. Thus, the spin
density matrix after returning from CSS was
assumed to be given by
rpostp¼rprep
1
2
pSSQSrprepþrprepQS
1
2
pTTQTrprepþrprepQT
ð 2 Þ
whererpostpis the density matrix immediately
after the push pulse,rprepis the density matrix
immediately before the push pulse, andQS
andQTare the projection operators onto
the singlet and triplet manifolds, respectively.
Comparing Fig. 2, A and B, shows that the
model described the essential features of the
processes well.
From a general, theoretical point of view,
the push pulses can be conceived as trigger-
ing a prompt Neumann-Wigner–type quan-
tum measurement of the spin state of the RP
(Fig. 3). By exciting the CSS to CSS, the re-
combination rates to singlet or triplet products
became so fast that the quantum state reduc-
tions to pure singlet or triplet were practically
instantaneous on the time scale of normal CSS
recombination kinetics or spin dynamics. It
should be kept in mind, however, that this type
of measurement differs from the notion of
quantum measurements applied in the litera-
ture to spin-selective reactions in undisturbed,
normal RP kinetics ( 12 , 36 ). In those cases, the
decoherence effect of the quantum measure-
ment on the surviving RPs has been the focus
of interest ( 37 ).
Quantum beats and magnetic
field dependence
The potential of the pump-push technique for
revealing the details of spin dynamics under-
lying the recombination of the CSS is demon-
strated in Fig. 4. Figure 4A shows a series of
TA pump-push signals taken at short intervals
of delay of the push pulse versus the pump
pulse. Clearly, the amplitudes of the signal
1472 17 DECEMBER 2021•VOL 374 ISSUE 6574 science.orgSCIENCE
Fig. 3. Schematic of push pulse triggered quan-
tum measurement.Although the total population of
the CSS can be followed by optical TA, the singlet
and triplet subpopulations are not immediately
apparent but can be read out through the signals
elicited by the push pulse, as shown in Fig. 2.
Fig. 2. Transient traces of the CSS,^3 PDI, and fluorescence in the pump-push experiment.(A)Timetraces
of TA signals of the CSS (at 14,100 cm−^1 ) and of the^3 PDI* (at 19,600 cm−^1 ) without push pulse (dashed lines in black
and red) and with push pulse atDt= 90 ns (solid lines in gray and red). Fluorescence signals (at 17,200 cm−^1 )
are given in blue. They appear synchronously with the pump and push pulses, respectively. Att= 0, the fluorescence
and CSS signals are normalized to 1, and the^3 PDI/GSB signal is normalized to−1. (B) Simulation of the signals
by the quantum theoretical model, assuming delta-shaped pump and push pulses and parameter valuespSS= 0.5
andpTT= 0.9 (see the text).
RESEARCH | RESEARCH ARTICLES