Measurements of Pulsewidth
A typical daily pulsewidth measurement by transient grating-frequency resolved optical
gating (TG-FROG) is shown in Fig. S1. The nonlinear response of pure solvent is measured
using our femtosecond interferometer, the same instrument that measures 2D electronic spectra.
Pure solvent is flowed through the sample cell, and the coherence time is set to 0, temporally
overlapping the first two laser pulses. These pulses create a spatial modulation of the dielectric
constant within the area of beam overlap that functions as a grating. Scatter of the third beam off
of this grating is homodyne detected as the waiting time is scanned over a small range.
Integration of the total signal at each waiting time yields an autocorrelation, which can be fit to a
Gaussian to extract a pulsewidth, typically ~12 fs. This result can be verified by more detailed
fitting of the entire FROG measurement, which we accomplish using FROG Fastguide software
from femtosoft technologies.
Data Binning
Since only absolute value spectra are considered in this work, little information can be
inferred from lineshapes and thus detailed peak fitting is unnecessary. After Fourier windowing
and processing into energy space, 2DES are initially ~200 x 1600 pixel arrays at each waiting
time (coherence dimension x rephasing dimension), with 50-200 waiting times measured for
each experiment. With several repetitions of each experiment to check repeatability and the
possibility of considering combined, rephasing and nonrephasing spectra for each experiment,
processing, viewing and analyzing the full data set without binning would be intractably time
consuming. Binning the 2D spectra into ~25 cm-1 pixels during processing substantially reduces
the size of the data sets being considered, generally to an approximately 100 x 100 pixel array
that makes display and integration routines substantially faster. All energies reported in this work
are repeatable across multiple experiments carried out on different days, with slightly different
laser spectra and pulse power, and thus are not affected by the binning procedure. Since neither
lineshapes nor peak shifts are considered in a quantitative way in this work, this course-graining
of the dataset has no effect on the measured dynamics.
High Power Experiments and Solvent Response
2DES were measured at higher laser powers ranging from 2-14 nJ/pulse, for all 3 types of
nanocrystals. The long-time behavior in these systems was identical to that measured at the
lower powers discussed in the main text (0.5-2 nJ/pulse), but substantial differences emerge at
early times, and we assign these changes to interference from nonresonant solvent response
(NRSR). NRSR was measured daily with experimental conditions identical to those used to
measure the 2DES of CdSe nanocrystals. Fig. S2 shows comparisons of the integrated signal
from the lower cross peak position of rephasing 2DES of CdSe QDs, [18,800 cm-1, 17,500 cm-1],
and NRSR at that same spectral position, for 6 experiments conducted over using pulse powers
ranging from 1-13 nJ/pulse. At low powers, the maximum intensity of signal from the QD
samples and from NRSR is comparable but the dynamics are quite different. NRSR is at
maximum intensity at 0 fs waiting time and decays away quickly, reaching the baseline level by
~20 fs. The 2DES of the QD samples contain both signal from the nanocrystals and NRSR. In
the lower power 2DES shown here and in the spectra presented in the main text, QD signal at the
cross peak position increases rapidly with time, reaching maximum intensity at a waiting time
of~ 30 fs. In higher power spectra the NRSR overwhelms the nanocrystal signal near T=0 fs,
and is comparable to the signal level at longer times. This effect can be seen even more clearly
in Fig.S3, which shows the integrated intensity of the lower cross peak of rephasing 2DES of
QDs at several pulse powers, normalized to the long time intensity (100 fs waiting time.) The
signal at T=0 fs is shown to monotonically increase with increasing pulse power, washing out the
early time dynamics of the QD signal in all spectra with pulse powers ≥4 nJ. We note that the
lower cross peak signal at high powers shows a shape similar to the dynamics identified as signs
of coherence in CdSe QDs by Turner and Scholes (Fig. 4 from main text reference #31),
however there are several reasons why we believe this similarity to be coincidental. Primarily,
the 2DES presented by Turner and Scholes were phased, and only the real parts were integrated
to generate dynamics measurements. NRSR should contribute only to the imaginary part of the
spectrum, and so should not be present.
Comparison of Comined, Rephasing and Nonrephasing Spectra
Rephasing 2DES of CdSe nanoparticles are described and analyzed in the main text.
Combined spectra and nonrephasing spectra were also generated and analysed, yeilding similar
results, and a breif comparison is presented here. Fig. S4 shows combined, rephasing and
nonrephasing spectra of CdSe QDs, NRs and NPs. The spectra for each type of nanoparticle
show similar features to those described in the main text. Combined spectra (top row) exhibit
less diagonal elongation than the rephasing spectra described in the main text (middle row), and
the lower cross peak in the QD spectra is less well resolved. In addition, the lower energy
diagonal peak appears on the diagonal at T=0 fs (not shown) and slightly redshifted at later
waiting times by ~50 cm-1. Nonrephasing spectra (bottom row) are stretched out in the
coherence dimension slightly, and show no diagonal elongation and a redshift of the most intense
feature with increasing waiting time similar to that seen in the combined spectra.
Interpretation of 2DES using Feynmann Pathways
A 2DES can be thought of as the result of the sum of contributions from a number of
processes including ground state bleaching, stimulated emission and excited state absorption. In
other words, the signal at each set of frequency coordinates [ωcoh,ωreph] is the sum of all
processes that interact with the first pulse with energy ωcoh and emit a signal field with frequency
ωreph. 2DES is blind to the energies at which the second and third pulses interact, and so multiple
signals can contribute to each spectral position. Feynmann pathways are a diagrammatic
bookkeeping method for describing and accounting for these contributions. For illustrative
purposes, Feynmann diagrams representing the contributions to the lower energy diagonal
feature and the lower cross peak in the rephasing 2DES of QDs described in the main text are
shown below in Fig. S5. The diagrams are read from with time increasing from bottom to top.
The state of the system during periods of free evolution are labelled by text in the center, and
changes upon each interaction with a laser pulse, represented by arrows. The wavevector of each
interacting photon is indictated by the pointing direction of the arrows, and convention for phase
matching in the boxcar geometry is that pulse 1 and the signal pulse point to the left while pulses
2 and 3 point to the right. Arrows pointing toward the text in the diagram represent absorption of
a photon upon interaction with the laser pulse, while arrows pointing away from the text
represent stimulated emission. Relaxation dynamics occuring during the waiting time are
diagrammed by writing down the states seperated by a dotted line. Looking at rephasing spectra
adds the additional restriction that pulse 1 must interact before pulse 2, reducing the number of
pathways contributing to the signal and simplifying interpretation. The different contributions
can often be identified dynamically, since the intensity of the contribution from each pathway
will exhibit the dynamics of the state the system is in during the waiting time, between the
interactions with pulses 2 and 3. For example, for the contributions to the lower cross peak
diagrammed in Fig S5 we would expect several distinct dynamic behaviors during the waiting
time. Considering the contributions from left to right in the diagram: Ground state bleaching
signals should show no change with waiting time. Members of the ensemble that are in a
superposition of the the e’ and e excited states during the waiting time contribute to the
coherence pathway, and this signal should oscillate at a frequency ωe’e, in this case ~1300 cm-1
corresponding to an oscillation with a period of ~25 fs, until dephasing is complete. For room
temperature samples typical dephasing rates are a few tens of femtoseconds. Signal from the
stimulated emission pathway should decay away with the lifetime of the e’ excited state. Signal
from the electronic relaxation pathway should increase exponentially with increasing waiting
time according to the timescale for relaxation from the e’ excited state to the lower lying e
excited state.
Linear Spectra
Linear absorption spectra are routinely used to characterize and compare semiconductor
nanoparticle samples. Fig. S6a shows the linear absorption spectra of our QD and NR samples in
wavelength range of interest, along with the typical spectrum of a compressed laser pulse
measured at the sample postion. The sharp defects in the laser spectrum at ~585 nm is the result
of a 2π phase roll between adjacent pixels in the SLM, and does note effect the observed 2D
spectrum substantially. Both QD and NR samples could be investigated using the same laser
pulses, because the samples were synthesized with nearly identical lowest energy exciton
states.Fig. 6B shows the linear absorption spectrum of the NPL sample, along with a typical
spectrum of a compressed laser pulse at the sample position. The blueshifted resonances of the
NPL relative to QD and NR samples required a different tuning of the NOPA, resulting in
slightly different overall shape, bandwidth and temporal pulsewidth. This difference are
incidental and do not cause differences in the observed dynamics.
X-Ray Diffraction Verification of Crystal Structures
Fig. S7 shows X-Ray diffraction data from films of typical QD, NR and NPL samples.
QD and NR samples yield similar results, both indicating a wurtzite crystal structure. The NPL
sample is distinct from the other two, and indicates a zinc-blende crystal structure.
Figure Captions:
Figure S1: (A) TG-FROG measurement of a well compressed pulse. Low intensity signals
shown at |T| ≥ 20 fs result from the interference of background scattering of pulses 1 and 2 into
the detection direction. (B) Autocorrelation trace generated by integration of the total TG-FROG
signal at each waiting time (blue dots) and a gaussian fit (black line). Fitting to a normalized
Gaussian yields a width of σ = 7.6 fs, giving a pulsewidth of ~12.6 fs full width at half
maximum.
Figure S2: Integrated intensity at the lower cross peak position, centered at [18600 cm-1, 17500
cm-1], inside a circle with radius 250 cm-1, forrephasing 2DES of both CdSe QDs (blue) and
NRSR (green), measured at several pulse powers (1-13 nJ.)
Figure S3: Integrated intensity at the lower cross peak in rephasing 2DES of CdSe QDs using
pulse powers ranging from 1-13 nJ, normalized to the intensity at a waiting time of 100 fs.
Figure S4: Combined, rephasing and nonrephasing 2DES of CdSe QDs, NRs and NPs at 100 fs
waiting time.
Figure S5: Feynman diagrams for contributions to the lower energy diagonal feature (top) and
the lower cross peak (bottom) in the rephasing 2DES of QDs presented in the main text. The
ground state (g), the 1S3/2-1Se exciton state (e), the 2S3/2-1Se state (e’) and unspecified higher
lying excited states (f) are involved in the pathways contributing to these two features. Diagrams
can be read as described above. Pathways shown in the upper panel, from left to right, are from
ground state bleaching, stimulated emission and excited state absorption. In the lower panel,
again from left to right, we show pathways for contributions from ground state bleaching, the ee’ coherence, stimulated emission and electronic relaxation from the e’ state to the e state.
Figure S6: Comparison of linear absorption spectra of (A) QD and NR samples and (B) NPL
samples with typical laser spectra. The laser spectrum was blueshifted for the NPL experiments
by retuning the NOPA. QD and NR experiments were performed with similar laser spectra.
Figure S7: X-Ray diffraction data from typical samples of QD, NR and NPL nanocrystals,
synthesized using the methods described in the main text, normalized for easy comparison. QD
and NR samples show patterns typical of a wurtzite crystal structure. NPL samples show patterns
typical of a zinc-blende crystal structure.