1
Entangled Photon Correlations Allow a Continuous
-
Wave Laser Diode to Measure
Single
-
Photon
,
Time
-
Resolved Fluorescence
Nathan Harper
1
†
, Bryce P. Hickam
1
†
, Manni He
1
, Scott K. Cushing
1
*
1
Department of Chemistry and Chemical Engineering,
California Institute of Technology, 1200
E. California Blvd. Pasadena, CA
AUTHOR INFORMATION
†
These authors contributed equally to this work
Corresponding Author
*
Corresponding author:
scushing@caltech.edu
2
Select Optical Properties of ICG
in solvents
from literature
Table 1: Select optical properties of ICG
in methanol, ethanol, and DMSO from ref.
1
Solvent
Peak
absorption/emission
wavelength (nm)
(
cm
-
1
mol
-
1
)
at
max
Methanol
784/809
221,000
0.09
Ethanol
787/811
167,000
0.11
DMSO
794/817
170,000
0.12
3
Confirmation of Fluorescence
.
While t
he results presented in the main text of the publication suggest that
the coincidences
observed with the sample present originate from fluorescence due to the good agreement
between the observed histograms and fits,
a
control experiment as additional evidence
w
as
performed to rule out the role of scatter from the excitation
beam
.
Additionally, a blank scan was
performed, where the dye solution was replaced with only methanol
. Figure S
1
displays this
histogram, as well as a side
-
by
-
side comparison of the histograms observed with and without the
dye
. The lack of an obvious coin
cidence peak sugge
sts that the SPDC flux is sufficiently filtered
from the fluorescence detector, and that the coincidences observed in the experiment originated
from fluorescence of the sample.
Figure S
1
: (a)
Coincidence histogram
from methanol blank
experiment
. (b)
Coincidence
rates
for blank
methanol and ICG/methanol solutions.
4
Experiment Stability and Background
Over the course of the 14
-
16 hour scans presented in Figure
3
, minimal drift or sample degradation
were observed. Figure S
2
shows the
singles and coincidence count rates over the course of the
experiment. Coincidence count rates were obtained by summing all coincidence counts between
24 and 34 nanoseconds and sub
tracting the product of accidentals per bin and the number of bins
in
this window. The accidental rate per bin was obtained by averaging the number of coincidences
observed from 50 to 70 ns, far from the coincidence peak. While a slight decrease in the heralding
channel (
C
hannel 0) is observed
in the DMSO data
over time like
ly due to drift in the alignment,
this change in intensity is
about
1
% of the original value.
The singles rate in the fluorescence arm
(Channel 1)
as well as the coincidence rate appear to remain steady over time.
While ICG is known
to exhibit degradation
over time due to a number of factors, we do not observe a loss in coincidence
counts likely because the sample is exposed to low light levels, and the sealed cuvette containing
the dye had minimal headspace.
The observed
fluctuations in the coincidence dat
a is not due to
technical noise
, but rather the Poissonian statistics of a shot
-
noise limited system, as the variance
of the observed rates is nearly equivalent to the mean of the rate (Table S1).
Figure S
2
: Count rates
in Channel 0 (reference photons
), Channel 1 (fluorescence photons),
and coincidences
from
100
μ
M ICG in
methanol, ethanol, and
DMSO experiment over
the
course of the scan
.
5
Table S1: Count rate means and variances
demonstrating nearly shot
-
noise limited statistics
Parameter
Mean Rate
(counts per second)
Rate Variance
(counts per second)
2
Heralding Singles
1
2
600
393
00
Fluorescent Singles
870
8
80
Raw Coincidences
8.3
8.0
Accidental Coincidences
0.78
0.77
True Coincidences
7.5
8.7
The background of the experiments presented here are low, but some stray light is likely still
present. From the blank experiment, the
singles rate
at the fluorescence detector was 28
±
5
counts
per second, slightly higher than the specified dark count rat
e of the detectors at 10 counts per
second. Regardless, the fluorescence counts observed during experiments with dye are
substantially higher, suggesting that these counts are mostly fluorescence and not background.
6
Lifetime Fits with Residuals
Fits of t
he raw histograms are shown in Figure S
3
on a logarithmic scale to show the accuracy of
the fit extending to the tails of the coincidence peaks over several decades of intensity.
The weighted residuals are shown in Figure S
4
, the lack of obvious trends in the data suggest that
the model used for fitting the data is reasonable. Here, the residuals are weighted by the inverse
square of the fit value at each timepoint, as the uncertainty of the counts is proportional to this
val
ue
for Poissonian data.
Figure
S
3
: Raw coincidence data and fits
for ICG in methanol
(left)
, eth
anol
(center)
, and
DMSO
(right)
on a logarithmic scale
.
Figure S
4
: Weighted residuals of the fits from Figure 3.
7
Fitting Algorithm
The fits presented in this work were performed in a custom Matlab program using the iterative
reconvolution
technique. First, the accidentals present in the IRF, as obtained by averaging the
histogram coincidence counts from 50
-
70 ns, were subtracted from the raw data, and the data were
truncated to a 20
-
40 ns window to reduce the amount of baseline present in
the fit. The resulting
true coincidence curve was then scaled so that the sum of counts over the IRF was unity. The
experimental data from each sample were also truncated to a 20
-
40 ns window. The accidental
counts were not subtracted from the sample coinc
idence curve, as these were treated as a fit
parameter. The accidental data was also normalized so that the sum of counts was equal to unity.
The sample response model functions were of the form:
푅
(
푡
푖
)
=
푐
(
푒
−
푡
푖
/
휏
+
퐴
)
Where
τ
, the fluorescence lifetime,
and
A
̧a factor accounting for accidentals, are the fit parameters.
The constant
c
is used to normalize the area of the sample response to unity. The normalization in
all three cases is necessary because the convolved response of two functions has an area
equal to
the product of the areas of the original functions. The experiment response function was calculated
as a discrete convolution of the sample response and the IRF, truncated to the length of the
experimental data, and normalized to an area of one.
T
hen, a trust
-
region nonlinear regression
algorithm was performed to estimate the parameters
τ and
A
that minimize the sum of squared
errors between the experimental data and the fit.
References
(1)
Berezin, M. Y.; Lee, H.; Akers, W.; Achilefu, S. Near Infrared Dyes as Lifetime
Solvatochromic Probes for Micropolarity Measurements of Biological Systems.
Biophys J
2007
,
93
(8), 2892
–
2899.