Quantum Efficiency Measurements of Dark Matter
PMT
Adam Snyder
August 27, 2013
Abstract
In this paper, improvements were made to procedure for measuring
the quantum efficiency of dark matter photomultiplier tubes (PMTs),
via LabVIEW automation software. Current dark matter detectors,
such as the XENON100 experiment, as well as future detectors, such
as the XENON1T, rely on the characterization of the component PMTs
in order to properly analyze the data obtained during the course of the
experiment. The quantum efficiency is, in general, a function of wavelength, and must be tested in order to determine the number of incident
photons on the PMTs, that may be indicative of a dark matter signal.
To allow for this process to be done more efficienctly, LabVIEW software was developed to allow for wavelength scans between 155 nm and
380 nm. This software was tested by performing several room temperature quantum efficiency scans. The results were in agreement with the
manufacturers specifications and were self-consistent, indicating that
the software performed properly. The applicability of the software to
the quantum efficiency measurement experimental set-up will allow for
measurements to be made more quickly, in present and future testing
of PMTs, at both room temperature and low temperature.
1
Introduction
One of the greatest mysteries in cosmology and astrophysics is the identity
of the so called dark matter, that is non-baryonic, highly exotic matter that
is believed to compose approximately 25% of the mass-energy density of
the universe. The first evidence for this dark matter was provided by Fritz
Zwicky in 1933, who determined that the velocity dispersions of galaxies
in the Coma cluster could not be accounted for by the ”luminous matter”
[4]. Measurements of rotational curves of individual galaxies, weak and
1
strong lensing, and other astronomical measurements further supported the
necessity for non-luminous matter [2]. Dark Matter is also necessary for the
formation of large scale structure in the universe, providing gravitational
potential wells whereby luminous matter could coalesce [3]
1.1
Dark Matter Candidates
The possible candidates for dark matter can be categorized into two classes:
Massive Compact Halo Objects (MACHOs) and Weakly Interacting Massive
Particles (WIMPs), of which there exists two sub-classes for the latter. MACHOs would consist of non-luminous baryonic matter such as brown dwarfs
or black holes. WIMPS would be either relativistic (hot) or non-relativistic
(cold). An example of a relativistic WIMP would be a heavy neutrino, while
an example of a non-relativistic WIMP would be the ”neutralino”, or the
least massive supersymmetric particle. It is known that neutrinos as well as
MACHOs cannot be a significant portion of the dark matter [3]. Most current direct detection experiments, such as the XENON1T experiment, focus
on the detection of WIMPs. WIMPs would need a mass on the order of 10
GeV to properly account for the dark matter in the universe [3]. WIMPS
are an ideal candidate for dark matter because their theoretical relic density,
as determined from various particle physics theories would be in agreement
with cosmological measurements, and they may be readily detected [2].
Figure 1: The Standard Model particles and their theoretical supersymmetric partners
WIMPs, being supersymmetric particles, would be indicative of physics
beyond the Standard Model. Supersymmetry is a proposed symmetry that
would exist between fermions and bosons, whereby a fermion would have a
2
corresponding supersymmetric boson partner, and vice-versa (Figure 1) [3].
Of these supersymmetric particles, the dark matter ”neutralino” is predicted
to be the corresponding W, Z or Higgs supersymmetric particles, known
as the Wino, Zino, and Higgsino. The magnitude of interaction would be
roughly at the same scale as that of the weak interaction [3].
1.2
XENON1T Experiment
Figure 2: Diagram of the XENON1T dark matter direct detection experiment
The XENON1T experiment, like its predecesor the XENON100, uses
direct detection methods to detect dark matter interactions with nuclei. Although weakly interacting, dark matter particles have a non-zero interaction
cross section, allowing elastic scattering events off of nuclei such as Xenon
or Argon, used in a liquid form [1]. This interaction creates both excited
atoms, which emit ultraviolet photons, and ionized atoms. This signal may
then be measured using photomultiplier tubes (PMTs). A diagram of the
XENON1T detector is shown in Figure 2. Direct detection experiments such
as the XENON100 and XENON1T detectors seek to detect the 178nm light
that is released by the interaction between dark matter and a Xenon nucleus. However in order to detect a statistically significant signal, any such
experiment was have a low background signal and proper characterization
of the detector PMTs.
The PMTs that will be used in the XENON1T experiment are Hamamatsu R11410 PMTs (Figure 3), which are specifically designed to have low
3
Figure 3: Hamamatsu R11410 PMT to be used in XENON1T experiment
radioactivity, a feature important in limiting the possible background signals, and to operate at low temperatures. In order to achieve stable liquid
Xenon, the detector must be cooled to −100◦ C. A PMT operates using
the photoelectric effect to cause incident light to release a photoelectron at
the photocathode. This single electron will be amplified in by the dynodes
within the body of the PMT, in order to allow for a measurable signal at
the anode. A diagram of this process is shown in Figure 4.
Figure 4: A diagram of a photomultiplier tube, showing the detection of an
incident photon
The output signal of the PMT is
E = Nγ · QE · CE · G
(1)
where Nγ is the number of incident photons, QE is the quantum efficiency of the PMT, CE is the collection efficiency of the PMT, and G is the
gain. The collection efficiency is the ratio of photoelectrons released at the
photocathode to incident photoelectrons at the first dynode, as their exists
a non-zero probability that an initial photoelectron will fail to be directed
4
onto the first dynode. The gain refers to the increase in number of electrons at each of the dynodes and is expressed as a product of the individual
dynode gains. Finally, the quantum efficiency is the ratio of photoelectrons
released at the photocathode to incident photons (Equation 2). By purely
geometric means, the quantum efficiency is < 50%, and in general, due to
the non-zero thickness of the photocathode, the quantum efficiency is lower.
QE =
Nphotoelectrons
Nphotons
(2)
In order to optimize the measurement of the quantum efficiency, LabVIEW software was developed to provide complete automation of the unique
quantum efficiency measurement set-up used. Measurements of the quantum
efficiency of a representative PMT at room temperature over the wavelength
band of 155 nm to 380 nm were in agreement with the manufacturers specifications. The quantum efficiency peak value at approximately 175 nanometers was confirmed. This sets the stage for low temperature measurements of
the Hamamatsu PMTs in order to determine the quantum efficiency of the
PMTs at the XENON1T operating temperatures. The experimental procedure used in this experiment, including the set-up and automation software
is also easy to modify for future testing of alternative PMTs, or PMTs to
be used in future, larger scale dark matter direct detection experiments.
This outline of quantum efficiency measurements first proceeds by outlining the general experimental set-up used to test dark matter PMTs, in
Section 2.1. The mathematical theory and specific procedure is outlined
in Section 2.2, while the LabVIEW software developed over the course of
the summer is presented in Section 2.3. In Section 3 the results of the first
automated quantum efficiency scans are presented and discussed, including
the significance of the measurements and possible sources of error. Finally,
in Section 4 discusses how the procedure used in this experiment can be
applied to future testing of PMTs.
2
Methods
One of the major challenges towards the detection of these events is the
need to properly characterize the photomultiplier tubes (PMTs) used in the
experiment. In other words, such properties as linearity, gain, excess noise
factor and quantum efficiency must be measured. In this experiment, the
measurement of the quantum efficiency of the PMTs used in dark matter
detectors was done utilizing LabVIEW automation software.
5
2.1
Experimental Set-up
The quantum efficiency measurement set-up used is highly unique. In this
experiment, a McPherson Model 632 Ultraviolet deuterium lamp was used,
allowing for measurements to be made for wavelengths between 115 nm and
400 nm. Wavelength selection was made using a McPherson Model 218
vacuum monochromator, composed of a snap-in diffraction grating and controlled by a McPherson Model 789A-3 stepper motor. A beam splitter was
used to split the incident light between a reference PMT and a calibrated
photodiode or the PMT to be tested. The test PMT is connected to a liquid
nitrogen dewar that can be used to cool the PMT down to XENON1T operational temperatures of −100◦ C. Current measurements for the signal of
the reference PMT, photodiode and test PMT were measured using Keithley
486 or 6485 picoammeters.
Figure 5: Quantum Efficiency set-up. Physical image on the left, diagram
on the right.
2.2
Quantum Efficiency Measurements
In order to minimize error in the quantum efficiency measurements, measurements were made using a two step process. First, using the beam splitter,
light was made to be incident on the reference PMT and the calibrated
photodiode, and the wavelength scan was performed. The reference PMT
was necessary in order to account for fluctuations in the deuterium lamp.
The photodiode has a known quantum efficiency. While these fluctuations
are not very rapid, it is still necessary to measure them in order to properly
analyze the resultant signals. Next, the light was made to be incident on the
6
reference PMT and the test PMT, and the wavelength scan was repeated.
The current from each of the components is expressed as
I = F · QE · A
(3)
where F is the incident flux per area, QE is the quantum efficiency,
and A is the illuminated area. Thus, there are four equations total, one for
each of the reference PMT during the first scan (Ref, 1), the reference PMT
during the second scan (Ref, 2), the photodiode (PD), and the test PMT
(PMT). Since for each scan, the ratios of the incident fluxes is the same
(Equation 4) the four current equations can be solved for their respective
fluxes.
FPD
FPMT
=
.
FRef,1
FRef,2
(4)
Since the illuminated areas are the same, after canceling of terms, the
quantum efficiency of the test PMT can be expressed as
QEPMT =
IPMT IRef,1
QEPD
IPD IRef,2
(5)
where the currents are measured quantities and the quantum efficiency
of the photodiode is known. It is also important to take into consideration
the dark current present in the reference PMT, photodiode, and test PMT.
Dark current is an result of quantum fluctuations at the photocathode that
cause a non-zero signal even in the absence of incident light, and must be
subtracted from all of the current signals.
The region of interest for quantum efficiency measurements is between
155 nm and 380 nm. The Hamamatsu PMTs are designed to have a local
maximum at approximately 175 nm wavelength, in correspondance to the
178 nm ultraviolet light that would be released by interaction of a dark
matter particle with a Xenon nucleus. A complete scan from over the entire
region of interest consists of three separate scans, from 155 nm to 200 nm,
from 200 nm to 230 nm, and 220 nm to 380 nm. For the last of the three
scans, a filter is used to decrease the intensity of the incident light.
2.3
LabVIEW Automation
Due to nature of quantum efficiency measurements using the above procedure, a complete scan over the wavelength range of interest is a lengthy
process due to the need to measure several components at once. Thus, in
7
order to allow for quantum efficiency measurements to be made more efficiently, with minimal loss in accuracy, automating software was developed.
Automation of the system required the synchronization of the picoammeter current measurements for the PMTs and the McPherson 789A-3 stepper
motor. This was achieved through the use of a LabVIEW virtual instrument
program, developed over the course of the summer in order to record and
output the current measurements of the picoammeters and the corresponding wavelength.
LabVIEW was chosen due to the advantages it offerred in providing
a user-friendly interface that did not demand an extensive knowledge in
programming languages to properly utilize. This would also allow for the
final exportation of an executable file that would not rely on specific software
packages, drivers, or other utilities not necessarily available to all users. The
”Front Panel” for the quantum efficiency program is shown in Figure 6.
Figure 6: User interface for the Quantum Efficiency Measurement Program
The specific program developed allows for two types of scans. The first
consists of a start and end point, along with a increment value (as low as
0.002 nm). The second allows for measurements to be made at specific userspecified points. Since both Keithley 486 and 6485 picoammeters were used
in the experiment, both models are fully supported. Finally, the program
8
supports up to three picoammeters, which may be toggled ON/OFF. Automation is performed first by using the McPherson 789A-3 to move to the
start of scan point. Measurements are then made from the picoammeters,
consisting of the average of 50 measurements per point per picoammeter,
before the wavelength is incremented to the next point. The results of the
scan are saved as a CSV file type.
The program was tested by performing scans over the entire wavelength
region, using increment step sizes of 5 nm. The results were then used to
determine the quantum efficiency of the PMT, following corrections for dark
current.
3
Results and Discussion
Figure 7: Three quantum efficiency scans from 155 nm to 380 nm performed
at room temperature.
The results of three complete scans are shown in Figure 7. The quantum
efficiency rises rapidly from 155 nm to reach a peak around 175 nm before
falling to a local minimum. It then rises gradually for wavelengths greater
then 250 nm. The steep decrease in quantum efficiency for wavelengths
below 160 nm is due to the opacity of the quartz window of the PMTs
9
being tested for light below these wavelengths. The sharp peak is consistent
with the design of the PMTs, and corresponds with the wavelength of dark
matter interaction emissions of 178 nm.
The three scans depicted in Figure 7 were performed on different days,
but exhibit remarkable consistency. However, there are some discrepancies
that must be addressed. The peak quantum efficiency of approximately
0.40 or 40% is relatively high. Secondly, the measured quantum efficiency
for wavelengths greater then 250 nm is relatively low. The most likely source
of error is dark current measurements. For wavelengths greater then 250 nm
the dark current was a significant portion of the output signal, at times almost as high as 50%. This could be alleviated in the future by changing the
intensity of the incident light from the deuterium laser. However the general
trend of the data is in agreement with quantum efficiency measurements provided by the manufacturer. Thus, the automation of the quantum efficiency
set-up provided consistent results in a more timely fashion then previous
measurements made by hand. It should be noted that the discrepancies
discussed previously are not a product of the automation, as confirmed by
manual measurements.
Finally, while the quantum efficiency of the photodiode is known, it only
available in discrete points. Thus, there is a certain need to interpolate
between points, for wavelengths between them. To do this, the LabVIEW
program uses a spline method.
4
Conclusion
The implementation of automation software in the quantum efficiency measurements of the dark matter PMTs allows for measurements over a larger
wavelength, and in small increment step sizes, to be performed more quickly
in the past. This will greatly aid in the development of both the XENON1T
detector and future large-scale dark matter detectors. The automation software is not dependent on the PMT, and works in conjunction with the
current experimental set-up, as well as allowing for certain flexibility in
equipment used. Thus it successfully optimizes the quantum efficiency measurements of current and future PMTs.
5
Acknowledgements
I would like to thank my mentor, Professor Katsushi Arisaka for his help
this summer and for giving me the opportunity to work in his dark matter
10
laboratory this summer, as well as the members of my lab group for their
assistance. I would also like to thank Francoise Queval for her work in
organizing the UCLA REU program and the National Science Foundation
for providing the funding necessary for this great research experience.
References
[1] Beltrame, P., 2013. Direct Dark Matter search with XENON Program.
arXiv:1305.2719
[2] Feng, J. L., 2010. Dark Matter Candidates from Particle Physics and
Methods of Detection. Annual Reviews of Astronomy and Astrophysics
Vol 48.
[3] Raffelt, G.G., 1997. Dark Matter: Motivation, Candidates and Searches.
Lectures at European School of High-Energy Physics.
[4] Zwicky, F., 1933. Spectral displacement of extra galactic nebulae. Helv.
Phys. Acta 6. 110-127.
11