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Title: Photon-number discriminating superconducting transition-edge sensors
Author(s): Rajteri, M.; Taralli, E.; Portesi, C.; Monticone, E.; Beyer, J.
Journal: Metrologia
Year: 2009, Volume: 46, Issue: 4
DOI: doi:10.1088/0026-1394/46/4/S28
Funding programme: iMERA-Plus: Call 2007 SI and Fundamental Metrology
Project title: T1.J2.3: qu-Candela: Candela: towards quantum-based photon standards
Copyright note: This is an author-created, un-copyedited version of an article accepted for
publication in Metrologia. IOP Publishing Ltd is not responsible for any errors or omissions in this
version of the manuscript or any version derived from it. The definitive publisher-authenticated
version is available online at doi:10.1088/0026-1394/46/4/S28
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Photon-number Discriminating Superconducting Transition-Edge Sensors
Mauro Rajteri1, Emanuele Taralli1, Chiara Portesi1, Eugenio Monticone1, and Jörn Beyer2
1
Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle Cacce 91, 10135 Torino, Italy
2
Physikalisch-Technische Bundesanstalt, Berlin, Germany
Corresponding e-mail address: m.rajteri@inrim.it
Abstract
Photon number discriminating detectors are fundamentals for new quantum photon based
standards. We report results on superconducting transition-edge sensors based on Ti/Au and
Ti/Pd bilayers allowing pulses containing up to five photons to be discriminated.
1. Introduction
The development of single-photon detectors able to discriminate the number of photons emitted
in a light pulse is a key issue towards quantum photon-based standards for optical radiation [1].
This goal needs stretching the limits of measurement capabilities in many different fields of
optical science and technology like quantum metrology (absolute calibration of detectors, nanopositioning), quantum imaging (sub shot-noise weak images detection, ghost imaging), and
quantum information (coding, elaboration and communication of information by exploiting
quantum systems).
The development of photon number resolving (PNR) detectors is a crucial issue in the
measurement of photon number distribution of single photon emitters and is a key requirement
for the progress of quantum information technology. Furthermore they are needed for the
development of sources that deterministically produce single photon upon request (on-demand
sources)
The application of multi-photon states strongly depends on the availability of advanced lownoise, high-efficiency and photon-number resolving photon detectors. Conventional singlephoton counting detectors are not suitable for these applications as they cannot distinguish
between one or more photons arriving at the same time.
An important breakthrough in single-photon resolving detectors is the development of cryogenic
devices based on superconductors operated close to the transition temperature (Transition-Edge
Sensors, TES) [2]. The absorption of a single photon moves the device through the
superconducting to normal transition with a huge change in electrical resistance that allows to
detect the corresponding current change with a dc-SQUID amplifier. By operating at
temperatures lower than 0.4 K, TESs are able to resolve the number of absorbed photons.
In this work we present the characterization as a single-photon detector of TESs based on Ti/Au
and Ti/Pd bilayers. The normal metal layer is adopted to adjust the transition temperature Tc of Ti
bulk (390 mK) down to 100 mK, caused by the proximity effect, i.e. the diffusion of Cooper
pairs into the normal material and by the diffusion of electronic excitations in the superconductor
[3]. In this way detectors are obtained with a better energy resolution when working at lower
temperatures, or with a faster response time when working at higher temperatures.
Ti/Au TESs have been already applied as x-ray detectors [4], while Ti/Pd TESs have been
developed only recently at INRIM. Pd has been chosen as normal layer due to its interesting
properties. Actually, among non magnetic metals, Pd causes the strongest Tc reduction in a
normal-superconducting structure and its Cooper pair correlation length is half that of metals
with high electrical conductance like Au [5]. Therefore, by using Ti/Pd bilayers, in principle
thinner structures are feasible, with good morphological (lower roughness) and optical
properties. Moreover, interdiffusion in a Ti/Pd multilayer is negligible up to about 250 °C [6] and
hence devices based on them are expected to be stable over photolithographic processes and
thermal cycles.
2. The devices
TESs were fabricated on double side polished Si wafers covered on both sides by a 500 nm thick
SiN layer grown by LPCVD. The pressure in the evaporation chamber was lower than 2x10-7
mbar before deposition. The substrate temperature was settled at 100 °C. Ti films have been
prepared by starting from a 99.99+% bulk Ti. The distance between crucible and substrate was
10 cm and the deposition rate was about 1.5 nm/sec for Ti, Au and Pd. The fabrication process
consisted of three steps. First, 10-15 nm of Ti was deposited on SiN substrate in order to improve
the adhesion of the Pd or Au layer. The last step was the deposition of the superconducting Ti
film. Previous work [7] shows that inverting the traditional order superconductor-normal metal
can help avoiding undesirable effects on the reproducibility of the Tc.
Devices were fabricated by standard photolithographic process. For Ti/Au TESs the unwanted
material was usually removed using chemical wet etching. Ti/Pd TESs and few samples of Ti/Au
were etched by RIE (Ti) and ion-milling (Au, Pd). The superconducting wiring of Al, with
thickness between 100 and 150 nm, was defined by lift-off technique combined with rfsputtering of the superconducting films.
We report here results obtained with both 20 µm x 20 µm Ti(55 nm)/Au(72 nm) TES and Ti(65
nm)/Pd(16 nm) TES with a transition temperature Tc of 103 mK and 105 mK, respectively. Fig. 1
shows the electrical circuit used to bias the devices and to read out the signal. A bias resistance
Rbias= 9.5 mΩ much lower than the TES normal resistance (RN = 225 mΩ and RN = 1.6 Ω for the
Ti/Au and Ti/Pd, respectively) allows to transform the bias current Ibias into a bias voltage Vbias
for the sensor. When the TES resistance rises due to an absorbed photon, a sudden decrease of Ites
occurs. Consequently, the electrical power P=Vbias/Rtes2 diminishes because the Vbias is fixed and
the TES resistance is increased. The variation of Ites is read out using a single commercial dcSQUID amplifier, mounted on the 4K flange of a dilution refrigerator and running in flux-locked
loop mode through the feedback resistor Rfb. This biasing method called Electro-Thermal
Feedback (ETF) [8] allows to bias the detector working with a bath temperature lower than the
transition temperature and also to reduce the effective response time of the sensors that can be
expressed as τetf = τth/(ℓ +1), where ℓ = αRtes Ites2/GTc is the loop gain, α = (T0/R0)(dR/dT) the
logarithmic sensitivity of the thermometer, τth=C/G is the thermal time constant, C and G are the
sensor heat capacity and the thermal conductance, respectively.
The working point of our devices is settled considering the Ites vs Ibias curve. As an example,
Fig.2 reports a bias curve obtained at a bath temperature of 47.8 mK for the Ti/Pd detector. At
low Ibias values a superconducting vertical region is present, except for a parasitic resistance of ~
7.5 mΩ; for Ibias>60 µA a normal region, corresponding to the 1.6 Ω straight line, is observed.
The intermediate region corresponds to the superconducting to normal transition. Measurements
of such characteristics at different temperatures provide information about resistance, thermal
coupling, dissipated power and electrothermal feedback loop gain of TES thermometer. From
our experimental data, by applying a standard method [2] the detector conductance G for Ti/Pd
and Ti/Au TES have been calculated to be 8.4 pW/K, and 212 pW/K, respectively.
The heat capacity C of our TESs is calculated as the sum of every layer capacity. For the case of
Ti/Au TES, at the transition temperature of Tc = 103 mK we have [9] C = 2.43x0.93 (Ti) fJ/K +
0.19 (Au) fJ/K = 2.45 fJ/K, where the factor 2.43 takes into account the increase of the heat
capacity of the superconducting material at the transition temperature. For the case of Ti/Pd TES,
at the transition temperature of Tc = 105 mK we have C = 0.65 (Pd) fJ/K + 2.43x1.09 (Ti) fJ/K =
3.3 fJ/K where the Pd specific heat is taken from [5]
3. Experimental results
The detectors were irradiated by 0.5 µs wide pulses from a 690 nm modulated diode laser,
attenuated by proper neutral density filters and coupled to a 50 µm multimodal optical fiber
aligned with the TES at a distance of 600 µm. This distance limits the collection efficiency, as
the ratio between the impinging photons on the detector area with respect to the incoming
photons from the fiber, to a value on the order of 1%. A packaging is under development to
collect almost all the light coming from the fiber.
Figures 3 and 4 show the distribution of the pulse amplitudes of the single photon events for
Ti/Au and Ti/Pd respectively. The histograms have been obtained by measuring the pulse heights
using a digital oscilloscope, without any filtering of the signal apart from a low-pass filter. The
bins of the measurements have been converted to photon numbers. In both cases we distinguish
up to five photons at λ=690 nm (E=1.79 eV), but photons are discriminated only in a statistical
sense due to the broad overlap of the Gaussian distributions. To assign the correct number of
photons to a pulse with an uncertainty lower than 1% two adjacent Gaussian distributions should
overlap at 3σ from their mean values, i.e. with a signal to noise ratio higher than 2.5.
By averaging the pulses with amplitudes close to the values corresponding to the maximum of
each peak of the pulse amplitudes distributions, one can obtain the expected current pulses
corresponding to the absorption of up to 5 photons. These results are shown in Fig. 5 and Fig. 6
for the case of Ti/Au and Ti/Pd TES, respectively.
The amplitudes of the current pulses for one absorbed photon are very small, about 70 nA for
Ti/Au and 24 nA for Ti/Pd. For this reason the SQUID amplifier plays a key role for the read out
of the signal. The commercial SQUID amplifier used in these measurements has a gain A=84212
V/A, an equivalent flux noise <2.25 pA/Hz1/2, and is mounted on the 4 K flange of our dilution
refrigerator, 20 cm far away from the detector. In order to improve the read-out of our TESs a
new sample setup is under study. This setup will use SQUID current sensors designed and
fabricated at PTB Berlin [10], specifically developed for the readout of cryogenic radiation
detectors. The current sensors are compact single-stage 16-SQUID series arrays (16-SSAs) or
alternatively integrated two-stage SQUID configurations. The two-stage sensors have a single
SQUID front-end read out by a second-stage SSA. Compared to a single SQUID front-end, the
16-SSA sensor achieves a higher dynamic range, ca. 2·10-5 Hz½, at an input referred total current
noise of <5 pA/Hz½ for frequencies above ca. 1 kHz. The white current noise of the integrated 2stage sensor is about a factor of 3 lower. For both sensor types the input inductance is <3 nH.
The sensors are highly magnetically robust and can be operated at typical TES operating
temperatures of around 100 mK. The power dissipation of the current sensors amounts to ca. 2
nW. In our new setup the current sensor chips are placed directly next to the TES chips, and
electrical connection is made by chip-to-chip wire bonding. The SQUID current sensors are read
out using the XXF-1 electronics from Magnicon [11] which will allow a bandwidth of the TES
readout in excess of 5 MHz.
The current pulses related to one photon absorption for both sensors are fitted with the
exponential function A1e
τ
− ( t − t0 ) / el
τ
+ A2 e
− ( t − t0 ) / etf
+ B ,where A1, A2 and B are constants and the
values of the two time constants τetf and τel are listed in Table 1. In the inset of Fig. 6 the fit for
the Ti/Pd TES is reported. The rise time of the pulse τel is related to the electrical time constant
L/R of the bias circuit, where L and R are the sum of all the components of the circuit, including
residual resistance and stray inductance. The lower τel for Ti/Pd is due to the higher resistance of
the bias point enabled by the higher normal resistance of the sensor. The difference in time
constant τetf between the two detectors is mainly affected by the higher thermal conductance G of
the Ti/Au sensor. From τetf , known τth, we can estimate loop gain ℓ and sensitivity α, also listed
in Table 1.
In strong electrothermal feedback, the energy deposited into the film corresponds to the
reduction of the electrical power supplied by the bias circuit [2], i.e. the integral of the current
pulse times the TES voltage. Due to the presence of the SQUID input coil in series with the TES
(Fig. 1), when the TES current is changing the TES voltage is not constant [12], but equal to the
difference between the bias voltage and the voltage drop across Lin. A comparison between the
theoretical energy of the absorbed photons and the corresponding experimental energy
(computed as described before) is shown in Fig. 7 for Ti/Au. From the linear fit, the slope of the
line corresponds to the fraction ε of the photon energy that is actually detected. The obtained
value ε = 0.80 is very close to the value obtained for Ti TES [13]. A similar analysis on the Ti/Pd
data gives ε = 0.71. The inset of Fig. 7 reports the amplitude of the pulses versus their theoretical
energy . The good linearity is an evidence that there is not saturation of the response of our
device up to 5 photons and that the pulse amplitudes can be considered proportional to the
photon energies.
4. Conclusions
TESs are single-photon detectors with a photon-number discrimination capability, a key feature
for the development of the new quantum technologies. TESs have been shown to be able to
discriminate up to 5 photons with an effective response time of the order of 5 µs and 40 µs for
Ti/Au and Ti/Pd TESs, respectively. Further improvements are expected by the implementation
of SQUID amplifiers close to the detector and by reducing the TES thickness, in order to
increase the pulse amplitudes and to reduce the response times.
Acknowledgments
The research leading to these results has received funding from the European Community’s
Seventh Framework Programme, ERA-NET Plus, under Grant Agreement No. 217257.
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Figure and table captions
Figure 1. ETF-TES bias circuit with DC-SQUID read-out
Figure 2. Ti/Pd TES current (Ites) vs bias current (Ibias) at 47.8 mK (dot curve). Solid lines represent the
current distribution for fixed resistance values (as reported in the legend) of the TES branch.
Figure 3. Histogram of the pulse amplitudes for Ti/Au TES.
Figure 4. Histogram of the pulse amplitudes for Ti/Pd TES.
Figure 5. Ti/Au TES current pulses, averaged over 10 samples, corresponding to 1 (solid line) ÷ 5
(dotted line) detected photons at 690 nm.
Figure 6. Ti/Pd TES current pulses, averaged over more than 100 samples, corresponding to 1 (solid
line) ÷ 5 (dotted line) incident photons at 690 nm. In the inset is reported the one photon pulse (dots)
with the exponential fit described in the text (solid line).
Figure 7. Comparison between the computed energy from the measured pulses and the theoretical
energy for 1 to 5 photons detected at 690 nm (1.79 eV) for Ti/Au TES. The solid line represents a
linear fit. In the inset the comparison is made with the measured pulse amplitudes and the behaviour is
still linear.
Table 1. Measured time constants τetf and τel, and deduced parameters ℓ and α for Ti/Au and Ti/Pd
TES, obtained from the one photon pulses.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
τetf
τel
(µs)
(µs)
ℓ
Ti/Au TES 5.52 5.44 1.1
Ti/Pd TES 40.1
Table 1
2.1
α
6
8.7 110