Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors

Transcription

1 University of Colorado, Boulder CU Scholar Undergraduate Honors Theses Honors Program Spring 2017 Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors Natalie Mujica-schwahn Natalie.Mujicaschwahn@Colorado.EDU Follow this and additional works at: Part of the Atomic, Molecular and Optical Physics Commons, and the Optics Commons Recommended Citation Mujica-schwahn, Natalie, "Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors" (2017). Undergraduate Honors Theses This Thesis is brought to you for free and open access by Honors Program at CU Scholar. It has been accepted for inclusion in Undergraduate Honors Theses by an authorized administrator of CU Scholar. For more information, please contact cuscholaradmin@colorado.edu.

2 Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors by Natalie Mujica-Schwahn A thesis submitted to the Faculty of the Honors Council of the University of Colorado in partial fulfillment of the requirements for the award of departmental honors in the Department of Physics 2017

3 This thesis entitled: Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors written by Natalie Mujica-Schwahn has been approved for the Department of Physics Dr. Michelle Stephens Prof. Konrad Lenhert Prof. Nils Halverson Prof. Paul Beale Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline.

4 iii Mujica-Schwahn, Natalie (B.A., Physics) Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors Thesis directed by Dr. Michelle Stephens Superconducting tungsten in an optical stack has demonstrated near unity absorption at 1550 nm. High detection efficiency and a low operational temperature (0.16 K) provide energy resolution sufficient for single-photon counting. The spatial dependence of the device response has been measured, revealing dependencies in detected photon number, energy resolution, and thermalization that result from small misalignment from the device center. Additional measurements at 785 nm demonstrating the position-dependent behavior of this Transition Edge Sensor (TES) at a suboptimal wavelength are also reported. Single photon measurements at 785 nm and higher photon energy have demonstrated a characteristic half photon anomaly that may be due to one of several proposed interactions. Preliminary results of the position dependence of this phenomenon supports the hypothesis of thermal absorptions off-detector in the substrate. The next steps necessary for confirming this result are laid out.

5 iv Acknowledgements I can hardly express my appreciation for the commitment, assistance, patience, and support of my project advisor, Michelle Stephens, and my technical advisor, Thomas Gerrits. This has been a challenging year for each of us, and that makes me all the more grateful for all of your assistance and advice. Thank you for taking so much time to help me edit my writing and troubleshoot my ideas. I have to thank my entire support group (Division 686 and others) at NIST for their continual support in every step of the project. This experiment would have been impossible without the fabrication work done by Adriana Lita. I also want to thank Erich Grossman for his past mentoring which has helped to prepare me for this project and my future. Also thanks for allowing me brief use of your microscope to photograph my sample.

6 Position Dependence of High Efficiency Single Photon Detectors: A Route to Better Understanding of Transition Edge Sensors by: Natalie Mujica-Schwahn Chapter 1 Background Bolometry, Radiometry, and Calorimetry Superconducting Transition Edge Sensors Phenomenon: Half Photon Detections Superconductivity Energy Transport in a Type-I Superconductor Electronic States of a Type-I Superconductor Experimental Details TES Chip Design Cryogenic Cooling Electronics Superconducting Quantum Interference Devices Pulse Generation & Coupling Piezoelectric Micropositioners Data Acquisition TES Mapping Photon Pulses

7 2 3 Results Data Analysis Limitations of Chosen Filter Results Summary nm Results nm Results Conclusions 44 Bibliography 46

8 List of Tables and Figures Table 1.1 R(T) for the Superconducting Transition Photograph of W-TES Half Photon Signals Electron-Phonon Coupling in a TES Electron Density of States of a Superconductor Select Elemental Superconducting Energy Gap Values TES Cross-sectional Diagram Through Chip Imaging: Diagram Cryogenic Refrigerator Diagram and Photograph Experimental Circuit Diagram DC SQUID Operation Experimental Optics Diagram Piezoelectric Positioner Characteristics Photograph of Piezoelectric Stages Through Chip Imaging: 3K Through Chip Imaging: Room Temperature Single Photon Pulses (Raw) Data Analysis Flowchart

9 4 3.2 Data Analysis Flowchart Data Analysis Flowchart Filtering: Effect on Energy Resolution Photon Energy Histograms (linear) N γ at 1550 nm (logarithmic) < N γ > Position Dependence at 1550 nm Energy histogram at 785 nm (linear) N γ at 785 nm (logarithmic) < N γ > Position Dependence at 785 nm

10 Introduction The purpose of this experiment was to investigate the spatial variations in the photon counting statistics of a tungsten transition edge sensor at 1550 nm. Transition Edge Sensors (TES) are incredibly efficient (typically > 90%, recently up to 95% [1]), highly sensitive detectors capable of counting individual photons from a few photon source. The limitations inherent to how we currently use these detectors include a limited dynamic range, a lack of inherent calibration, and detector sizes restricted by heat capacities capable of resolving single photons. Of course the energy of the photons being detected is extremely important, as many TES have narrow windows of acceptance and higher energy photons are prone to degrading the detector itself. The TES in this work is optimized for optical telecommunications (UV-IR), but TES that detect x-rays, gamma rays, and neutrinos have been developed [2][3], while detectors for more exotic sources such as dark matter have been proposed[4]. One proposed dark matter detector is a tungsten transition edge sensor, similar to the one described here, except with a mass of 1kg (!) [5]. This won t be necessary at the energies of optical photons used in this work, but these active areas of research motivate the development of ever better TES detectors. Improving a device with a naturally high efficiency requires careful analysis of any nonequivalence between ideal theory and measurements. One way to explore discrepancies is to vary one parameter, in this case 2D position, while holding all others constant. Variation of the wavelength of the incident beam can offer additional information about unexpected interactions, thermal dispersion, and detector response at secondary wavelengths (785 nm for this experiment) that lie outside of a predesigned detection band.

11 Chapter 1 Background Resistive thermometry is a common method of measuring optical power and changes in temperature. Precision low power measurements are being developed and used for a range of applications and experiments that rely on maximizing information from a low photon flux including quantum information, the search for dark matter, bond-selective spectroscopy, and exoplanet detection [6][5][3]. Transition edge sensors are perfectly suited to these applications, due to their ability to resolve single photons with zero dark counts [7]. They are also highly tunable during the fabrication process. Varying the materials and thicknesses of the various layers sandwiching the transition edge sensor allows for increased absorptivity (approaching 99.8% absorptivity [1]) at a range of wavelengths. 1.1 Bolometry, Radiometry, and Calorimetry The field of radiometry is one of the oldest sciences, due to the human eye s capability to detect visible light. The eye is sensitive to a small portion of the available electromagnetic frequencies, and eventually radiation detectors were built to detect and measure both visible and non-visible wavelengths of light. One reliable way to measure electromagnetic radiation is through heat transfer. If light is absorbed in the detector, the detector s temperature will increase proportionally to the heat capacity of the absorbing element. Because of this, temperature changes are quite readily measurable with high precision, and it is simple enough to couple a separate variable to a change in temperature. Many temperature-dependent systems have been engineered for different

12 7 applications: thermocouples couple temperature change to a change in voltage; bimetallic strips couple temperature change to a change in position; and thermistors couple temperature change to a change in resistance [8]. It is important to distinguish between two types of radiometric measurements: calorimetric and bolometric. Calorimeters detect heat, which is an energy packet (such as a discrete number of photons, or a burning peanut), by a transient response to a change in temperature. Bolometers detect power (a stream of energy) by establishing an equilibrium between source and sink. A calorimetric measurement can also be thought of as integration over a bolometric measurement taken during a discrete amount of time. The transition edge sensor is able to operate as a bolometer or a calorimeter, but only the calorimetric state will be considered here. The operating principle behind a calorimeter is the equivalence of absorbed heat and photon energy, written as: E = hν Q = C T Where: T is a change in temperature, in Kelvin C is the heat capacity of the detector, in J/K h is Planck s constant ν is the frequency of a photon with energy E. E is the energy of a single photon, measured in Joules (or ev) Q is also energy measured in Joules (or ev) All that is needed is a basis for equating the two different energy transport mechanisms. One such case is 100% absorption, where all incident photon energy is deposited as heat. Another is electrical substitution (equating optical power with resistively generated heat), but this is only useful for bolometric measurements [2].

13 8 1.2 Superconducting Transition Edge Sensors Any Transition Edge Sensor (TES) relies on the phase change between superconductivity and ohmic resistance shown in Figure 1.1. When operating as a single photon detector, the TES response can be modeled as a small perturbation from an equilibrium within the linearizable transition regime (the segment labeled bc in Figure 1.1) [4]. This can be stated as dr dt is a constant. = αr, where to first order, α By rearranging to dr R = αdt and integrating, you get ln(r) = αt, then R = AeαT. This is approximated as a locally linear region around the temperature region of interest. The nonsuperconducting region (segment cd in Figure 1.1) can also be approximated as linear, but the temperature coefficient of resistivity, α is much smaller here [4]. α should then be considered to be two values, α transition = α t and α normal = α n. Superconductors can also exhibit a third α impurities = α i from residual materials and deformities from fabrication. However, since α t >> α n >> α i this effect is negligible for this experiment. Materials with larger values of α are more sensitive to heat, giving a larger response that can be measured more accurately. For very small heat packets, such as a single photon, a larger response to a smaller signal is ideal. This motivates the superconductor being biased within the Figure 1.1: Resistive transition of a voltage biased (C.V.) superconductor. The point of operation of a TES is between points b and c. The normal state is segment cd, while the superconducting state is segment ab. Reproduced from [9].

14 9 transition region, where α = α t. The typical signal size of a superconducting detector is typically a few ohms of resistance change over a millikelvin range. For example, a 1 ev photon will increase the temperature of a µm detector with a heat capacity of 0.5 fj K by 0.4 mk. This should produce an increase in resistance of around 100 mω. More power would eventually saturate the TES, driving it out of the superconducting transition to a less responsive state (segment cd in Figure 1.1). There are methods to count higher photon numbers based on the thermal relaxation time for a saturated detector to return to its bias point, but this won t be necessary for the low photon numbers studied in this work. Electrothermal feedback will automatically self-bias the TES within the transition region, provided that the voltage supplied to the system is held constant. This stability condition can be seen by differentiating P = V 2 R with respect to R, and comparing it to the constant current equivalent, d dr (P = I2 R): dp 2 dr = V R 2 dp dr = I2 C.V. : Constant Voltage C.C. : Constant Current A small increase in resistivity generated by a photon being absorbed will decrease power dissipated in the TES by the voltage bias. A current bias would cause the TES to lose superconductivity upon an equivalent increase in resistivity. The low T C (or operation temperature) of tungsten is well suited for single photon detection, because the electron heat capacity is relatively low even through the superconducting transition, where heat capacity increases by 252% [10]. A lower heat capacity produces a larger thermal response. The maximum response in the linearizable regime determines the dynamic range of the detector, which is constrained by the bias point, width of the superconducting transition, and the heat capacity of the absorbing element.

15 10 Once a TES has been driven out of the transition, or saturated, other methods exist to calculate the photon number, but these are less accurate and unnecessary here [7]. An image of the TES studied in this work and a schematic of the layout can be found in Figures 1.2 and 2.1. Figure 1.2: Digital microscope image of TES chip at 200 magnification. The TES is the square in the center, with the Nb wires leading up and to the left. Also visible are the W and Nb guide arrows, which point towards the TES. This is to assist positioning. The scale bar in the bottom right shows the approximate width of the TES absorber (20 20 µm without the wires included, µm with the wires) Phenomenon: Half Photon Detections Previous studies have reported the detection of signals at half the photon energy [11]. This was briefly explained as photons which hit the rails, referring to the superconducting Al wires leading up to the TES, but this assumption wasn t justified any further. The results of the study, shown in Figure 1.3, are as follows: Use of a monochromatic source produced a characteristic peak at half the energy of the incoming photon. This experiment, which was similar in design to the experiment conducted for this thesis, was repeated at six wavelengths, all of which demonstrate

16 11 this same characteristic. The inset shown in the top right of Figure 1.3 highlights this point by normalizing all of the energy distributions that emphasize that the peak is at half the photon energy for all measured wavelengths. Figure 1.3: Half photon pulses measured at multiple wavelengths with a W-TES with Si substrate and Al rails. Original caption: Pulse height spectra using incident photons from a monochromator at 480, 540, 600, 660, 720, and 780 nm. The counts have been normalized to the same peak height and show a low energy feature below 0.6 ev (2 µm) due to IR emission, and features near half the peak energy (see inset with normalized energy) due to photons which hit the rails. Reproduced from [11]. The presence of unexplained signals in the detector complicates the use of TES in experiments that study uncalibrated sources, where it is desirable to precisely measure an unknown energy. If the full energy is unknown, a half energy peak cannot be eliminated by data processing alone. The source of these signals must be identified and mitigated for the intrinsic energy resolving capabilities of TES to be predictable. A working hypothesis needs to explain how half the photon energy is lost, and why half photon signals are seen at 785 nm (also 480, 540, 600, 660, 720, and 780 nm, from Figure 1.3) but not at 1550 nm. Note: This is only true for detectors with nonabsorptive (at 1550 nm) off-detector elements.

17 12 A previous measurement at 1550 nm by another group detected the appearance of a weak half photon pulse [12]. The TES and wiring are tungsten and niobium, respectively, with an SiO 2 substrate. In the two papers discussed here, two hypotheses attempting to explaining the signal are proposed. Presented here are five hypotheses on the source of these signals, and how they can be tested: Photons that are more energetic break superconducting Cooper pairs in the wires leading up to the TES. The two electrons carry half the photon energy each, but one heads down the wire away from the TES while the other enters and interacts with the TES system, contributing half the photon energy. This can be investigated with position dependent measurement, since illumination of the wires (and not the TES) should produce only half photon signals. Before that though, a simpler mathematical analysis of the size of the superconducting energy gap of the wires versus the TES shows that this cannot be the mechanism responsible for this phenomenon. This is discussed further in Section Photons that are more energetic break a superconducting Cooper pair in the TES with enough energy for one of the electrons to overcome the potential barrier between the two superconductors (the TES and the wires). Thus half the energy is carried away. This hypothesis can be tested by measuring the position dependence of the probability of a half photon detection with respect to the wires point of contact with the TES. Parametric downconversion in the fiber generates unwanted photons that travel down to the detector and are detected.

18 13 A filter at the end of the fiber could rule this process out, but this is already highly unlikely. The probability of downconversion is on the order of 10 6, but the appearance of the half photon pulses is much more probable than this (between 25% and 40%, as shown in the normalized inset of Figure 1.3), so this mechanism can be safely ruled out. The multiple mode-locking system used to generate ultrafast laser pulses could be releasing unwanted photons at multiples of the cavity length. A filter along the optical path could also disprove this hypothesis, but this isn t strictly necessary. The study that generated Figure 1.3 used a monochromator that was able to generate a well known wavelength. A filter could test whether the laser is producing half photon pulses in my experiment, but this mechanism cannot be responsible for the larger phenomenon, and can be ruled out. This is because half photon pulses were detected in the study referenced in Figure 1.3, which used single wavelength sources that generated photons through a different method, and used a filter [11]. Photons that are more energetic and land off the detector are absorbed by the silicon substrate, where just a fraction of the absorbed energy reaches the detector. The simplest way to test this hypothesis is by measuring the position dependence of the probability of detecting a half photon signal off the detector. As the beam moves away from the TES, the fraction of the thermal energy reaching the detector should decrease, slowly decreasing the probability of a half photon detection and the fraction of energy that makes it to the detector. This is supported by the evidence of half photon detections at 1550 nm for TES with impure SiO 2 substrates [12].

19 Superconductivity Less obvious than the operational properties of a TES are the physical properties of superconductors that give the TES these properties. Several theories have been developed to explain the superconducting state. One of the first (and most predictive for its time) theories of superconductivity, developed by Bardeen, Cooper, and Schrieffer (BCS), describes most elemental superconductors (Type 1 superconductors) quite well, and accounts for all of the major phenomena seen in typical low temperature ( K) superconductors [10]. Other types of superconductors have since been discovered, called Type 2 superconductors. These are characterized by the formation of flux-quantized magnetic vortices inside the superconductor. Type 2 superconductors have more complex molecular structures built of cuprates and/or metal alloys which exhibits a high transition temperature ( 70 K) that can be more practical for applications that need to operate at these higher temperatures. Type 2 materials don t follow BCS predictions, but they do follow more complex formalisms that will not be necessary here since all materials in this experiment are either dielectrics or Type 1 superconductors (although niobium does exhibit some Type 2 characteristics). The hallmarks of superconductivity are zero resistivity (supercurrent) and the expulsion of magnetic field from the interior of the superconductor (the Messinger effect), both of which occur below some critical temperature, T C (as well as a critical current I C and a critical magnetic field H C ). For this experiment, only the phenomenon of the transition to zero resistivity as it relates to the critical temperature need be discussed in detail Energy Transport in a Type-I Superconductor Supercurrent can be described as an electronic superfluid that flows with zero viscosity, but more enlightening in the context of this experiment is the Cooper pair quasiparticle description. Consider a free electron embedded in an positively charged lattice. The lattice will distort near the electron as it feels a Coulombic attraction. If another electron is nearby, the Coulombic repulsion of the first electron will be lessened by the shielding provided by the lattice distortion.

20 15 If this distortion is great enough, the space around this electron will become positively charged, and the two electrons will feel a net attraction. This multiparticle interaction, between the two electrons and the lattice, is a Cooper pair. The lattice distortion can be thought of as a virtual phonon (as opposed to a thermal, acoustic, or optical phonon) [10]. A two electron quasiparticle is effectively a boson, and thus no longer restricted by the Pauli exclusion principle. This allows the Cooper pairs to occupy a singular lower energy state, giving rise to a band gap in the electronic structure of a many-electron superconductor according to BCS theory [10]. The thermoelectric properties are simple in the ground state (T = 0), but for greater temperatures, and more importantly, near to the superconducting transition, the picture is much more complicated. Superconducting Cooper Pairs carry no heat, since they have no energetic freedom with which to conduct excess energy. This is responsible for zero resistivity in superconducting materials, as Joule heating only occurs from energetic electrons relaxing to lower energy states (which a Cooper pair cannot do) via collisions. Upon phase change into the superconducting state, thermal transport is coupled more weakly to electronic conduction than at T > T C (in the normal state) [9]. The lattice contribution to heat conduction is proportional to T 3 for a conducting metal, so for low temperatures the lattice contribution is negligible compared to the linearly dependent electronic heat conduction [5]. For non-zero temperatures, excited Cooper pairs will carry thermal energy. Excited Cooper pairs are simply two free electrons, in a superconductor that is below transition, that would form a Cooper pair at lower energies. Thus, a superconductor transports electric energy via bound Cooper pairs, while thermal energy is mainly transported by broken Cooper pairs for T C > T > 0. Hot electrons that have absorbed one or more photons will rapidly thermalize, returning the excess energy to the lattice as heat. A steady state can be obtained by balancing this thermalization time with the optical and thermal power input rate. This is a bolometric measurement. The heat

21 16 equation governing this steady state heat transfer is [7]: Where: C e = γ e V T e, electronic heat capacity C e (T e ) dt e dt = Σ e pv (T e 5 T B 5 ) + P J + P γ T e = 0.16 K (on transition), electron temperature γ e 140 Σ e p 0.4 aj µm 3 K 2, electron specific heat capacity [7] nw µm 3 K 5, electron-phonon coupling constant [7] V = 8 µm 3, TES absorber volume T B = K, bath temperature P J = Joule power deposited by voltage bias P γ = P photon Figure 1.4: Thermal transport of deposited photon energy between a TES and a cooler bath. A photon with energy E = hν will raise T e by an amount determined by C e, the electronic heat capacity. This heat slowly (τ 1 50 µs) dissipates into the tungsten phonon system via the weak thermal link characterized by Σ e p. This time constant is shortened (τ 2 2 µs)by the electrothermal feedback of the voltage bias. The two phonon systems are strongly coupled, so the heat disperses rapidly (τ 3 10 ns) into the substrate once it passes into the lattice. Reproduced from [7]. When: dte dt = 0, this equation simplifies to: Σ e p V (T e 5 T B 5 ) = P J + P γ Calorimetric TES measurements can be thought of as a small perturbation from this steady state equation, where an initially cold ( 0 K) electron that has absorbed a 1550 nm photon will have a rapid temperature rise to 9282 K (or K for 785 nm light). This hot electron will collide and lose energy, eventually thermalizing in a relaxation time τ. The electron-electron relaxation

22 17 time, or the time for the electron system to reach a thermal equilibrium is much shorter than the electron-phonon relaxation time. The application of pulsed light allows for a measurement of this longer relaxation time [9][13]. A system in quasi-equilibrium is a steady state with a gradient. The steady-state case for a TES implies that the electron and phonon systems of the detector are (at least initially) in quasi-equilibrium with each other (meaning T e T B ). This is the Hot Electron model or Two temperature model that well approximates the behavior of an electrically biased superconductor [4][14]. A further extension of this could consider T e T l T B where T l is the phonon/lattice temperature of the tungsten. This is the case shown in Figure 1.4. The model used here assumes that the thermalization time of the electrons (time for T e to become uniform throughout the detector) is negligible, which is a sufficient approximation for most cases Electronic States of a Type-I Superconductor Three types of electrons are present in a superconductor. Bound electrons below the condensation gap do not form Cooper pairs (although they are paired) and are not able to participate in the superconducting state or the lattice interactions. A diagram of the ground state population of electron states at various temperatures can be found in Figure 1.5. The Cooper pairing attraction of the superconducting electrons modifies the conventional electron gas model, introducing a small band gap on the order of mev. Electrons near the Fermi Level condense into Cooper pairs. These pairs occupy a lower energy state, creating a temperature-dependent energy gap (T) in the electron energy band structure [10][15]. Electrons are excited above the energy gap at nonzero temperatures, where they are unpaired and act like ordinary metallic conduction electrons. Near transition, there will be many excited Cooper pairs. Estimates of the size of the superconducting energy gap give insight into the available energy states of this dynamic system. Exact formulas for the gap at T = 0 are known, and formulas for near T C give the approximate behavior of the superconducting gap before it vanishes.

23 Figure 1.5: Density of states of the electrons in a superconductor, with temperature increasing towards the right. Graph A shows the occupation (shaded region) at T = 0 K, where the superconducting gap is at a maximum. Note that the gap is centered around the Fermi Energy, E F. The electrons normally occupying the gap up to E F occupy lower states beneath the gap in Cooper Pairs, lowering the total energy of the ground state wave function. In Graph B the nonzero temperature has excited (i.e. broken into two free electrons) a fraction of the Cooper pairs above the gap, which reduces in size with increasing temperature. Graph C shows a superconductor returning to the normal state, where the density of states is the same as that of a regular metal at nonzero temperatures. Here there is no gap. Reproduced from [16]. 18

24 19 The formulas for the zero temperature (T = 0 K) gap ( (0)) and the gap for T near T C ( (T)) are [10]: (0) = 1.75k B T C (T ) = 3.2k B T C (1 T T C )) 1 2 This approximates the size and temperature dependence of the superconducting energy gap for type I superconductors. Calculations for relevant materials, along with values of T C used are listed in Table 1.6. Table 1.6: T C for tungsten was determined experimentally for our device. Other T C values are from literature. Gap values for T = 0.9T C show the behavior of as T T C. Beyond T C, = 0. Note the small change in (compared to E γ = 800 mev) despite the relatively large change in T C. W Al Nb T C [K] [4] 9.5 [4] (0) [mev] ( T T C = 0.9) [mev] The values of between T = 0 and T T C = 0.9 listed in Table 1.6 are strong evidence that the breaking of Cooper pairs in the wires cannot be the source of the half photon signal. This is made evident by comparing the energies known to produce integer or half integer signals. A 1550 nm photon has an energy E 1550 = 0.8 ev, producing only integer signals. A 785 nm photon (as well as photons ranging between 480 and 780 nm from Figure 1.3) has an energy E 785 = 1.6 ev (or greater), producing both integer and half integer signals. Comparing the maximum values of ( Max = (0)) to the two photon energies shows that E 785 > E 1550 > (0) for all three materials. This means that if Cooper pairs in the wires were the source of the half photon signal, that it should be seen at 1550 nm too. Results in Section 3.3 show that this is not the case, so this hypothesis can be ruled out.

25 Chapter 2 Experimental Details The main experimental challenges were monitoring the environmental controls needed to reach sub-kelvin temperatures, characterization of the piezoelectric positioning system, and testing the tungsten transition edge sensor (W-TES), superconducting quantum interference devices (SQUIDs), and all supporting electronics and optics. The W-TES acts as the absorber element, while the SQUIDs act as signal amplifiers. 2.1 TES Chip Design The TES studied for this project was designed and built by a group studying the TES fabrication process. They have demonstrated that precision control of the deposition process and material layering sequence provides tunability of the transition temperature(t C ) and the maximum absorptivity at some optimal wavelength. [17][18]. Using these methods, they have fabricated a tungsten TES with a measured absorptivity of 96% at the design wavelength of 1550 nm. The absorptivity at the second experimental wavelength (785 nm) is 74%. The superconductor is embedded in a dielectric stack. This stack was engineered by the fabrication group to be impedance matched to free space at the designed wavelength. This prevents reflection while promoting absorption. The mirror at the bottom of the stack boosts net absorptivity by reflecting back transmitted light. The vertical dimensions and ordering of the layers making up the TES are visible in Figure 2.1. The superconducting element, tungsten, is very thin, only 20 nm thick. Superconducting niobium wires leading to the TES ensure that no unwanted resistive

26 heat is dissipated near the TES itself. The transition temperature of niobium is well above that of tungsten (see Table 1.6), so the wires are not near to transition during TES operation. 21 Figure 2.1: Diagram of TES stack components indicating the composition, thickness, and function of each layer. The diagram is not to scale. The Si layer on bottom is much thicker (545 µm is typical) than the layers of the TES. Guide arrows point towards the center of the TES, while a photodiode underneath the substrate provides through chip imaging capabilities. To facilitate the positioning process, guide arrows and a photodiode are included in the design. The guide arrows point towards the TES, and are visible in the large photographs and maps of the TES in Figures 1.2, 2.9, and 2.10.

27 22 Guide arrows are used for rough positioning of the beam on the TES. For finer positioning the photodiode is used to generate a map of where absorptive elements block the beam. A diagram of this setup is shown in Figure 2.2. Maps made from the photodiode response are shown in Figures 2.9 and These types of scans were run at nominal power levels between mw. Figure 2.2: Absorption locations of experimental wavelengths (1550 nm and 785 nm). Tungsten absorbs both frequencies well. Si absorbs 785 nm light while allowing 1550 nm light through to the photodiode, where it is detected. This is useful for mapping the chip when the tungsten is not superconducting.

28 Cryogenic Cooling Maintaining a bath temperature at temperatures below the critical temperature of the TES (T C = 0.16 K, T B = K) required a multi-stage helium dilution refrigerator (pictured in Figure 2.3). Figure 2.3: Setup at the lab with stages labeled by temperature. Thermal shields and vacuum isolate each cold plate from one another and the surroundings. The TES is housed on the final (15 mk) stage. The piezoelectric positioners are mounted to the 100 mk stage. The SQUIDs are mounted to the 1 K stage. Diagram on the left reprinted from [19]. 2.3 Electronics Three inductively coupled circuits amplify the photon signal. These circuits are referred to as the TES circuit, the SQUID circuit, and the feedback (FB) circuit (left to right) in Figure 2.4. The TES in its circuit acts as a variable resistor. The lead resistors, (R L ) draw a steady current towards the junction, where the current supplied to the TES circuit is split unevenly between the two paths. On the TES circuit (left, Figure 2.4), the shunt resistor (R s ) offers a constant path of

29 24 least resistance for the current, routing just a fraction (between 1% and 0.2%) of the total current through the TES (while maintaining the voltage bias that stabilizes the TES on the superconducting transition). The parasitic resistance (R p ) in series with the TES is small (compared to the resistance of the TES), and is caused by any impurities and/or non-superconducting regions along this path. The varying current generates magnetic flux from the inductor that is mounted next to the SQUID. SQUIDs will be discussed in more detail in Section The inductor in series with the TES is coupled to the SQUID amplifier array, shown as a single SQUID in Figure 2.4. As the inductor s current supply is decreased from the increase in resistivity, the magnetic flux of the inductor falls. The corresponding small change in flux measured by the SQUID response will be amplified and coupled out of the cryostat for measurement. Figure 2.4: Diagram of TES, SQUID, and feedback circuits. The supply indicates the controlled bias for each circuit, either current or voltage, for this setup all are voltage biased. V SQUID is where the output signal is measured. R s = 10 mω R p 50 mω R L = 5 kω R T ES = 1 5 Ω (varies) L F B = 8L T ES 20 nh Note: The inductor L TES includes a contribution to the total inductance from the TES and wires, L TES = L W TES + L wires + L inductor, all of which are small (on the order of nh)

30 Superconducting Quantum Interference Devices SQUIDs are magnetometers which can measure the smallest quantized unit of magnetic flux, Φ 0. They are commonly used in low temperature applications to measure and amplify small signals by converting the signal into a varying flux (usually by addition of an inductor to the circuit). SQUIDs have two operational modes, DC and RF. Only DC SQUIDs will be discussed, as these are the only type used for this experiment. A Josephson junction is a thin layer of non-superconducting material that acts as a barrier between two superconducting current carrying wires. The superconducting current is actually able to quantum mechanically tunnel through the junction, which is typically called an S/I/S (superconducting/insulating/superconducting) junction. Two of these junctions in parallel makes a SQUID. To amplify the minute signal generated by the absorption of a single photon, the signal from an array of 100 SQUIDs leads out of the refrigerator to an amplifier with a gain of 100. With this factor of 10,000 amplification, a single photon signal is a transient pulse lasting 3 µs, which peaks at 5 mv (see Figure 2.11). Since the SQUID is so sensitive, it requires strong shielding from external magnetic interference. The heat shields on the cryostat offer a small degree of magnetic shielding, but are mostly for thermal isolation. Leads going in and electronics housed inside the refrigerator itself are more likely to generate unwanted magnetic flux. The SQUIDs are also isolated by being housed on a different stage than the other electronics. The final stage of shielding is a precision machined Nb box that the SQUIDs are housed in. This superconducting box is the most effective at protecting the SQUIDs from external fields. The SQUID array (and its neighboring inductors, as shown in Figure 2.5) are located on the 1 K plate of the cryostat, with an 18 wire between the TES and inductor/squid board. This is feasible because the operational temperature of the SQUIDs ( 7 K) is not as low as that of the TES ( 0.1 K).

31 26 Figure 2.5: Large solid arrows show the flux generated by feedback and TES inductors. Dashed arrows show the opposing flux generated by the SQUID. Direction of the generated current in the SQUID is indicated by small solid arrows. X marks the two Josephson junctions. The change in the ratio of flux from the two inductors creates a ratio of current in the two SQUID branches that is measured as a the indicated voltage, V SQUID. 2.4 Pulse Generation & Coupling A single photon source can be generated many ways, and there are many methods of varying the mean photon number of the beam. The lasers operated in the lab generate massive numbers of photons in coherent pulses that would saturate a TES. These sources have been calibrated, and have frequency and power outputs that are reliable with a narrow linewidth and drift. To turn down the beam to single photon levels, the quick and dirty way is to pull the fiber connector partially out of the mating port, so that the beam is barely coupled into the cryostat. This has the downfall of being extremely unstable and totally unrepeatable, so a more refined, but still fairly quick/dirty method was devised: a free space decoupler. Moving the decoupling mechanism onto an optical mount greatly improves the stability of the beam alignment that is now maintained precisely for further measurements. Two mirrors couple the beam into a fiber lens, where the coupling can be verified by a conventional power meter. Once

32 27 the fiber output has been verified to match expectations, the fiber is plugged (firmly this time) into the mating port of the cryostat. The detector will initially be flooded, but slow movement of the mirrors will eventually worsen the alignment to the point that only a few photons couple into the fiber each laser pulse. This provides a stable source with a constant mean photon number, < N γ > that can be used for a position dependent scan. Once the fiber passes into the vacuum chamber it is threaded down each level until it is aimed at the 15 mk stage. Here the piezoelectric positioners hold a graded index fiber lens that focuses the beam. The beam then passes through vacuum before hitting the TES. Figure 2.6: Layout of source to detector optics showing the two laser sources used. The 1550 diode laser is pulsed with an external trigger. The 785 fs Ti:Sapph (Titanium Sapphire) laser is pulsed without a trigger, so it goes straight to the free space decoupler when active. The decoupler itself is merely a method of reducing the beam intensity to a fixed level. The power is measured with the beam well coupled to the fiber before passing the signal to the cryostat. This ensures that the laser is behaving before turning the intensity down by tuning the micrometers on the mirrors.

33 Piezoelectric Micropositioners An optical fiber feeds directly into the refrigerator, ending in a graded index lens. The lens is mounted on a multi-stage piezoelectric positioner, pictured in Figure 2.8. The first stage offers 3D motion with a range of 4 mm with a step size of 1 µm. Two types of piezoelectric positioners were used. The range, stability, and limitations of these stages are listed in Table 2.7. Table 2.7: Summary of the two complementary piezoelectric stages. Stage 1 Stage 2 Range: 4 mm 4 mm 4 mm: Region A 33 µm 33 µm: Region B (See Figure 2.9) Motion: 3D Stick-slip 2D Continuously expanding Advantages: Large range, measures absolute position Low noise (DC) Disadvantage: Noisy (RF) Small range, requires calibration While these piezoelectric stages are designed to operate under vacuum at 4 K, the stage they are mounted to reaches 100 mk. Before measuring the position dependent response of the TES, it was imperative to verify that it was even possible to push this hardware beyond its designed specifications. The first task was monitoring the shifting of the positioners during the cooldown. A shift of 10 µm after a 270 degree cooldown was measured and corrected for. At 3 K, another scan was taken, shown in Figure 2.9. Next, careful monitoring of the chamber temperature verified that operation of the piezoelectrics did not generate more heat than the sink could wick away, even at these subkelvin temperatures. The large scan range shown in Figures 2.9 and 2.10 is only viable for measurements taken with the through-chip imaging diode. The noise generated by the repetitious slip-then-stick motion that drives the first positioner dominates the sensitive TES and SQUID electronics. Even when stationary, the RF pickup noise generated by the positioner leads was greater than the photon signal size. To circumvent this the first stage is disconnected, and a secondary stage is turned on. The DC stage has a smaller range, so the beam waist must lie on the TES before this stage is used.

34 Figure 2.8: Photograph of piezoelectric stages mounted on the cryostat. The piezoelectrics are mounted on the 100 mk stage to reduce the thermal load on the final stage. The TES itself is visible beneath the positioners. The substrate of the TES is thermally linked to the 10 mk stage. Fibers on the left and cables in the rear lead to other experiments located nearby. 29

35 Figure 2.9: Position dependent scan of TES and Nb wires at 3K using the photodiode. This scan covers an area of mm 2. The boxed area labeled Scan Region B shows the range of the secondary positioner stage. This subregion extends from the center of the TES to the substrate. Guide arrows are also visible. 30

36 Data Acquisition TES Mapping At such low power levels, any source of loss can drastically cut efficiency. Therefore fiberdetector alignment (both in plane and in focus) is critical for achieving a near unity efficiency. Proper alignment was achieved by repeated scans of the TES in 3D space with the first stage piezoelectric actuators. A photodiode beneath the TES creates a map of the detector from the voltage response, which is a minimum beneath the highly absorptive detector. The principle is shown in Figure 2.2. Scanning the edge of the device produces an image that is a 2D gaussian (the beam spot) convolved with a square step function (the TES). Deconvolution of the gaussian beam indicates how close the center of the TES is to the beam waist (in Z), R w 10 µm at the focal point. Figure 2.10: Position dependent response of photodiode, scanned over a large chip area (0.92 mm 2 ). The hot spots are where the 1550 nm light passes through the Si substrate, while the cooler regions are absorptive Nb and W.

37 Photon Pulses Each pulse is represented by a 256 point vector, representing V (t), where t is evenly spaced at the sample rate of 20 MHz. Raw data representing the TES response to the detection of increasing numbers of photons (up to < N γ > = 7) are shown in Figure The amount of data had to be downsampled by a factor of 2 (from 2 29 to 2 28 bits of data) to allow for computer analysis. Figure 2.11: Voltage versus time plot of SQUID amplification output. Each pulse is sorted in time and grouped by energy. Only traces corresponding to the peak 0, 1, 2, 3, 4, 5, 6, 7 photon bins are plotted. Note that the 0 bin truly is a null detection, with a flat and distinguishable result from that of a detection of an absorption event.

38 Chapter 3 Results 3.1 Data Analysis A large amount of data was acquired, specifically more than a million traces were collected per position, and 36 positions were measured for two different wavelengths. Careful management of these large data sets was a key challenge of this project. The first stage of data analysis (shown in Figure 3.1) consisted of ordering the pulses with a spatial-temporal index that correlates elapsed time with the motion of the scanner. Each indexed pulse lasts for 12.5 µs, and is sampled 256 times. These vectors, V (t), are ordered to build an array of pulses whose order encodes the motion of the piezoelectric scanner. These pulses are individually assigned a height, calculated as the inner product of an optimal filter and each raw pulse. This height distribution will eventually determine < N γ >, the mean photon number. Matched (or optimal) filters are designed to maximally boost the signal-to-noise ratio. This filter, shown in Figure 3.1, was computed as the average of many (2 27 ) real pulses. This is effectively the mean pulse shape for a mean photon number (< N γ >) of 1. While this choice of filter used works well for unsaturated pulses it becomes less accurate with increasing N γ, due to the nonlinear change in pulse shape. Looking at the generated histogram, distinct peaks are clearly visible. These peaks are identifiable as discrete events with a finite uncertainty. The spacing between each peak will be the photon energy, E = hν. Looking at the raw pulses, shown in Figure 2.11, it is obvious that the first peak in the histogram is truly a null detection, and is not a peak in voltage. This justifies setting

39 34 Figure 3.1: Process of binning raw SQUID voltage data (photon pulses) into height sorted histograms, where height is a measure of energy. Note that the ordering of these data in time captures the motion of the piezoelectric scanner, allowing construction of a 2D image. This generated Figures 3.5, 3.6, and 3.8. the center of this peak to be the detector zero. The next peak is identified as the first photon peak, allowing for a calibrated energy scale to be affixed to the previously arbitrary scale. This method is limited to lower photon numbers due to a nonlinear increase in pulse height with deposited energy. The energy scale could be parametrically fit to higher order to this change in pulse height, but that wasn t necessary for this analysis. Next, the uncertainty in the energy measurement is calculated as the full width half maximum of a series sum of gaussian distributions fit to the calibrated histograms. The process is shown for a single peak in Figure 3.2.

40 35 Figure 3.2: Binned histogram sets the energy scale by assigning photon numbers to each peak. The photon energy is precisely known, so the energy spread due to thermal noise is calculable as the full width half maximum (FWHM) of the distribution for 0, 1,..., etc. photons. This was performed on datasets shown in Figures 3.5, 3.6, and 3.8. Characterizing these distributions is simple, due to the fact that photons arrive at the detector according to a Poisson distribution, expressible as [20]: Where: P(n) is the probability of measuring a number n P (n) = e N N n n! n is an integer, representing a single measurement outcome N is the mean photon number (< N γ >) for this distribution The final energy histograms are Poissonian distributions (characterized by < N γ >) convolved with Gaussian noise (characterized by E FWHM ) [1]. Therefore, each of these histograms is characterizable by four numbers: mean photon number (< N γ >), noise ( E FWHM ), position (1-36), and wavelength (785 or 1550). Noise had little variance, but the position dependence of < N γ > was largely dependent on the illumination of the TES. This allowed for a map to be constructed solely from the change in < N γ > by following the process outlined in Figure 3.3.

41 36 Figure 3.3: Once the energy scale is established, the photon number scale is also established. By reevaluating these spatially dependent data with known photon numbers assigned to each distribution, a map of the TES is created. This generated Figures 3.7 and Limitations of Chosen Filter Since the pulse height is strictly monotonically increasing with respect to increasing energy, the use of fixed filter is valid for initial characterization of the pulse energy distributions. For larger photon numbers, a better algorithm is needed; either an integration-under-the-curve as height or a moving optimum filter that changes shape according to the pulse height (or integrated area). A cursory attempt at integrating under the curve quickly showed that this method is noisier than the fixed optimum filter. A variable filter seems more promising and as shown in Figure 3.4, this has been demonstrated to improve the uniformity of energy resolution with increasing photon numbers [21]. Photon numbers above a threshold (N γ > 8 for my detector, N γ > 6 for the detector shown in Figure 3.4) necessitate the development of a moving filter to maintain an energy resolution able to differentiate between N γ from N γ + 1. This limit is clearly visible in Figure 3.6.

42 37 Figure 3.4: Energy resolution vs photon number for two choices of filter. The upper line shows the resulting increase in E F W HM with increasing photon number from using a single filter as a global optimum. The lower line shows the increased resolution (especially at higher N γ ) provided by a robust variable filter that changes with increasing energy. Reproduced from [21].

43 Results Summary Comparison of the position independent histograms in Figure 3.5 illustrates the characteristic behavior of the TES response at 785 and 1550 nm. A half photon peak is visible at half the energy of the 785 nm photon. That this half photon energy is nearly equal to the energy of the 1550 nm photon is coincidental (E 1550 = ev, E 785 /2 = ev). Figure 3.5: Counted events vs energy of TES response over scan region B to two wavelengths, with position dependence removed by summation. These histograms of pulse heights were used for calibration. Every 0.8 ev has been labeled (0.8 ev = E 1550 ) in order to make visible the deviation of the linear calibration from the nonlinear increase in pulse height with energy nm Results At 1550 nm, the W-TES design efficiency of 96% gives a typical TES response [1][7], from which the energy resolution of the TES, mean photon number of the beam, and position dependence of their interactions have been determined. The position independent energy resolution E FWHM = 0.27 ev is more than sufficient to resolve single photons at this photon energy. For this study, it is important to note that there are no half photon detections seen at this photon energy level.

44 39 Figure 3.6: Semilog plot showing energy distributions of photon pulses. Peaks are well resolved up to N γ > 7. This is a summation over all position dependent data. The energy resolution here is 0.27 ev. Further analysis of the energy histograms as described in Section 3.1 determined the position dependencies of the mean photon number shown in Figure 3.7. The TES is maximally responsive at (0, 0) volts on the secondary scanner where the beam is centered on the TES, and it is minimally responsive (< N γ > 0) at (100, 100) where the beam waist lies off the detector. The scan range used is Region B, shown in Figure 2.9.

45 40 Figure 3.7: Position dependent measured mean photon number over region B (boxed in Figure 2.9) at 1550 nm. The distance is measured in volts applied to an axis on the piezoelectric scanner. The correspondence from volts to distance was determined to be 1µm 3V. The maximum response is the center of the TES, while the minimum response is off the TES.

46 nm Results At 785 nm, the W-TES design efficiency of 74% gives a less typical (though not unique, see Figure 1.3 [11]) response, shown in Figure 3.8. This sort of response is characterized by the appearance of peaks in the energy spectrum at half the energy of the incident photons. The position independent energy resolution of the main pulses is ev. This is sufficient to resolve single photons at this energy, although it isn t sufficient to distinguish between integer photons and half photons in the region where their tails overlap. An estimate of the energy resolution of the secondary pulses was calculated by doubling the width of the tail, giving E FWHM = ev. The locations of the secondary peaks are much easier to locate on a semilog scale, as shown in Figure 3.9. Figure 3.8: Counts vs energy for 785 nm photon detections. Position dependence has been removed via summation. Note the apparent half photon pulses, and the drift away from the energy calibration (marked by dashed red lines) as N γ increases. Running a position dependent analysis on this dataset required a little more creativity, as the uncertainties on the distributions threw into question which integer to assign to which bin. The only certain measure of the distributions was the height of each peak. By using this as a measure the data was effectively downsampled, but for a distribution generated from a large number of

47 42 Figure 3.9: Semilog plot of counts vs energy at 785 nm. Here the maximum distinguishable photon number is N γ = 5. Position dependence has been removed via summation. samples this gives a good measure of the overall counts (as if the data had been sampled fewer times with a higher resolution). This allowed me to generate two separate distributions at each position. Fitting a Poissonian, as described in Section 3.1, to the integer distribution determined the fit parameter, < N γ > at each position. This generated a map (top, Figure 3.10) that has the expected shape of the TES. Equivocal to the 1550 nm case, the mean number of detections is at a maximum at (0, 0) on the piezoelectric scanner, and at a minimum (< N γ > 0) at (100, 100), where the beam lies off the detector. Of more interest is the result of the position dependence of the fit to the half integer data. This fit was generated by mapping the set of half integers to a corresponding set of integers, as the Poisson distribution only accepts integer arguments ( 1 2 1, 3 2 2, etc). The resulting distribution returns a fit parameter, < N γ >, that can be thought of as the mean number of half integer detections. Since zero counts were included in the distribution of integer detections and not in the half integer analysis, the number of half integer detections are artificially increased relative

48 43 to the integers. Relative numbers between the two plots are not as useful as the range of deviation in < N γ >. A plot of the position dependence of this parameter, shown in Figure 3.9, reveals that the fall off in mean half integer detections as the beam travels off the detector is a factor of 10 less than that of the integers. Figure 3.10: Position dependence of the mean photon number, separately plotted for integer (top) and half integer (bottom) photon detections.these plots were obtained by separating the integer (taller) peaks from the half-integer (smaller) peaks (shown in Figure 3.8 before calculating the mean photon number position dependence. This shows that the integer pulses behave as they did for 1550 nm light, falling off as the scanner moves off the detector. However, the half integer pulses show a markedly different behavior, characterized by a nearly uniform distribution everywhere. The correspondence from volts to distance was determined to be 1µm 3V.