Measurements of the thermal properties of nanoscale electron systems have ignored the effect of electrical noise radiated between the electron gas and the environment, through the electrical leads. Here we calculate the effect of this photon-mediated process, and show that the low-temperature thermal conductance is equal to the quantum of thermal conductance, GQ = pi2kB2T/3h, times a coupling coefficient. We find that, at very low temperatures, the photon conductance is the dominant route for thermal equilibration, while at moderate temperatures this relaxation mode adds one quantum of thermal conductance to that due to phonon transport.

Time-division multiplexing (TDM) is a mature scheme for the readout of arrays of transition-edge sensors (TESs). TDM is based on superconducting-quantum-interference-device (SQUID) current amplifiers. Multiple spectrometers based on gamma-ray and X-ray microcalorimeters have been operated with TDM readout, each at the scale of 200 sensors per spectrometer, as have several astronomical cameras with thousands of sub-mm or microwave bolometers. Here we present the details of two different versions of our TDM system designed to read out X-ray TESs. The first has been field-deployed in two 160-sensor (8 columns × 20 rows) spectrometers and four 240-sensor (8 columns × 30 rows) spectrometers. It has a three-SQUID-stage architecture, switches rows every 320 ns, and has total readout noise of 0.41 μΦ0/√Hz. The second, which is presently under development, has a two-SQUID-stage architecture, switches rows every 160 ns, and has total readout noise of 0.19 μΦ0/√Hz. Both quoted noise values are non-multiplexed and referred to the first-stage SQUID. In a demonstration of this new architecture, a multiplexed 1-column × 32-row array of NIST TESs achieved average energy resolution of 2.55±0.01 eV at 6 keV.

We describe a series of microcalorimeter X-ray spectrometers designed for a broad suite of measurement applications. The chief advantage of this type of spectrometer is that it can be orders of magnitude more efficient at collecting X-rays than more traditional high-resolution spectrometers that rely on wavelength-dispersive techniques. This advantage is most useful in applications that are traditionally photon-starved and/or involve radiation-sensitive samples. Each energy-dispersive spectrometer is built around an array of several hundred transition-edge sensors (TESs). TESs are superconducting thin films that are biased into their superconducting-to-normal-metal transitions. The spectrometers share a common readout architecture and many design elements, such as a compact, 65 mK detector package, 8-column time-division-multiplexed superconducting quantum-interference device readout, and a liquid-cryogen-free cryogenic system that is a two-stage adiabatic-demagnetization refrigerator backed by a pulse-tube cryocooler. We have adapted this flexible architecture to mate to a variety of sample chambers and measurement systems that encompass a range of observing geometries. There are two different types of TES pixels employed. The first, designed for X-ray energies below 10 keV, has a best demonstrated energy resolution of 2.1 eV (full-width-at-half-maximum or FWHM) at 5.9 keV. The second, designed for X-ray energies below 2 keV, has a best demonstrated resolution of 1.0 eV (FWHM) at 500 eV. Our team has now deployed seven of these X-ray spectrometers to a variety of light sources, accelerator facilities, and laboratory-scale experiments; these seven spectrometers have already performed measurements related to their applications. Another five of these spectrometers will come online in the near future. We have applied our TES spectrometers to the following measurement applications: synchrotron-based absorption and emission spectroscopy and energy-resolved scattering; accelerator-based spectroscopy of hadronic atoms and particle-induced-emission spectroscopy; laboratory-based time-resolved absorption and emission spectroscopy with a tabletop, broadband source; and laboratory-based metrology of X-ray-emission lines. Here, we discuss the design, construction, and operation of our TES spectrometers and show first-light measurements from the various systems. Finally, because X-ray-TES technology continues to mature, we discuss improvements to array size, energy resolution, and counting speed that we anticipate in our next generation of TES-X-ray spectrometers and beyond.

We experimentally demonstrate the high bandwidth readout of a thermometer based on a superconductor-insulator-normal metal ͑SIN͒ tunnel junction, embedded in a rf resonant circuit. Our implementation enables basic studies of the thermodynamics of mesoscopic nanostructures. It can also be applied to the development of fast calorimeters, as well as ultrasensitive bolometers for the detection of far-infrared radiation. We discuss the operational details of this device, and estimate the ultimate temperature sensitivity and measurement bandwidth.

We demonstrate very high resolution photon spectroscopy with a microwave-multiplexed two-pixel transitionedge sensor (TES) array. We measured a 153 Gd photon source and achieved an energy resolution of 63 eV full-width-at-half-maximum at 97 keV and an equivalent readout system noise of 86 pA/ √ Hz at the TES. The readout circuit consists of superconducting microwave resonators coupled to radio-frequency superconductingquantum-interference-devices (SQUID) and transduces changes in input current to changes in phase of a microwave signal. We use flux-ramp modulation to linearize the response and evade low-frequency noise. This demonstration establishes one path for the readout of cryogenic X-ray and gamma-ray sensor arrays with more than 10 3 elements and spectral resolving powers R = λ/∆λ > 10 3 .Multiplexed readout of sub-Kelvin cryogenic detectors is an essential requirement for large focal plane arrays. Next-generation instruments for the detection of electromagnetic radiation from gamma-ray to far-infrared wavelengths will have pixel counts in the 10 3 -10 6 range and require readout techniques that do not compromise their sensitivity. To date, many instruments have used time-, frequency-, or code-domain SQUID multiplexing schemes 1-3 . One such instrument, the TES bolometer camera SCUBA2, has achieved background-limited sensitivity in 10 4 pixels using time-domain multiplexing (TDM) 4 . Similarly, calorimetric gamma-ray/X-ray spectrometers that use TDM have reached excellent energy resolutions of δE ≈ 50 eV at 100 keV in a 256-pixel array 5 . However, the scalability of these readout approaches is limited by the finite measurement bandwidth (∼ 10 MHz) achievable in a flux-locked loop.Kinetic Inductance Detectors (KIDs) 6,7 , on the other hand, provide a possible path to higher multiplexing factors. These devices are naturally frequency-multiplexed and the ultimate limit on the available bandwidth is many gigahertz, which is set by the readout cryogenic amplifier. Present limits in room-temperature electronics impose a 550 MHz bandwidth limit 8 , but this figure will improve steadily. However, the sensing element is part of a thin-film superconducting resonator, so readout and signal generation can be difficult to simultaneously optimize. This challenge is particularly severe for spectroscopic X-ray and gamma-ray detectors, which must stop high-energy photons and where spatial variation in the device response must be smaller than 0.1%. X-ray and gamma-ray spectroscopy results achieved to date with KIDs are not yet compellingly better than conventional semiconducting detectors 9,10 . a) Electronic mail: omid.noroozian@nist.govMicrowave SQUID multiplexing 11,12 (µMux) is a readout technique that potentially combines the proven sensitivity of TESs and the scalable multiplexing power found in KIDs. Microwave SQUID multiplexing uses radiofrequency (rf) SQUIDs coupled to high quality-factor (Q) microwave resonators and has sufficiently low noise to read out the most sensitive cryogenic detectors. Additionally, it al...