Calibration and Testing of Small High-Resolution Transition Edge Sensor Microcalorimeters with Optical Photons.

Pulses of narrow line-width optical photons can be used to calibrate and test sub-2 eV full-width at halfmaximum (FWHM) energy resolution transition-edge sensor (TES) microcalorimeters at low energies (< 1 keV), where it is very challenging to obtain X-ray calibration lines comparable to (or narrower than) the detector resolution. This scheme depends on the ability to resolve the number of 3 eV photons in each pulse, which we have recently demonstrated up to photon numbers of about 300. At LTD-18 we showed preliminary results obtained with this technique on a 0.25 eV baseline resolution TES microcalorimeter designed for the ultra-high-resolution subarray of the Lynx mission. The line-shape was well described by a simple Gaussian. However, the difficulty of delivering photons to the small 46 µm square absorbers resulted in a large thermal crosstalk signal, whose random nature is expected to rapidly degrade the observed energy resolution towards higher photon numbers/energies. We have since improved the coupling between the optical fiber and the TES absorber and report here our current results.

Energy calibration of high-resolution X-Ray TES microcalorimeters with 3 eV optical photons.

With the improving energy resolution of transitionedge sensor (TES) based microcalorimeters, performance verification and calibration of these detectors has become increasingly challenging, especially in the energy range below 1 keV where fluorescent atomic X-ray lines have linewidths that are wider than the detector energy resolution and require impractically high statistics to determine the gain and deconvolve the instrumental profile. Better behaved calibration sources such as grating monochromators are too cumbersome for space missions and are difficult to use in the lab. As an alternative, we are exploring the use of pulses of 3 eV optical photons delivered by an optical fiber to generate combs of known energies with known arrival times. Here, we discuss initial results of this technique obtained with 2 eV and 0.7 eV resolution X-ray microcalorimeters. With the 2 eV detector, we have achieved photon number resolution for pulses with mean photon number up to 133 (corresponding to 0.4 keV).

Mapping TES Temperature Sensitivity and Current Sensitivity as a Function of Temperature, Current, and Magnetic Field with IV curve and Complex Admittance Measurements.

We have specialized astronomical applications for X-ray microcalorimeters with superconducting transition edge sensors (TESs) that require exceptionally good TES performance, but which operate in the small-signal regime. We have therefore begun a program to carefully characterize the entire transition surface of TESs with and without the usual zebra stripes to see if there are reproducible local "sweet spots" where the performance is much better than average. These measurements require precise knowledge of the circuit parameters. Here, we show how the Shapiro effect can be used to precisely calibrate the value of the shunt-resistor. We are also investigating the effects of stress and external magnetic fields to better understand reproducibility problems.

Dynamics and energy spectra of aperiodic discrete-time quantum walks.

We investigate the role of different aperiodic sequences in the dynamics of single quantum particles in discrete space and time. For this we consider three aperiodic sequences, namely, the Fibonacci, Thue-Morse, and Rudin-Shapiro sequences, as examples of tilings the diffraction spectra of which have pure point, singular continuous, and absolutely continuous support, respectively. Our interest is to understand how the order, intrinsically introduced by the deterministic rule used to generate the aperiodic sequences, is reflected in the dynamical properties of the quantum system. For this system we consider a single particle undergoing a discrete-time quantum walk (DTQW), where the aperiodic sequences are used to distribute the coin operations at different lattice positions (inhomogeneous DTQW) or by applying the same coin operation at all lattice sites at a given time but choosing different coin operation at each time step according to the chosen aperiodic sequence (time dependent DTQW). We study the energy spectra and the spreading of an initially localized wave packet for different cases, finding that in the case of Fibonacci and Thue-Morse tilings the system is superdiffusive, whereas in the Rudin-Shapiro case it is strongly subdiffusive. Trying to understand this behavior in terms of the energy spectra, we look at the survival amplitude as a function of time. By means of the echo we present strong evidence that, although the three orderings are very different as evidenced by their diffraction spectra, the energy spectra are all singular continuous except for the inhomogeneous DTQW with the Rudin-Shapiro sequence where it is discrete. This is in agreement with the observed strong localization both in real space and in the Hilbert space. Our paper is particularly interesting because quantum walks can be engineered in laboratories by means of ultracold gases or in optical waveguides, and therefore would be a perfect playground to study singular continuous energy spectra in a completely controlled quantum setup.