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.

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).

We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the octagonally symmetric Ammann-Beenker tiling. The dynamics of the quantum particle are modelled using the continuous-time quantum walk (CTQW) formalism. We present a comparison of the behaviour of the CTQW on the two aperiodic quasicrystal lattices and the square lattice when all the vertices are connected and when disorder is introduced in the form of disconnections between the vertices. Unlike on a square lattice, we see a significant fraction of the quantum state localized around the origin in the quasicrystal lattices. With increase in disorder, the percolation probability of a particle on a quasicrystal lattice decreases significantly faster when compared to the square lattice. This study also sheds light on the fraction of disconnections allowed to see percolation of quantum particle on these quasicrystal lattices.

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.