Dilution Refrigerator for Nuclear Refrigeration and Cryogenic Thermometry Studies

This study explores the design and construction of an ultra-low temperature facility in order to realize the Provisional low-temperature scale from 0.9 mK to 1 K (PLTS-2000) in Japan, to disseminate its use through calibration services, and to study thermometry at low temperatures below 1 K. To this end, a dilution refrigerator was constructed in-house that has four sintered silver discrete heat exchangers for use as a precooling stage of a copper nuclear demagnetization stage. A \(^{3}\text {He}\) melting curve thermometer attached to the mixing chamber flange could be cooled continuously to 4.0 mK using the refrigerator. The dependence of minimum temperatures on circulation rates can be explained by the calculation of Frossati’s formula based on a perfect continuous counterflow heat exchanger model, assuming that the Kapitza resistance has a \(T^{-3}\) temperature dependence. Residual heat leakage to the mixing chamber was estimated to be around 86 nW. A nuclear demagnetization cryostat with a nuclear stage containing an effective amount of copper (51 mol in a 9 T magnetic field) is under construction, and we will presently start to work toward the realization of the PLTS-2000. In this article, the design and performance of the dilution refrigerator are reported.     

An Aboveground Pulse-Tube-Based Bolometric Test Facility for the Validation of the LUMINEU \hbox {ZnMoO}_4 Crystals

The LUMINEU project aims at developing a pilot double beta decay experiment using scintillating bolometers based on ZnMoO \(_4\) crystals enriched in \(^{100}\hbox {Mo}\) . In the next months regular deliveries of large-mass \(\hbox {ZnMoO}_4\) crystals are expected from the Nikolaev Institute of Inorganic Chemistry (Novosibirsk, Russia). It is therefore crucial for the LUMINEU program to test systematically and in real time these samples in terms of bolometric properties, light yield and internal radioactive contamination. In this paper we describe an aboveground cryogenic facility based on a dilution refrigerator coupled to a pulse-tube cooler capable performing these measurements. A 23.8 g \(\hbox {ZnMoO}_4\) crystal was fully characterised in this setup. We show also that macro-bolometers can be operated with high signal-to-noise ratio in liquid-free dilution refrigerators.     

Magnetic Shielding of an Adiabatic Demagnetization Refrigerator for TES Microcalorimeter Operation

We are developing a compact adiabatic demagnetization refrigerator (ADR) dedicated for TES X-ray microcalorimeter operation. Ferric ammonium alum (FAA) was grown in a stainless-steel container in our laboratory. This salt pill was mounted together with a superconducting magnet and a conventional mechanical heat-switch in a dedicated helium cryostat. Using this system, we achieved \({<}40\)  mK and a hold time of \({>}20\) h below 100 mK. Initially, we used a 3 mm thick silicon steel shield around the ADR magnet and a Nb/Cryoperm double shield around the detector. However, this silicon steel shield allowed a \({\sim }50\)  mT field at the detector position when a full field (3 T) was applied, and caused the Nb shield around the detector to trap a magnetic field. The observed transition curve of a TES was broad ( \({\sim }20\)  mK) compared to \({\sim }4\)  mK obtained in a dilution refrigerator. By increasing the shield thickness to 12 mm, transition width was improved to \({\sim }4\)  mK, which suggests that the shields work as expected. When we operated a TES microcalorimeter, energy resolution was \(14.5\pm 0.7\)  eV (FWHM) at 5.9 keV.     

MicroSQUID Force Microscopy in a Dilution Refrigerator

We present a new generation of a scanning microSQUID microscope operating in an inverted dilution refrigerator. The microSQUIDs have a size of 1.21 $ \ \upmu $ m $^{2}$ and a magnetic flux sensitivity of 120 $\upmu \Phi _{0} / \sqrt{\text {Hz}}$ and thus a field sensitivity of 550 $ \ \upmu \text {G}/ \sqrt{\text {Hz}}$ . The scan range at low temperatures is about 80 $\upmu $ m and a coarse displacement of 5 mm in x and y direction has been implemented. The microSQUID-to-sample distance is regulated using a tuning fork based force detection. A microSQUID-to-sample distance of 420 nm has been obtained. The reliable knowledge of this distance is necessary to obtain a trustworthy estimate of the absolute value of the superconducting penetration depth. An outlook will be given on the ongoing direction of development.     

Experimental Apparatus to Search for Supersolidity in Monolayer ^4He on Graphite

We describe some details of a new experimental setup for torsional oscillator (TO) measurement of $^4$ He monolayers adsorbed on a graphite surface. This setup is designed to seek for the possible supersolid phase, in which crystalline order coexists with superfluidity, in two dimensional (2D) solid $^4$ He below 300 mK. Among such 2D solids, the commensurate phase in the second layer on graphite is the most hopeful candidate for the novel supersolid phase since it is the lowest-density quantum solid ever found. An exfoliated graphite substrate we used is ZYX which has at least ten times longer surface coherence length compared to Grafoil, an exfoliated graphite most commonly used in previous experiments. The first version of TO we made has the resonant frequency of 786.8 Hz and the Q value of $1.1\times 10^5$ at $T \le 10$  mK. The resonant frequency of this particular TO without any He samples ( $f_{\mathrm {cell}}$ ) showed unexpectedly large temperature variation and non-reproducibility below 1 K as well as sudden jumps when mechanical shocks are applied to the experimental apparatus. We found the stability of $f_{\mathrm {cell}}$ is highly correlated with the temperature stability of 1 K pot in dilution refrigerator.     

Results of Quenching Factor Measurements of CaWO_4 at mK Temperatures for the Direct Dark Matter Search Experiment CRESST

The CRESST experiment aims at a direct detection of WIMP dark matter (DM) using scintillating CaWO \(_4\) crystals operated as phonon detectors at mK temperatures. An important feature of the experiment is the active background discrimination technique exploiting the different light outputs depending on the kind of particle interaction. The reduced light yield of nuclear recoils compared to electron recoils is quantified by quenching factors (QFs). The precise measurement of the QFs and thus the identification of the individual recoiling nucleus in the multi-target material CaWO \(_4\) is crucial for neutron background discrimination and assuming a positive DM signal would allow to a certain extent WIMP-mass spectroscopy. At the Munich tandem accelerator a dedicated neutron scattering facility has been set up to measure the QFs of CaWO \(_4\) , in particular that of tungsten, at mK temperatures. Monoenergetic neutrons (11 MeV) produced by the accelerator are scattered off a CRESST-like detector module that is operated in a dilution refrigerator. In this setup, the recoiling nucleus (O, Ca and W) is identified by time-of-flight measurement in liquid-scintillator detectors placed at fixed scattering angles. The QF of W could be determined with unprecedented accuracy at mK temperatures and under realistic measurement conditions: \(QF_W=0.0196\pm 0.0022\) (preliminary value).     

Crystal growth and magnetic property of YFeO 3 crystal

YFeO $_{\boldsymbol 3}$ and other rare earth substituted crystals with distorted orthorhombic pervoskite-like structure (space group, Pbnm) have attracted much attention due to their remarkable magnetic properties of primary significance for technological applications. In the present work, the floating zone growth of YFeO $_{\boldsymbol 3}$ crystals has been systematically investigated and high quality YFeO $_{\boldsymbol 3}$ crystal was obtained by optimized process. The magnetic properties of YFeO $_{\boldsymbol 3}$ crystal were investigated, and it indicated the high magneto-optical property in YFeO $_{\boldsymbol 3}$ crystals with specific orientation due to its anisotropy. YFeO $_{\boldsymbol 3}$ crystals display superior performance in the application magneto-optical current sensors and fast latching optical switches.     

Development of Ta-based STJ X-ray Detector Arrays for Synchrotron Science

We are developing a cryogen-free Ta-based superconducting tunnel junction (STJ) detector for soft X-ray spectroscopy at synchrotrons. With an energy resolution 10 times higher than conventional solid-state X-ray detectors and count-rate capabilities above 5 kHz/pixel, STJ detectors offer potentially increased sensitivity for fluorescence-yield X-ray absorption spectroscopy (FY-XAS). We have developed 36-pixel arrays of 208 \(\times \) 208 \(\upmu \) m Ta STJs with an energy resolution of \(\sim \) 9 eV FWHM at the 525 eV oxygen K line. Compared to earlier Nb-based STJs, Ta-STJs offer improved energy resolution and absorption efficiency and extend the operating range to several keV. Here we describe the integration of the 36-pixel arrays into a cryogen-free, user-friendly X-ray spectrometer. A computer-controlled adiabatic demagnetization refrigerator coupled to a two-stage pulse tube refrigerator allows operation below 100 mK. The detector chip is located at the end of a 42 cm shielded snout for insertion into the analysis chamber. The system is currently being commissioned at the Advanced Light Source synchrotron.     

Determination of thermodynamic interactions of poly(l-lactide) and biphasic calcium phosphate/poly(l-lactide) composite by inverse gas chromatography at infinite dilution

Inverse gas chromatography at infinite dilution was applied to determine the thermodynamic interactions of poly(l-lactide) (PLLA) and the composite of biphasic calcium phosphate and PLLA (BCP/PLLA). The specific retention volumes, $ V_{\text{g}}^{0} $ , of 11 organic compounds of different chemical nature and polarity (non-polar, donor or acceptor) were determined in the temperature range of 308–378 K for PLLA and 308–398 K for BCP/PLLA. The weight fraction activity coefficients of test sorbates, $ \Omega_{1}^{\infty } $ , and the Flory–Huggins interaction parameters, $ \chi_{12}^{\infty } $ , were estimated and discussed in terms of interactions of the sorbates with PLLA and BCP/PLLA. Also, the partial molar free energy, $ \Delta G_{1}^{\infty } $ , the partial molar heat of mixing, $ \Delta H_{1}^{\infty } $ , the sorption molar free energy, $ \Delta G_{1}^{\text{S}} $ , the sorption enthalpy, $ \Delta H_{1}^{\text{S}} $ , and the sorption entropy, $ \Delta S_{1}^{\text{S}} $ , were analyzed. A different chromatographic behavior of the two investigated samples, PLLA and BCP/PLLA, was observed. The values of $ \Omega_{1}^{\infty } $ indicated n-alkanes, diethyl ether, tetrahydrofurane (THF), cyclohexane, benzene, dioxane (except for 338 K), and ethyl acetate (EtAc) (except for 338 K) as non-solvents, and chloroform (CHCl₃) as good solvent (except for 378 K) for PLLA. For BCP/PLLA, CHCl₃, EtAc (for 378 K), dioxane (except for 378 K), and THF were indicated as good solvents.     

Contribution of the space charge to the grain boundary energy in yttria-stabilized zirconia

A model based on the effect of a modest applied dc electric field on grain growth is proposed for the contribution of the space charge to the grain boundary (GB) energy in 3 mol % yttria-stabilized zirconia (3 YSZ). The model considers that the total GB energy \( \gamma_{\text{b}}^0 \) (the capillary driving force for grain growth) consists of three major components: (a) \( \gamma_{\text{b}}^\varSigma \) due to the misorientation between neighboring grains, (b) \( \gamma_{\text{b}}^{\text{s}} \) due to the size misfit between the segregated solute and the solvent cations, and (c) \( \gamma_{\text{b}}^{\text{e}} \) the electrostatic (space charge) component, which results from the segregation of the aliovalent yttrium ions to the grain boundaries. The former two components combined comprise 40 % of the total GB energy in 3 YSZ and the electrostatic component 60 %. Based on the model, the calculated magnitudes of the three components were in qualitative accord with theoretical considerations and with values reported in the literature. A reduction in \( \gamma_{\text{b}}^{\text{e}} , \) and in turn in \( \gamma_{\text{b}}^0 , \) results from the bias exerted by the applied field on the space charge potential that occurs with the segregation of the yttrium ions to the grain boundaries. The observed reduction of grain growth in 3 YSZ by an applied electric field is attributed mainly to the reduction in \( \gamma_{\text{b}}^{\text{e}} \) by the field.     

On the automorphism group of a binary self-dual [120, 60, 24] code

We prove that an automorphism of order 3 of a putative binary self-dual $[120, 60, 24]$ [ 120 , 60 , 24 ] code $C$ C has no fixed points. Moreover, the order of the automorphism group of $C$ C divides $2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$ 2 a · 3 · 5 · 7 · 19 · 23 · 29 with $a\in \mathbb N _0$ a ∈ N 0 . Automorphisms of odd composite order $r$ r may occur only for $r=15, 57$ r = 15 , 57 or $r=115$ r = 115 with corresponding cycle structures $3 \cdot 5$ 3 · 5 - $(0,0,8;0), 3\cdot 19$ ( 0 , 0 , 8 ; 0 ) , 3 · 19 - $(2,0,2;0)$ ( 2 , 0 , 2 ; 0 ) or $5 \cdot 23$ 5 · 23 - $(1,0,1;0)$ ( 1 , 0 , 1 ; 0 ) respectively. In case that all involutions act fixed point freely we have $|\mathrm{Aut}(C)| \le 920$ | Aut ( C ) | ≤ 920 , and $\mathrm{Aut}(C)$ Aut ( C ) is solvable if it contains an element of prime order $p \ge 7$ p ≥ 7 . Moreover, the alternating group $\mathrm{A}_5$ A 5 is the only non-abelian composition factor which may occur in $\mathrm{Aut}(C)$ Aut ( C ) .     

Study on Optical Filter Heating in Background Limited Detector Experiments

Cryogenic test setups with controlled stray light environments capable of reaching ultra-low radiative background levels are required to test far infrared (FIR) and submillimeter (sub-mm) wave radiation detectors for future space based observatories. In recent experiments (Nature Commun 5:3130, 2014), in which 1.54 THz radiation was coupled onto an antenna-coupled kinetic inductance detector (KID), we found a higher than expected optical loading. We show that this can be explained by assuming heating of the metal mesh IR filters and re-radiation onto the KID. Note that the total power from the cryogenic black body source used in the experiments (at T = \(3\) – \(25\) K) is much larger than the power inside the \(1.5\) – \(1.6\) THz band we use to calibrate our detector. The out-of-band radiation can have up to 5 orders of magnitude more power than inside the \(1.5\) – \(1.6\)  THz band of interest. A strategy to mitigate the filter heating problem is presented, and when it is implemented, the validated upper limit for stray light at the detector level is down to few aW.     

Some results on the differential functions over finite fields

Let \(g\) be a function over \(\mathbb {F}_q\) . If there exist a function \(f\) and \(a\in \mathbb {F}_q^*\) such that \(g(x)=f(x+a)-f(x)\) , then we call \(g\) a differential function and call \(f\) a differential-inverse of \(g\) . We present two criteria to decide whether a given \(g\) is a differential function. The set of the degrees of all differential functions over \({\mathbb {F}}_q\) is determined. Then we give a lower bound and an upper bound on the number of differential functions over \({\mathbb {F}}_q\) . Besides, we show how to construct differential inverses of a given differential function. At last, some applications of our results are introduced.     

Nonlinear grain–grain forces and the width of the solitary wave in granular chains: a numerical study

Any impulse results in the formation of a solitary wave of time averaged width $W$ in a granular chain. If the grain–grain interaction potential $V\sim \delta ^n$ , where $\delta $ is the distance by which the grains approach each other, then it is well established that $n\ge 2$ . Here we present dynamical simulation based results which suggest that $W-1\propto (n-2)^{-\alpha }$ where $\alpha =0.3283$ or $\approx $ 1/3. While in qualitative agreement, the result is quantitatively different from the formula for $W$ proposed earlier by Nesterenko.     

Density dependent macro-micro behavior of granular materials in general triaxial loading for varying intermediate principal stress using DEM

This study presents the density dependent behavior of granular materials for varying intermediate principal stress $(\sigma _{{{2}}})$ ( σ 2 ) in general triaxial loading using the discrete element method (DEM). The variation of intermediate principal stress is represented by a non-dimensional parameter $b[={(\sigma _{{{2}}}-\sigma _{{{3}}})}/{(\sigma _{{{1}}} -\sigma _{{{3}}})}]$ b [ = ( σ 2 ? σ 3 ) / ( σ 1 ? σ 3 ) ] , where $\sigma _{{{1}}}$ σ 1 and $\sigma _{{{3}}}$ σ 3 are the major and minor principal stresses, respectively. Isotropically compressed dense and loose samples were prepared numerically using the periodic boundaries. The numerical dense and loose samples were subjected to shear deformation under strain controlled condition for different $b$ b values ranging from 0 to 1. The simulated macro results depict that the friction angle increases with $b$ b until it reaches a peak value and beyond the peak, the friction angle decreases with $b$ b regardless of the density of sample. A unique relationship between dilatancy index and equivalent deviatoric strain exists at small strain level for different $b$ b values when dense sample is considered. By contrast, the same relationship for loose sample does not show uniqueness. The relationships among the major, intermediate and minor principal strains depict non-linear behavior. The non-linearity is dominant for loose sample. The fluctuation in the evolution of strain increment vector direction is dominant in loose sample than dense sample. The evolution of different micro results is presented as well. It is noted that a unique relationship exists between the stress ratio and the fabric measure regardless of $b$ b and the density of sample when strong contacts are considered.     

A note on cyclic codes from APN functions

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014) constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN function $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$ . From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty }$ defined by $s_t={\mathrm {Tr}}((1+\alpha ^t)^e)$ , where $\alpha $ is a primitive element in ${\mathrm {GF}}(q)$ . These techniques can also be applied to other open problems in Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014).     

Containerless Measurements of Density and Viscosity for a Cu_{48}Zr_{52} Liquid

The densities of solid and liquid Cu \(_{48}\) Zr \(_{52}\) and the viscosity of the liquid were measured in a containerless electrostatic levitation system using optical techniques. The measured density of the liquid at the liquidus temperature (1223 K) is (7.02 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) and the density of the solid extrapolated to that temperature is (7.15 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) . The thermal expansion coefficients measured at 1223 K are (6.4 \(\pm \) 0.1) \(\,\times \,10^{-5}\) K \(^{-1}\) in the liquid phase and (3.5 \(\pm \) 0.3) \(\,\times \,10^{-5}\) K \(^{-1}\) in the solid phase. The viscosity of the liquid, measured with the oscillating drop technique, is of the form \(A\exp \left[ \left( {{E}_{0}}+{{E}_{1}}\left( 1/T-1/{{T}_{0}} \right) \right) \times \left( 1/T-1/{{T}_{0}} \right) \right] \) , where \({{T}_{0}}=1223\) K, \(A= (0.0254 \pm 0.0004)\) Pa \(\cdot \) s, \({{E}_{0}}\) =  (8.43 \(\pm \) 0.26) \(\,\times \,10^3\) K and \({{E}_{1}}\) =  (1.7 \(\pm \) 0.2) \(\,\times 10^7\) K \(^{2}\) .     

First- and Second-Order Phase Transition in Parallel Triple Quantum Dots: The Roles of Symmetric and Asymmetric Hopping

By means of the numerical renormalization group method, I study the quantum phase transition (QPT) and the electronic transport in parallel triple quantum dot system with symmetric and/or asymmetric hopping. For symmetric hopping \(t_{1} = t_{2}\) and zero magnetic field \(B = 0\) , I find a first order transition between spin quadruplet and doublet as \(t_{1}\) ( \(t_{2}\) ) increases. With increasing \(B\) , a second order QPT between \(S_{z} = 1/2\) of the doublet and \(S_{z} = 3/2\) of the quadruplet is observed. For asymmetric hopping \(t_{1} \ne t_{2}\) , the QPT depends closely on the other hopping. For fixed \(t_{1} < \varGamma \) , where \(\varGamma \) is the hybridization function between the dots and the leads, a first order transition is observed as \(t_{2}\) increases, while for \(t_{1} \ge \varGamma \) , a crossover occurs. In the presence of \(B\) , the transition between \(S_{z} = 1/2\) and \(S_{z} = 3/2\) is a first order QPT for \(t_{1} < \varGamma \) , while a second order for \(t_{1} \ge \varGamma \) .