Quantum Mechanics as a Framework for Dealing with Uncertainty

Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that were available in the realm of classical physics. The birth of quantum information science was due to the realization that such obstructions can be turned into powerful resources. Here we review how the utilization of quantum fuzziness makes room for a notion of approximate joint measurement of noncommuting observables. We also show how from a classical perspective quantum uncertainty is due to a limitation of measurability reflected in a fuzzy event structure -- all quantum events are fundamentally unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku 2009

Transport, atom blockade and output coupling in a Tonks-Girardeau gas

Recent experiments have demonstrated how quantum-mechanical impurities can be created within strongly correlated quantum gases and used to probe the coherence properties of these systems [S. Palzer, C. Zipkes, C. Sias, and M. K\"ohl, Phys. Rev. Lett. 103, 150601 (2009).]. Here we present a phenomenological model to simulate such an output coupler for a Tonks-Girardeau gas that shows qualitative agreement with the experimental results for atom transport and output coupling. Our model allows us to explore nonequilibrium transport phenomena in ultracold quantum gases and leads us to predict a regime of atom blockade, where the impurity component becomes localized in the parent cloud despite the presence of gravity. We show that this provides a stable mixed-species quantum gas in the strongly correlated limit

Thermodynamics and kinetics of the undercooled liquid and the glass transition of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy

Differential scanning calorimetry (DSC) was used to determine the thermodynamic functions of the undercooled liquid and the amorphous phase with respect to the crystalline state of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5bulk metallic glass forming alloy. The specific heat capacities of this alloy in the undercooled liquid, the amorphous state and the crystal were determined. The differences in enthalpy, ∆H, entropy, ∆S, and Gibbs free energy, ∆G, between crystal and the undercooled liquid were calculated using the measured specific heat capacity data as well as the heat of fusion. The results indicate that the Gibbs free energy difference between metastable undercooled liquid and crystalline solid, ∆G, stays small compared to conventional metallic glass forming alloys even for large undercoolings. Furthermore, the Kauzmann temperature, TK, where the entropy of the undercooled liquid equals to that of the crystal, was determined to be 560 K. The Kauzmann temperature is compared with the experimentally observed rate-dependent glass transition temperature, Tg. Both onset and end temperatures of the glass transition depend linearly on the logarithm of the heating rate based on the DSC experiments. Those characteristic temperatures for the kinetically observed glass transition become equal close to the Kauzmann temperature in this alloy, which suggests an underlying thermodynamic glass transition as a lower bound for the kinetically observed freezing process

New spin squeezing and other entanglement tests for two mode systems of identical bosons

For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrization principle (SP) and conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for massive bosons, where both the system and sub-systems are modes (or sets of modes) and particle numbers for quantum states are determined from the mode occupancies. Defining non-entangled or separable states as those prepared via local operations (on the sub-systems) and classical communication processes, the sub-system density operators are also required to satisfy the SP and conform to the SSR, in contrast to some other approaches. Whilst in the presence of this additional constraint the previously obtained sufficiency criteria for entanglement, such as the sum of the ˆSx and ˆSy variances for the Schwinger spin components being less than half the mean boson number, and the strong correlation test of |haˆm (bˆ†)ni|2 being greater than h(aˆ†)maˆm (bˆ†)nbˆni(m, n = 1, 2, . . .) are still valid, new tests are obtained in our work. We show that the presence of spin squeezing in at least one of the spin components ˆSx , ˆSy and ˆSz is a sufficient criterion for the presence of entanglement and a simple correlation test can be constructed of |haˆm (bˆ†)ni|2 merely being greater than zero.We show that for the case of relative phase eigenstates, the new spin squeezing test for entanglement is satisfied (for the principle spin operators), whilst the test involving the sum of the ˆSx and ˆSy variances is not. However, another spin squeezing entanglement test for Bose–Einstein condensates involving the variance in ˆSz being less than the sum of the squared mean values for ˆSx and ˆSy divided by the boson number was based on a concept of entanglement inconsistent with the SP, and here we present a revised treatment which again leads to spin squeezing as an entanglement test

Experimental determination of a time–temperature-transformation diagram of the undercooled Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy using the containerless electrostatic levitation processing technique

High temperature high vacuum electrostatic levitation was used to determine the complete time–temperature–transformation (TTT) diagram of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass forming alloy in the undercooled liquid state. This is the first report of experimental data on the crystallization kinetics of a metallic system covering the entire temperature range of the undercooled melt down to the glass transition temperature. The measured TTT diagram exhibits the expected "C" shape. Existing models that assume polymorphic crystallization cannot satisfactorily explain the experimentally obtained TTT diagram. This originates from the complex crystallization mechanisms that occur in this bulk glass-forming system, involving large composition fluctuations prior to crystallization as well as phase separation in the undercooled liquid state below 800 K

Metallic glass formation in highly undercooled Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 during containerless electrostatic levitation processing

Various sample sizes of Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 with masses up to 80 mg were undercooled below Tg (the glass transition temperature) while electrostatically levitated. The final solidification product of the sample was determined by x-ray diffraction to have an amorphous phase. Differential scanning calorimetry was used to confirm the absence of crystallinity in the processes sample. The amorphous phase could be formed only after heating the samples above the melting temperature for extended periods of time in order to break down and dissolve oxides or other contaminants which would otherwise initiate heterogeneous nucleation of crystals. Noncontact pyrometry was used to monitor the sample temperature throughout processing. The critical cooling rate required to avoid crystallization during solidification of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy fell between 0.9 and 1.2 K/s

Hemispherical total emissivity and specific heat capacity of deeply undercooled Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 melts

High-temperature high-vacuum electrostatic levitation (HTHVESL) and differential scanning calorimetry (DSC) were combined to determine the hemispherical total emissivity epsilon T, and the specific heat capacity cp, of the undercooled liquid and throughout the glass transition of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass forming alloy. The ratio of cp/epsilon T as a function of undercooling was determining from radiative cooling curves measured in the HTHVESL. Using specific heat capacity data obtained by DSC investigations close to the glass transition and above the melting point, epsilon T and cp were separated and the specific heat capacity of the whole undercooled liquid region was determined. Furthermore, the hemispherical total emissivity of the liquid was found to be about 0.22 at 980 K. On undercooling the liquid, the emissivity decreases to approximately 0.18 at about 670 K, where the undercooled liquid starts to freeze to a glass. No significant changes of the emissivity are observed as the alloy undergoes the glass transition

Immunofluorescent Examination of Biopsies from Long-Term Renal Allografts

Immunofluorescent examination of open renal biopsies revealed clear-cut glomerular localization of immunoglobulins not related clearly to the quality of donor-recipient histocompatibility in 19 of 34 renal allografts. The biopsies were obtained 18 to 31 months after transplantations primarily from related donors with a variable quality of histocompatibility match. IgG was the predominant immunoglobulin class fixed in 13 biopsies, and IgM in six. The pattern of immunoglobulin deposition was linear, connoting anti-GBM antibody in four of the 19; it was granular and discontinuous, connoting antigen–antibodycomplex deposits, in 13. An immune process may affect glomeruli of renal allografts by mechanisms comparable to those that cause glomerulonephritis in native kidneys. The transplant glomerulonephritis may represent a persistence of the same disease that originally destroyed the host kidneys or the consequence of a new humoral antibody response to allograft antigens. © 1970, Massachusetts Medical Society. All rights reserved