The effect of impurities on the evolution of the melting front analyzed in a two-dimensional representation for the eutectic Pt–C

The paper discusses the effect of two-front melting on the liquidus temperature of the eutectic Pt–C and the eutectic temperature of the system in its pure state. This influence factor has not been considered thus far in the uncertainty budget associated with the assignment of thermodynamic temperatures to the eutectics Co–C (1597.15 K), Pt–C (2011.05 K), and Re–C (2747.35 K), selected in the European Metrology Research Programme project Implementing the New Kelvin. For Pt–C, simulation of the effect of two-front melting on the melting process has been done before in a 1D analytical model, and this formed the starting point to the present study. In this study the melting process is analyzed by means of a 2D axisymmetrical finite-volume model. In the model, freezing and melting are considered for an impure ingot and for a pure ingot. As to the impure ingot, the impurity concentrations are the concentrations met in current practice of the realization of the high-temperature reference fixed point, but formulated in terms of an effective concentration and associated effective distribution coefficient k<1, related to a Scheil fit to the melting curve at given melting conditions as measured for the eutectic Pt–C. Heat injection rates for melting varied from 15000 W·m-2 down to 3000 W·m-2. In any case for the impure system, two melting fronts are showing up. For the pure system, only one melting front is generated, traveling from the outside of the ingot toward its inside

The effect of the rear cavity wall ingot shape on the evolution of the liquid–solid interface during melting for the eutectic Pt-C

When characterizing high-temperature fixed points, the fraction of the melting time of the regular part of the plateau with respect to the total melting time, is critical. Maximizing the melting duration minimizes the uncertainty associated with the determination of the fixed-point temperature. One factor that affects this quality is the effect of the thermal bridging between the external and internal surfaces of the ingot enclosed by the cell. This paper presents the results of simulations for the eutectic Pt-C, investigating the effects of different ingot shapes on the duration of the melt plateau. It was found that the formation of a thermal bridge from the rear of the blackbody cavity toward the outer surface of the ingot was critical and that its formation could be delayed or suppressed through a proper choice of the ingot shape. The shapes considered included, firstly, the shape of the rear of the cavity, in contact with the ingot, either cone-shaped or dome-shaped, and secondly, the inside rear surface of the cell, in contact with the ingot, being a cone, a convex dome, or flat. The presence of impurities in the alloy was taken into consideration, and its influence in the evolution of the liquid–solid interface compared with that for the pure alloy. The effect of changing the thermal isolation of the cell, at its front side, was also considered. A dome-shaped surface for the rear of the cavity was found to be more favorable for the development of a regular melting front, in conjunction with the segregation of impurities during melting. At the rear of the cell, a flat surface ensures the back wall is the last to experience thermal bridging, resulting in more extended melting plateaus

Shape of the spatial mode function of photons generated in noncollinear spontaneous parametric downconversion

We show experimentally how noncollinear geometries in spontaneous parametric downconversion induce ellipticity of the shape of the spatial mode function. The degree of ellipticity depends on the pump beam width, especially for highly focused beams. We also discuss the ellipticity induced by the spectrum of the pump beam

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states'', we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing non degenerate and degenerate multiphoton processes. We determine the coherent states associated to the canonical transformations, which generalize the non degenerate two--photon squeezed states. Such heterodyne multiphoton squeezed are defined as the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non Gaussian, highly non classical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two--mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.Comment: 16 pages, 23 figure

Vibrational dephasing in molecular mixed crystals:a picosecond time domain CARS study of pentacene in naphthalene and benzoic acid

Multiresonant time-domain coherent anti-Stokes Raman scattering (CARS) experiments have been employed in a study of the decay of vibrational coherences of pentacene doped into naphthalene and benzoic acid. In all cases, the CARS decay is found to be exponential, which indicates that the electronic and vibronic inhomogeneities in this system are strongly correlated. The temperature dependence of vibrational dephasing shows no effect of coupling to the lowest-frequency librational mode of pentacene that is known to dominate electronic dephasing. This surprising result can be understood on basis of a dephasing model where rapid coherence exchange exists between a cold vibrational transition and a corresponding near-resonant librationally hot one. For the 767 cm–1 vibrational transition, oscillations of the CARS signal as a function of delay are shown to arise from interference at the detector with a nearby naphthalene host signal. An inconsistency with a previously reported spontaneous Raman study is resolved by showing that the signal observed there is actually site-selected fluorescence

Multipole nonlinearity of metamaterials

We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media towards the realm of metamaterials.Comment: 7 pages, 3 figure

Comparison of Quantum and Classical Local-field Effects on Two-Level Atoms in a Dielectric

The macroscopic quantum theory of the electromagnetic field in a dielectric medium interacting with a dense collection of embedded two-level atoms fails to reproduce a result that is obtained from an application of the classical Lorentz local-field condition. Specifically, macroscopic quantum electrodynamics predicts that the Lorentz redshift of the resonance frequency of the atoms will be enhanced by a factor of the refractive index n of the host medium. However, an enhancement factor of (n*n+2)/3 is derived using the Bloembergen procedure in which the classical Lorentz local-field condition is applied to the optical Bloch equations. Both derivations are short and uncomplicated and are based on well-established physical theories, yet lead to contradictory results. Microscopic quantum electrodynamics confirms the classical local-field-based results. Then the application of macroscopic quantum electrodynamic theory to embedded atoms is proved false by a specific example in which both the correspondence principle and microscopic theory of quantum electrodynamics are violated.Comment: Published version with rewritten abstract and introductio

Controlling spin relaxation with a cavity

Spontaneous emission of radiation is one of the fundamental mechanisms by which an excited quantum system returns to equilibrium. For spins, however, spontaneous emission is generally negligible compared to other non-radiative relaxation processes because of the weak coupling between the magnetic dipole and the electromagnetic field. In 1946, Purcell realized that the spontaneous emission rate can be strongly enhanced by placing the quantum system in a resonant cavity -an effect which has since been used extensively to control the lifetime of atoms and semiconducting heterostructures coupled to microwave or optical cavities, underpinning single-photon sources. Here we report the first application of these ideas to spins in solids. By coupling donor spins in silicon to a superconducting microwave cavity of high quality factor and small mode volume, we reach for the first time the regime where spontaneous emission constitutes the dominant spin relaxation mechanism. The relaxation rate is increased by three orders of magnitude when the spins are tuned to the cavity resonance, showing that energy relaxation can be engineered and controlled on-demand. Our results provide a novel and general way to initialise spin systems into their ground state, with applications in magnetic resonance and quantum information processing. They also demonstrate that, contrary to popular belief, the coupling between the magnetic dipole of a spin and the electromagnetic field can be enhanced up to the point where quantum fluctuations have a dramatic effect on the spin dynamics; as such our work represents an important step towards the coherent magnetic coupling of individual spins to microwave photons.Comment: 8 pages, 6 figures, 1 tabl