Entanglement of Pure Two-Mode Gaussian States

The entanglement of general pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wavefunction. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for deriving local unitary transformations. These reproduce the results of other methods for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.Comment: 12 page

Two Qubits in the Dirac Representation

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.Comment: 11 page

Structure of the Phase in Pure Two-Mode Gaussian States

The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks

Probing Fermi surface shifts with spin resolved transverse magnetic focussing

Transverse magnetic focussing is the solid state equivalent of a mass spectrometer. It is unique among 2D measurement techniques as it is able to measure a well defined section of the Fermi surface, making it possible to detect changes that would be averaged out over the whole Fermi surface. Here, we utilise this unique property to probe non-adiabatic spin dynamics and spin dependent scattering of holes. We combine spin-resolved magnetic focussing with an additional independent in-plane magnetic field and observe a change in focussing peak amplitude that is not symmetric with respect to the field direction (i.e. $+B_{\parallel} \neq -B_{\parallel}$), and is extremely sensitive to the magnitude of the in-plane magnetic field. We show that the magnetic focussing signal is extremely sensitive to small changes in the Fermi velocity, which can be used to detect small shifts in the Fermi surface caused by an in-plane magnetic field. We also find that focussing can be used to detect the proximity between spin-split Fermi surfaces, which cause non-adiabatic spin dynamics

Surface shape resonances in lamellar metallic gratings

The specular reflectivity of lamellar gratings of gold with grooves 0.5 microns wide separated by a distance of 3.5 microns was measured on the 2000 cm$^{-1}$ - 7000 cm$^{-1}$ spectral range for p-polarized light. For the first time, experimental evidence of the excitation of electromagnetic surface shape resonances for optical frequencies is given. In these resonances the electric field is highly localized inside the grooves and is almost zero in all other regions. For grooves of depth equal to 0.6 microns, we have analyzed one of these modes whose wavelength (3.3 microns) is much greater than the lateral dimension of the grooves.Comment: 4 pages (LaTex), 5 postscript figures, to be published in Physical Review Letter

Commensurability oscillations in the rf conductivity of unidirectional lateral superlattices: measurement of anisotropic conductivity by coplanar waveguide

We have measured the rf magnetoconductivity of unidirectional lateral superlattices (ULSLs) by detecting the attenuation of microwave through a coplanar waveguide placed on the surface. ULSL samples with the principal axis of the modulation perpendicular (S_perp) and parallel (S_||) to the microwave electric field are examined. For low microwave power, we observe expected anisotropic behavior of the commensurability oscillations (CO), with CO in samples S_perp and S_|| dominated by the diffusion and the collisional contributions, respectively. Amplitude modulation of the Shubnikov-de Haas oscillations is observed to be more prominent in sample S_||. The difference between the two samples is washed out with the increase of the microwave power, letting the diffusion contribution govern the CO in both samples. The failure of the intended directional selectivity in the conductivity measured with high microwave power is interpreted in terms of large-angle electron-phonon scattering.Comment: 8 pages, 5 figure

Orthorhombicity mixing of s- and d- gap components in YBa2Cu3O7YBa_2Cu_3O_7 without involving the chains

Momentum decoupling develops when forward scattering dominates the pairing interaction and implies tendency for decorrelation between the physical behavior in the various regions of the Fermi surface. In this regime it is possible to obtain anisotropic s- or d-wave superconductivity even with isotropic pairing scattering. We show that in the momentum decoupling regime the distortion of the $CuO_2$ planes is enough to explain the experimental reports for s- mixing in the dominantly d-wave gap of $YBa_2Cu_3O_7$. In the case of spin fluctuations mediated pairing instead, a large part of the condensate must be located in the chains in order to understand the experiments.Comment: LATEX file and 3 Postscript figure

The complementary role of histology and proteomics for diagnosis and typing of systemic amyloidosis

The tissue diagnosis of amyloidosis and confirmation of fibril protein type, which are crucial for clinical management, have traditionally relied on Congo red (CR) staining followed by immunohistochemistry (IHC) using fibril protein specific antibodies. However, amyloid IHC is qualitative, non-standardised, requires operator expertise, and not infrequently fails to produce definitive results. More recently, laser dissection mass spectrometry (LDMS) has been developed as an alternative method to characterise amyloid in tissue sections. We sought to compare these techniques in a real world setting. During 2017, we performed LDMS on 640 formalin-fixed biopsies containing amyloid (CR+ve) comprising all 320 cases that could not be typed by IHC (IHC−ve) and 320 randomly selected CR+ve samples that had been typed (IHC+ve). In addition, we studied 60 biopsies from patients in whom there was a strong suspicion of amyloidosis, but in whom histology was non-diagnostic (CR–ve). Comprehensive clinical assessments were conducted in 532 (76%) of cases. Among the 640 CR+ve samples, 602 (94%) contained ≥2 of 3 amyloid signature proteins (ASPs) on LDMS (ASP+ve) supporting the presence of amyloid. A total of 49 of the 60 CR-ve samples were ASP–ve; 7 of 11 that were ASP+ve were glomerular. The amyloid fibril protein was identified by LDMS in 255 of 320 (80%) of the IHC–ve samples and in a total of 545 of 640 (85%) cases overall. The LDMS and IHC techniques yielded discordant results in only 7 of 320 (2%) cases. CR histology and LDMS are corroborative for diagnosis of amyloid, but LDMS is superior to IHC for confirming amyloid type