Broadband detection of squeezed vacuum: A spectrum of quantum states

We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the time domain we evaluated the first order correlation function of the squeezed output field, showing good agreement with the theory.Comment: 11 pages, 5 figure

Fresnel Representation of the Wigner Function: An Operational Approach

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] and in cavity QED [B. Varcoe et al., Nature 403, 743 (2000)]. The values of the Wigner functions of the underlying states at the origin of phase space are W(0)=+1.75 for the vibrational ground state and W(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.Comment: 4 pages include 4 figures, submitted to PR

Women candidates and councillors in Scottish local government, 1974-2012

While significant attention has been paid to the levels of representation of women in both the Westminster Parliament and the Scottish Parliament, much less considered has been given to the position within local government. This article addresses that deficit for Scotland. It shows that for twenty-five years following the reorganisation of local government in Scotland in 1974 there was a slow but relatively steady increase in the numbers of female candidates and councillors, although more recently this appears to have since plateaued somewhat, together with a similar increase in the number of women councillors taking up more senior roles in Scotland’s councils. The article analyses the representation of women in Scottish local government over the period from 1974 to 2012 against the backdrop of significant change in Scotland, including a further restructuring of local government and the introduction of the Single Transferable Vote for council elections, the creation of the Scottish Parliament, the rise of the SNP and the decline of the Conservative Party

Measuring the Quantum State of a Large Angular Momentum

We demonstrate a general method to measure the quantum state of an angular momentum of arbitrary magnitude. The (2F+1) x (2F+1) density matrix is completely determined from a set of Stern-Gerlach measurements with (4F+1) different orientations of the quantization axis. We implement the protocol for laser cooled Cesium atoms in the 6S_{1/2}(F=4) hyperfine ground state and apply it to a variety of test states prepared by optical pumping and Larmor precession. A comparison of input and measured states shows typical reconstruction fidelities of about 0.95.Comment: 4 pages, 6 figures, submitted to PR

Self-homodyne tomography of a twin-beam state

A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local oscillator and the signal modes, which is the main limitation to the overall quantum efficiency in conventional homodyning. The feasibility of the measurement is analyzed on the basis of Monte-Carlo simulations, studying the effect of non-unit quantum efficiency on detection of the correlation and the total photon-number oscillations of the twin-beam state.Comment: 13 pages (two-column ReVTeX) including 21 postscript figures; to appear on Phys. Rev.

Recovering coherence from decoherence: a method of quantum state reconstruction

We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.Comment: 8 pages, in RevTeX, 4 figures, accepted for publication in Phys. Rev. A (november 1999

Direct sampling of exponential phase moments of smoothed Wigner functions

We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.Comment: RevTeX, 8 pages, 6 figures, accepted Phys. Rev.

Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.Comment: REVTeX, 18 pages, no figure

Cytoplasmic PML promotes TGF-β-associated epithelial–mesenchymal transition and invasion in prostate cancer

Epithelial–mesenchymal transition (EMT) is a key event that is involved in the invasion and dissemination of cancer cells. Although typically considered as having tumour-suppressive properties, transforming growth factor (TGF)-β signalling is altered during cancer and has been associated with the invasion of cancer cells and metastasis. In this study, we report a previously unknown role for the cytoplasmic promyelocytic leukaemia (cPML) tumour suppressor in TGF-β signalling-induced regulation of prostate cancer-associated EMT and invasion. We demonstrate that cPML promotes a mesenchymal phenotype and increases the invasiveness of prostate cancer cells. This event is associated with activation of TGF-β canonical signalling pathway through the induction of Sma and Mad related family 2 and 3 (SMAD2 and SMAD3) phosphorylation. Furthermore, the cytoplasmic localization of promyelocytic leukaemia (PML) is mediated by its nuclear export in a chromosomal maintenance 1 (CRM1)-dependent manner. This was clinically tested in prostate cancer tissue and shown that cytoplasmic PML and CRM1 co-expression correlates with reduced disease-specific survival. In summary, we provide evidence of dysfunctional TGF-β signalling occurring at an early stage in prostate cancer. We show that this disease pathway is mediated by cPML and CRM1 and results in a more aggressive cancer cell phenotype. We propose that the targeting of this pathway could be therapeutically exploited for clinical benefit