Squeezed States for General Systems

We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-operator method.Comment: 8 pages, LAUR-93-1721, LaTe

Androgen signaling connects short isoform production to breakpoint formation at Ewing sarcoma breakpoint region 1

Ewing sarcoma breakpoint region 1 (EWSR1) encodes a multifunctional protein that can cooperate with the transcription factor ERG to promote prostate cancer. The EWSR1 gene is also commonly involved in oncogenic gene rearrangements in Ewing sarcoma. Despite the cancer relevance of EWSR1, its regulation is poorly understood. Here we find that in prostate cancer, androgen signaling upregulates a 5' EWSR1 isoform by promoting usage of an intronic polyadenylation site. This isoform encodes a cytoplasmic protein that can strongly promote cell migration and clonogenic growth. Deletion of an Androgen Receptor (AR) binding site near the 5' EWSR1 polyadenylation site abolished androgen-dependent upregulation. This polyadenylation site is also near the Ewing sarcoma breakpoint hotspot, and androgen signaling promoted R-loop and breakpoint formation. RNase H overexpression reduced breakage and 5' EWSR1 isoform expression suggesting an R-loop dependent mechanism. These data suggest that androgen signaling can promote R-loops internal to the EWSR1 gene leading to either early transcription termination, or breakpoint formation

Squeezing of a coupled state of two spinors

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.Comment: Typeset in LaTeX 2e using the style iopart, packages iopams,times,amssymb,graphicx; 17 pages, 5 eps figure file

Entangling macroscopic oscillators exploiting radiation pressure

It is shown that radiation pressure can be profitably used to entangle {\it macroscopic} oscillators like movable mirrors, using present technology. We prove a new sufficient criterion for entanglement and show that the achievable entanglement is robust against thermal noise. Its signature can be revealed using common optomechanical readout apparatus.Comment: 4 pages, 2 eps figures, new separability criterion added, new figure 2, authors list change

ELK1 Uses Different DNA Binding Modes to Regulate Functionally Distinct Classes of Target Genes

Eukaryotic transcription factors are grouped into families and, due to their similar DNA binding domains, often have the potential to bind to the same genomic regions. This can lead to redundancy at the level of DNA binding, and mechanisms are required to generate specific functional outcomes that enable distinct gene expression programmes to be controlled by a particular transcription factor. Here we used ChIP–seq to uncover two distinct binding modes for the ETS transcription factor ELK1. In one mode, other ETS transcription factors can bind regulatory regions in a redundant fashion; in the second, ELK1 binds in a unique fashion to another set of genomic targets. Each binding mode is associated with different binding site features and also distinct regulatory outcomes. Furthermore, the type of binding mode also determines the control of functionally distinct subclasses of genes and hence the phenotypic response elicited. This is demonstrated for the unique binding mode where a novel role for ELK1 in controlling cell migration is revealed. We have therefore uncovered an unexpected link between the type of binding mode employed by a transcription factor, the subsequent gene regulatory mechanisms used, and the functional categories of target genes controlled

Retrodictively Optimal Localisations in Phase Space

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalised to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a meaurement belongs to the class of generalised Husimi functions most recently discussed by Wuensche and Buzek. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vaccuum state.Comment: 11 pages, 2 figures. AMS Latex. Replaced with published versio

Thermalized Displaced and Squeezed Number States in Coordinate Representation

Within the framework of thermofield dynamics, the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation. Furthermore, the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation, and we also calculate the corresponding probability densities, average values and variances of position coordinate, which are consistent with results in the literature.Comment: 12 pages, no figures, Revtex. v3: substantially revise

Squeezing arbitrary cavity-field states through their interaction with a single driven atom

We propose an implementation of the parametric amplification of an arbitrary radiation-field state previously prepared in a high-Q cavity. This nonlinear process is accomplished through the dispersive interactions of a single three-level atom (fundamental |g>, intermediate |i>, and excited |e> levels) simultaneously with i) a classical driving field and ii) a previously prepared cavity mode whose state we wish to squeeze. We show that, in the adiabatic approximantion, the preparation of the initial atomic state in the intermediate level |i> becomes crucial for obtaing the degenerated parametric amplification process.Comment: Final published versio

Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group Sp(4,\Re)\/. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the Sp(4,\Re)-SO(3,2)\/ local isomorphism and the U(2)\/ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2)\/ is emphasized, and known experimental situations where all U(2)\/ elements can be reproduced are briefly described.Comment: Revtex 37 pages, Latex figures include

Novel approach to the study of quantum effects in the early universe

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions of the ''master equation'' to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor $a^{2}(\eta)$. A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous $\eta-$dependent Hamiltonian. An estimate in terms of $\sigma(\eta)$ and $a(\eta)$ of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of $\eta$ are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.Comment: 20 pages, to appear on PRD. Already published background material has been either settled up in a more compact form or eliminate