393 research outputs found
Inflationary spectra and partially decohered distributions
It is generally expected that decoherence processes will erase the quantum
properties of the inflationary primordial spectra. However, given the weakness
of gravitational interactions, one might end up with a distribution which is
only partially decohered. Below a certain critical change, we show that the
inflationary distribution retains quantum properties. We identify four of
these: a squeezed spread in some direction of phase space, non-vanishing
off-diagonal matrix elements, and two properties used in quantum optics called
non--representability and non-separability. The last two are necessary
conditions to violate Bell's inequalities. The critical value above which all
these properties are lost is associated to the `grain' of coherent states. The
corresponding value of the entropy is equal to half the maximal (thermal)
value. Moreover it coincides with the entropy of the effective distribution
obtained by neglecting the decaying modes. By considering backreaction effects,
we also provide an upper bound for this entropy at the onset of the adiabatic
era.Comment: 42 pages, 9 figures; 1 ref. adde
Oscillations of rapidly rotating relativistic stars
Non-axisymmetric oscillations of rapidly rotating relativistic stars are
studied using the Cowling approximation. The oscillation spectra have been
estimated by Fourier transforming the evolution equations describing the
perturbations. This is the first study of its kind and provides information on
the effect of fast rotation on the oscillation spectra while it offers the
possibility in studying the complete problem by including spacetime
perturbations. Our study includes both axisymmetric and non-axisymmetric
perturbations and provides limits for the onset of the secular bar mode
rotational instability. We also present approximate formulae for the dependence
of the oscillation spectrum from rotation. The results suggest that it is
possible to extract the relativistic star's parameters from the observed
gravitational wave spectrum.Comment: this article will be published in Physical Review
Achieving geodetic motion for LISA test masses: ground testing result
The low-frequency resolution of space-based gravitational wave observatories
such as LISA (Laser Interferometry Space Antenna) hinges on the orbital purity
of a free-falling reference test mass inside a satellite shield. We present
here a torsion pendulum study of the forces that will disturb an orbiting test
mass inside a LISA capacitive position sensor. The pendulum, with a measured
torque noise floor below 10 fNm/sqrt{Hz} from 0.6 to 10 mHz, has allowed
placement of an upper limit on sensor force noise contributions, measurement of
the sensor electrostatic stiffness at the 5% level, and detection and
compensation of stray DC electrostatic biases at the mV level.Comment: 4 pages (revtex4) with 4 figure
Sensitivity and parameter-estimation precision for alternate LISA configurations
We describe a simple framework to assess the LISA scientific performance
(more specifically, its sensitivity and expected parameter-estimation precision
for prescribed gravitational-wave signals) under the assumption of failure of
one or two inter-spacecraft laser measurements (links) and of one to four
intra-spacecraft laser measurements. We apply the framework to the simple case
of measuring the LISA sensitivity to monochromatic circular binaries, and the
LISA parameter-estimation precision for the gravitational-wave polarization
angle of these systems. Compared to the six-link baseline configuration, the
five-link case is characterized by a small loss in signal-to-noise ratio (SNR)
in the high-frequency section of the LISA band; the four-link case shows a
reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high
frequencies. The uncertainty in the estimate of polarization, as computed in
the Fisher-matrix formalism, also worsens when moving from six to five, and
then to four links: this can be explained by the reduced SNR available in those
configurations (except for observations shorter than three months, where five
and six links do better than four even with the same SNR). In addition, we
prove (for generic signals) that the SNR and Fisher matrix are invariant with
respect to the choice of a basis of TDI observables; rather, they depend only
on which inter-spacecraft and intra-spacecraft measurements are available.Comment: 17 pages, 4 EPS figures, IOP style, corrected CQG versio
Regularization of statistical inverse problems and the Bakushinskii veto
In the deterministic context Bakushinskii's theorem excludes the existence of
purely data driven convergent regularization for ill-posed problems. We will
prove in the present work that in the statistical setting we can either
construct a counter example or develop an equivalent formulation depending on
the considered class of probability distributions. Hence, Bakushinskii's
theorem does not generalize to the statistical context, although this has often
been assumed in the past. To arrive at this conclusion, we will deduce from the
classic theory new concepts for a general study of statistical inverse problems
and perform a systematic clarification of the key ideas of statistical
regularization.Comment: 20 page
Acceleration disturbances and requirements for ASTROD I
ASTRODynamical Space Test of Relativity using Optical Devices I (ASTROD I)
mainly aims at testing relativistic gravity and measuring the solar-system
parameters with high precision, by carrying out laser ranging between a
spacecraft in a solar orbit and ground stations. In order to achieve these
goals, the magnitude of the total acceleration disturbance of the proof mass
has to be less than 10−13 m s−2 Hz−1/2 at 0.1 m Hz. In this
paper, we give a preliminary overview of the sources and magnitude of
acceleration disturbances that could arise in the ASTROD I proof mass. Based on
the estimates of the acceleration disturbances and by assuming a simple
controlloop model, we infer requirements for ASTROD I. Our estimates show that
most of the requirements for ASTROD I can be relaxed in comparison with Laser
Interferometer Space Antenna (LISA).Comment: 19 pages, two figures, accepted for publication by Class. Quantum
Grav. (at press
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
The Coherent State Representation of Quantum Fluctuations in the Early Universe
Using the squeezed state formalism the coherent state representation of
quantum fluctuations in an expanding universe is derived. It is shown that this
provides a useful alternative to the Wigner function as a phase space
representation of quantum fluctuations. The quantum to classical transition of
fluctuations is naturally implemented by decohering the density matrix in this
representation. The entropy of the decohered vacua is derived. It is shown that
the decoherence process breaks the physical equivalence between vacua that
differ by a coordinate dependent phase generated by a surface term in the
Lagrangian. In particular, scale invariant power spectra are only obtained for
a special choice of surface term.Comment: 25 pages in revtex 3. This version is completely revised with
corrections and significant new calculation
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
Operational Theory of Homodyne Detection
We discuss a balanced homodyne detection scheme with imperfect detectors in
the framework of the operational approach to quantum measurement. We show that
a realistic homodyne measurement is described by a family of operational
observables that depends on the experimental setup, rather than a single field
quadrature operator. We find an explicit form of this family, which fully
characterizes the experimental device and is independent of a specific state of
the measured system. We also derive operational homodyne observables for the
setup with a random phase, which has been recently applied in an ultrafast
measurement of the photon statistics of a pulsed diode laser. The operational
formulation directly gives the relation between the detected noise and the
intrinsic quantum fluctuations of the measured field. We demonstrate this on
two examples: the operational uncertainty relation for the field quadratures,
and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe
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