1,042 research outputs found
Sensitivity limitations in optical speed meter topology of gravitational-wave antennae
The possible design of QND gravitational-wave detector based on speed meter
principle is considered with respect to optical losses. The detailed analysis
of speed meter interferometer is performed and the ultimate sensitivity that
can be achieved is calculated. It is shown that unlike the position meter
signal-recycling can hardly be implemented in speed meter topology to replace
the arm cavities as it is done in signal-recycled detectors, such as GEO 600.
It is also shown that speed meter can beat the Standard Quantum Limit (SQL) by
the factor of in relatively wide frequency band, and by the factor of
in narrow band. For wide band detection speed meter requires quite
reasonable amount of circulating power MW. The advantage of the
considered scheme is that it can be implemented with minimal changes in the
current optical layout of LIGO interferometer.Comment: 20 pages, 12 figure
QND measurements for future gravitational-wave detectors
Second-generation interferometric gravitational-wave detectors will be
operating at the Standard Quantum Limit, a sensitivity limitation set by the
trade off between measurement accuracy and quantum back action, which is
governed by the Heisenberg Uncertainty Principle. We review several schemes
that allows the quantum noise of interferometers to surpass the Standard
Quantum Limit significantly over a broad frequency band. Such schemes may be an
important component of the design of third-generation detectors.Comment: 22 pages, 6 figures, 1 table; In version 2, more tutorial information
on quantum noise in GW interferometer and several new items into Reference
list were adde
Chaos in a well : Effects of competing length scales
A discontinuous generalization of the standard map, which arises naturally as
the dynamics of a periodically kicked particle in a one dimensional infinite
square well potential, is examined. Existence of competing length scales,
namely the width of the well and the wavelength of the external field,
introduce novel dynamical behaviour. Deterministic chaos induced diffusion is
observed for weak field strengths as the length scales do not match. This is
related to an abrupt breakdown of rotationally invariant curves and in
particular KAM tori. An approximate stability theory is derived wherein the
usual standard map is a point of ``bifurcation''.Comment: 15 pages, 5 figure
Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals
We give a rigorous analytical derivation of low-temperature behavior of the
Casimir entropy in the framework of the Lifshitz formula combined with the
Drude dielectric function. An earlier result that the Casimir entropy at zero
temperature is not equal to zero and depends on the parameters of the system is
confirmed, i.e. the third law of thermodynamics (the Nernst heat theorem) is
violated. We illustrate the resolution of this thermodynamical puzzle in the
context of the surface impedance approach by several calculations of the
thermal Casimir force and entropy for both real metals and dielectrics.
Different representations for the impedances, which are equivalent for real
photons, are discussed. Finally, we argue in favor of the Leontovich boundary
condition which leads to results for the thermal Casimir force that are
consistent with thermodynamics.Comment: 24 pages, 3 figures, accepted for publication in Phys. Rev.
Surface-impedance approach solves problems with the thermal Casimir force between real metals
The surface impedance approach to the description of the thermal Casimir
effect in the case of real metals is elaborated starting from the free energy
of oscillators. The Lifshitz formula expressed in terms of the dielectric
permittivity depending only on frequency is shown to be inapplicable in the
frequency region where a real current may arise leading to Joule heating of the
metal. The standard concept of a fluctuating electromagnetic field on such
frequencies meets difficulties when used as a model for the zero-point
oscillations or thermal photons in the thermal equilibrium inside metals.
Instead, the surface impedance permits not to consider the electromagnetic
oscillations inside the metal but taking the realistic material properties into
account by means of the effective boundary condition. An independent derivation
of the Lifshitz-type formulas for the Casimir free energy and force between two
metal plates is presented within the impedance approach. It is shown that they
are free of the contradictions with thermodynamics which are specific to the
usual Lifshitz formula for dielectrics in combination with the Drude model. We
demonstrate that in the impedance approach the zero-frequency contribution is
uniquely fixed by the form of impedance function and does not need any of the
ad hoc prescriptions intensively discussed in the recent literature. As an
example, the computations of the Casimir free energy between two gold plates
are performed at different separations and temperatures. It is argued that the
surface impedance approach lays a reliable framework for the future
measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.
Drude model and Lifshitz formula
Since nearly 10 years, it is known that inserting the permittivity of the
Drude model into the Lifshitz formula for free energy causes a violation of the
third law of thermodynamics. In this paper we show that the standard Matsubara
formulation for free energy contains a contribution that is non-perturbative in
the relaxation parameter. We argue that the correct formula must have a
perturbative expansion and conclude that the standard Matsubara formulation
with the permittivity of the Drude model inserted is not correct. We trace the
non-perturbative contribution in the complex frequency plane, where it shows up
as a self-intersection or a bifurcation of the integration path.Comment: accepted for publication in EPJ
Sagnac Interferometer as a Speed-Meter-Type, Quantum-Nondemolition Gravitational-Wave Detector
According to quantum measurement theory, "speed meters" -- devices that
measure the momentum, or speed, of free test masses -- are immune to the
standard quantum limit (SQL). It is shown that a Sagnac-interferometer
gravitational-wave detector is a speed meter and therefore in principle it can
beat the SQL by large amounts over a wide band of frequencies. It is shown,
further, that, when one ignores optical losses, a signal-recycled Sagnac
interferometer with Fabry-Perot arm cavities has precisely the same
performance, for the same circulating light power, as the Michelson speed-meter
interferometer recently invented and studied by P. Purdue and the author. The
influence of optical losses is not studied, but it is plausible that they be
fairly unimportant for the Sagnac, as for other speed meters. With squeezed
vacuum (squeeze factor ) injected into its dark port, the
recycled Sagnac can beat the SQL by a factor over the
frequency band 10 {\rm Hz} \alt f \alt 150 {\rm Hz} using the same
circulating power kW as is used by the (quantum limited)
second-generation Advanced LIGO interferometers -- if other noise sources are
made sufficiently small. It is concluded that the Sagnac optical configuration,
with signal recycling and squeezed-vacuum injection, is an attractive candidate
for third-generation interferometric gravitational-wave detectors (LIGO-III and
EURO).Comment: 12 pages, 6 figure
Thermal correction to the Casimir force, radiative heat transfer, and an experiment
The low-temperature asymptotic expressions for the Casimir interaction
between two real metals described by Leontovich surface impedance are obtained
in the framework of thermal quantum field theory. It is shown that the Casimir
entropy computed using the impedance of infrared optics vanishes in the limit
of zero temperature. By contrast, the Casimir entropy computed using the
impedance of the Drude model attains at zero temperature a positive value which
depends on the parameters of a system, i.e., the Nernst heat theorem is
violated. Thus, the impedance of infrared optics withstands the thermodynamic
test, whereas the impedance of the Drude model does not. We also perform a
phenomenological analysis of the thermal Casimir force and of the radiative
heat transfer through a vacuum gap between real metal plates. The
characterization of a metal by means of the Leontovich impedance of the Drude
model is shown to be inconsistent with experiment at separations of a few
hundred nanometers. A modification of the impedance of infrared optics is
suggested taking into account relaxation processes. The power of radiative heat
transfer predicted from this impedance is several times less than previous
predictions due to different contributions from the transverse electric
evanescent waves. The physical meaning of low frequencies in the Lifshitz
formula is discussed. It is concluded that new measurements of radiative heat
transfer are required to find out the adequate description of a metal in the
theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.
Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme
We analyze and discuss the quantum noise in signal-recycled laser
interferometer gravitational-wave detectors, such as Advanced LIGO, using a
heterodyne readout scheme and taking into account the optomechanical dynamics.
Contrary to homodyne detection, a heterodyne readout scheme can simultaneously
measure more than one quadrature of the output field, providing an additional
way of optimizing the interferometer sensitivity, but at the price of
additional noise. Our analysis provides the framework needed to evaluate
whether a homodyne or heterodyne readout scheme is more optimal for second
generation interferometers from an astrophysical point of view. As a more
theoretical outcome of our analysis, we show that as a consequence of the
Heisenberg uncertainty principle the heterodyne scheme cannot convert
conventional interferometers into (broadband) quantum non-demolition
interferometers.Comment: 16 pages, 8 figure
Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurements
We report new constraints on extra-dimensional models and other physics
beyond the Standard Model based on measurements of the Casimir force between
two dissimilar metals for separations in the range 0.2--1.2 m. The Casimir
force between an Au-coated sphere and a Cu-coated plate of a
microelectromechanical torsional oscillator was measured statically with an
absolute error of 0.3 pN. In addition, the Casimir pressure between two
parallel plates was determined dynamically with an absolute error of mPa. Within the limits of experimental and theoretical errors, the results
are in agreement with a theory that takes into account the finite conductivity
and roughness of the two metals. The level of agreement between experiment and
theory was then used to set limits on the predictions of extra-dimensional
physics and thermal quantum field theory. It is shown that two theoretical
approaches to the thermal Casimir force which predict effects linear in
temperture are ruled out by these experiments. Finally, constraints on Yukawa
corrections to Newton's law of gravity are strengthened by more than an order
of magnitude in the range 56 nm to 330 nm.Comment: Revtex 4, 35 pages, 14 figures in .gif format, accepted for
publication in Phys. Rev.
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