95 research outputs found
An analysis of a QND speed-meter interferometer
In the quest to develop viable designs for third-generation optical
interferometric gravitational-wave detectors (e.g. LIGO-III and EURO), one
strategy is to monitor the relative momentum or speed of the test-mass mirrors,
rather than monitoring their relative position. This paper describes and
analyzes the most straightforward design for a {\it speed meter interferometer}
that accomplishes this -- a design (due to Braginsky, Gorodetsky, Khalili and
Thorne) that is analogous to a microwave-cavity speed meter conceived by
Braginsky and Khalili. A mathematical mapping between the microwave speed meter
and the optical interferometric speed meter is developed and is used to show
(in accord with the speed being a Quantum Nondemolition [QND] observable) that
{\it in principle} the interferometric speed meter can beat the
gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount,
over an arbitrarily wide range of frequencies, and can do so without the use of
squeezed vacuum or any auxiliary filter cavities at the interferometer's input
or output. However, {\it in practice}, to reach or beat the SQL, this specific
speed meter requires exorbitantly high input light power. The physical reason
for this is explored, along with other issues such as constraints on
performance due to optical dissipation. This analysis forms a foundation for
ongoing attempts to develop a more practical variant of an interferometric
speed meter and to combine the speed meter concept with other ideas to yield a
promising LIGO-III/EURO interferometer design that entails low laser power.Comment: 12 pages, 5 figures; corrected formula and some values describing
power requirement
Thermo-refractive noise in gravitational wave antennae
Thermodynamical fluctuations of temperature in mirrors of gravitational wave
antennae may be transformed into additional noise not only through thermal
expansion coefficient but also through temperature dependence of refraction
index. The intensity of this noise is comparable with other known noises and
must be taken into account in future steps of the antennas.Comment: 11 pages, 1 figure, the paper is revised as compared to one accepted
in Phys.Letts.A (new numerical estimates
The noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization
It is shown that photon shot noise and radiation-pressure back-action noise
are the sole forms of quantum noise in interferometric gravitational wave
detectors that operate near or below the standard quantum limit, if one filters
the interferometer output appropriately. No additional noise arises from the
test masses' initial quantum state or from reduction of the test-mass state due
to measurement of the interferometer output or from the uncertainty principle
associated with the test-mass state. Two features of interferometers are
central to these conclusions: (i) The interferometer output (the photon number
flux N(t) entering the final photodetector) commutes with itself at different
times in the Heisenberg Picture, [N(t), N(t')] = 0, and thus can be regarded as
classical. (ii) This number flux is linear in the test-mass initial position
and momentum operators x_o and p_o, and those operators influence the measured
photon flux N(t) in manners that can easily be removed by filtering -- e.g., in
most interferometers, by discarding data near the test masses' 1 Hz swinging
freqency. The test-mass operators x_o and p_o contained in the unfiltered
output N(t) make a nonzero contribution to the commutator [N(t), N(t')]. That
contribution is cancelled by a nonzero commutation of the photon shot noise and
radiation-pressure noise, which also are contained in N(t). This cancellation
of commutators is responsible for the fact that it is possible to derive an
interferometer's standard quantum limit from test-mass considerations, and
independently from photon-noise considerations. These conclusions are true for
a far wider class of measurements than just gravitational-wave interferometers.
To elucidate them, this paper presents a series of idealized thought
experiments that are free from the complexities of real measuring systems.Comment: Submitted to Physical Review D; Revtex, no figures, prints to 14
pages. Second Revision 1 December 2002: minor rewording for clarity,
especially in Sec. II.B.3; new footnote 3 and passages before Eq. (2.35) and
at end of Sec. III.B.
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
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
Analysis of Parametric Oscillatory Instability in Power Recycled LIGO Interferometer
We present the analysis of a nonlinear effect of parametric oscillatory
instability in power recycled LIGO interferometer with the Fabry-Perot (FP)
cavities in the arms. The basis for this effect is the excitation of the
additional (Stokes) optical mode and the mirror elastic mode, when the optical
energy stored in the main FP cavity main mode exceeds the certain threshold and
the frequencies are related so that sum of frequencies of Stokes and elastic
modes are approximately equal to frequencyof main mode. The presence of
anti-Stokes modes (with frequency approximately equal to sum of frequencies of
main and elastic modes) can depress parametric instability. However, it is very
likely that the anti-Stokes modes will not compensate the parametric
instability completely.Comment: 9 pages, 2 figures. submitted to Physics Letters
Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae
Thermodynamical fluctuations of temperature in mirrors of gravitational wave
antennae are transformed through thermal expansion coefficient into additional
noise. This source of noise, which may also be interpreted as fluctuations due
to thermoelastic damping, may not be neglected and leads to the necessity to
reexamine the choice of materials for the mirrors. Additional source of noise
are fluctuations of the mirrors' surfaces caused by optical power absorbed in
dielectrical reflective layers.Comment: 20 pages, 2 figure
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
Notes about Noise in Gravitational Wave Antennas Created by Cosmic Rays
Thermodynamical fluctuations of temperature in mirrors may produce surface
fluctuations not only through thermal expansion in mirror body but also through
thermal expansion in mirror coating. We analyze the last "surface" effect which
can be larger than the first "volume" one due to larger thermal expansion
coefficient of coating material and smaller effective volume. In particular,
these fluctuations may be important in laser interferometric gravitational
antennae.Comment: 9 pages, LaTe
Corner reflectors and Quantum-Non-Demolition Measurements in gravitational wave antennae
We propose Fabry-Perot cavity with corner reflectors instead of spherical
mirrors to reduce the contribution of thermoelastic noise in the coating which
is relatively large for spherical mirrors and which prevents the sensitivity
better than Standard Quantum Limit (SQL) from being achieved in laser
gravitational wave antenna. We demonstrate that thermo-refractive noise in
corner reflector (CR) is substantially smaller than SQL. We show that the
distortion of main mode of cavity with CR caused by tilt and displacement of
one reflector is smaller than for cavity with spherical mirrors. We also
consider the distortion caused by small nonperpendicularity of corner facets
and by optical inhomogeneity of fused silica which is proposed as a material
for corner reflectors.Comment: 12 pages, LaTex, 7 figure
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