616 research outputs found
Sub-SQL Sensitivity via Optical Rigidity in Advanced LIGO Interferometer with Optical Losses
The ``optical springs'' regime of the signal-recycled configuration of laser
interferometric gravitational-wave detectors is analyzed taking in account
optical losses in the interferometer arm cavities. This regime allows to obtain
sensitivity better than the Standard Quantum Limits both for a free test mass
and for a conventional harmonic oscillator. The optical losses restrict the
gain in sensitivity and achievable signal-to-noise ratio. Nevertheless, for
parameters values planned for the Advanced LIGO gravitational-wave detector,
this restriction is insignificant.Comment: 15 pages, 9 figure
How to reduce the suspension thermal noise in LIGO without improving the Q's of the pendulum and violin modes
The suspension noise in interferometric gravitational wave detectors is
caused by losses at the top and the bottom attachments of each suspension
fiber. We use the Fluctuation-Dissipation theorem to argue that by careful
positioning of the laser beam spot on the mirror face it is possible to reduce
the contribution of the bottom attachment point to the suspension noise by
several orders of magnitude. For example, for the initial and enhanced LIGO
design parameters (i.e. mirror masses and sizes, and suspension fibers' lengths
and diameters) we predict a reduction of in the "bottom" spectral
density throughout the band of serious thermal noise. We then
propose a readout scheme which suppresses the suspension noise contribution of
the top attachment point. The idea is to monitor an averaged horizontal
displacement of the fiber of length ; this allows one to record the
contribution of the top attachment point to the suspension noise, and later
subtract it it from the interferometer readout. For enhanced LIGO this would
allow a suppression factor about 100 in spectral density of suspension thermal
noise.Comment: a few misprints corrected; submitted to Classical and Quantum Gravit
Quantum statistical properties of the radiation field in a cavity with a movable mirror
A quantum system composed of a cavity radiation field interacting with a
movable mirror is considered and quantum statistical properties of the field
are studied. Such a system can serve in principle as an idealized meter for
detection of a weak classical force coupled to the mirror which is modelled by
a quantum harmonic oscillator. It is shown that the standard quantum limit on
the measurement of the mirror position arises naturally from the properties of
the system during its dynamical evolution. However, the force detection
sensitivity of the system falls short of the corresponding standard quantum
limit. We also study the effect of the nonlinear interaction between the moving
mirror and the radiation pressure on the quadrature fluctuations of the
initially coherent cavity field.Comment: REVTeX, 9 pages, 5 figures. More info on
http://www.ligo.caltech.edu/~cbrif/science.htm
Dual-Resonator Speed Meter for a Free Test Mass
A description and analysis are given of a ``speed meter'' for monitoring a
classical force that acts on a test mass. This speed meter is based on two
microwave resonators (``dual resonators''), one of which couples evanescently
to the position of the test mass. The sloshing of the resulting signal between
the resonators, and a wise choice of where to place the resonators' output
waveguide, produce a signal in the waveguide that (for sufficiently low
frequencies) is proportional to the test-mass velocity (speed) rather than its
position. This permits the speed meter to achieve force-measurement
sensitivities better than the standard quantum limit (SQL), both when operating
in a narrow-band mode and a wide-band mode. A scrutiny of experimental issues
shows that it is feasible, with current technology, to construct a
demonstration speed meter that beats the wide-band SQL by a factor 2. A concept
is sketched for an adaptation of this speed meter to optical frequencies; this
adaptation forms the basis for a possible LIGO-III interferometer that could
beat the gravitational-wave standard quantum limit h_SQL, but perhaps only by a
factor 1/xi = h_SQL/h ~ 3 (constrained by losses in the optics) and at the
price of a very high circulating optical power --- larger by 1/xi^2 than that
required to reach the SQL.Comment: RevTex: 13 pages with 4 embedded figures (two .eps format and two
drawn in TeX); Submitted to Physical Review
Speed Meter As a Quantum Nondemolition Measuring Device for Force
Quantum noise is an important issue for advanced LIGO. Although it is in
principle possible to beat the Standard Quantum Limit (SQL), no practical
recipe has been found yet. This paper dicusses quantum noise in the context of
speedmeter-a devise monitoring the speed of the testmass. The scheme proposed
to overcome SQL in this case might be more practical than the methods based on
monitoring position of the testmass.Comment: 7 pages of RevTex, 1 postscript figur
Optical noise correlations and beating the standard quantum limit in advanced gravitational-wave detectors
The uncertainty principle, applied naively to the test masses of a
laser-interferometer gravitational-wave detector, produces a Standard Quantum
Limit (SQL) on the interferometer's sensitivity. It has long been thought that
beating this SQL would require a radical redesign of interferometers. However,
we show that LIGO-II interferometers, currently planned for 2006, can beat the
SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their
thermal noise can be pushed low enough. This is due to dynamical correlations
between photon shot noise and radiation-pressure noise, produced by the LIGO-II
signal-recycling mirror.Comment: 12 pages, 2 figures; minor changes, some references adde
Conversion of conventional gravitational-wave interferometers into QND interferometers by modifying their input and/or output optics
The LIGO-II gravitational-wave interferometers (ca. 2006--2008) are designed
to have sensitivities at about the standard quantum limit (SQL) near 100 Hz.
This paper describes and analyzes possible designs for subsequent, LIGO-III
interferometers that can beat the SQL. These designs are identical to a
conventional broad-band interferometer (without signal recycling), except for
new input and/or output optics. Three designs are analyzed: (i) a
"squeezed-input interferometer" (conceived by Unruh based on earlier work of
Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is
injected into the interferometer's dark port; (ii) a "variational-output"
interferometer (conceived in a different form by Vyatchanin, Matsko and
Zubova), in which homodyne detection with FD homodyne phase is performed on the
output light; and (iii) a "squeezed-variational interferometer" with squeezed
input and FD-homodyne output. It is shown that the FD squeezed-input light can
be produced by sending ordinary squeezed light through two successive
Fabry-Perot filter cavities before injection into the interferometer, and
FD-homodyne detection can be achieved by sending the output light through two
filter cavities before ordinary homodyne detection. With anticipated technology
and with laser powers comparable to that planned for LIGO-II, these
interferometers can beat the amplitude SQL by factors in the range from 3 to 5,
corresponding to event rate increases between ~30 and ~100 over the rate for a
SQL-limited interferometer.Comment: Submitted to Physical Review D; RevTeX manuscript with 16 figures;
prints to 33 pages in Physical Review double column format. Minor revisions
have been made in response to referee repor
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.
Laser-interferometer gravitational-wave optical-spring detectors
Using a quantum mechanical approach, we show that in a gravitational-wave
interferometer composed of arm cavities and a signal recycling cavity, e.g.,
the LIGO-II configuration, the radiation-pressure force acting on the mirrors
not only disturbs the motion of the free masses randomly due to quantum
fluctuations, but also and more fundamentally, makes them respond to forces as
though they were connected to an (optical) spring with a specific rigidity.
This oscillatory response gives rise to a much richer dynamics than previously
known, which enhances the possibilities for reshaping the LIGO-II's noise
curves. However, the optical-mechanical system is dynamically unstable and an
appropriate control system must be introduced to quench the instability.Comment: 7 pages, 3 figures; to appear in the Proceedings of 4th Edoardo
Amaldi Conference on Gravitational Waves, Perth, Australia, 8-13 July 200
Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors
It has long been thought that the sensitivity of laser interferometric
gravitational-wave detectors is limited by the free-mass standard quantum
limit, unless radical redesigns of the interferometers or modifications of
their input/output optics are introduced. Within a fully quantum-mechanical
approach we show that in a second-generation interferometer composed of arm
cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i)
quantum shot noise and quantum radiation-pressure-fluctuation noise are
dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii)
the Standard Quantum Limit can be beaten by a factor of 2, over a frequency
range \Delta f/f \sim 1, but at the price of increasing noise at lower
frequencies.Comment: 35 pages, 9 figures; few misprints corrected and some references
adde
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