1,072 research outputs found
Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame
We analyze the interaction of plane '+'-polarized gravitational waves with a
Fabry-Perot cavity in the local Lorentz frame of the cavity input mirror
outside of the range of long-wave approximation with the force of radiation
pressure taken into account. The obtained detector response signal is
represented as a sum of two parts: (i) the phase shift due to displacement of
the movable mirror under the influence of gravitational wave and the force of
light pressure, and (ii) the phase shift due to direct interaction of
gravitational wave with light wave inside the cavity. We obtain formula for the
movable mirror law of motion paying close attention to the phenomena of optical
rigidity, radiative friction and direct coupling of gravitational wave to light
wave. Some issues concerning the detection of high-frequency gravitational
waves and the role of optical rigidity in it are discussed. We also examine in
detail special cases of optical resonance and small detuning from it and
compare our results with the known ones.Comment: 17 pages, 9 figures; corrected references [7,8,34], added 2 new
references (currently [35,36]), added comments on (i) relativistic
corrections, (ii) detector angular pattern, (iii) quantized electromagnetic
field, increased font in figure
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
Proof of the Standard Quantum Limit for Monitoring Free-Mass Position
The measurement result of the moved distance for a free mass m during the
time t between two position measurements cannot be predicted with uncertainty
smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit
(SQL) and it has been proven to always hold for the following position
measurement: a probe is set in a prescribed position before the measurement.
Just after the interaction of the mass with the probe, the probe position is
measured, and using this value, the measurement results of the pre-measurement
and post-measurement positions are estimated.Comment: 4 pages, no figur
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
Phase diffusion pattern in quantum nondemolition systems
We quantitatively analyze the dynamics of the quantum phase distribution
associated with the reduced density matrix of a system, as the system evolves
under the influence of its environment with an energy-preserving quantum
nondemolition (QND) type of coupling. We take the system to be either an
oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a
spin-1/2 system), and model the environment as a bath of harmonic oscillators,
initially in a general squeezed thermal state. The impact of the different
environmental parameters is explicitly brought out as the system starts out in
various initial states. The results are applicable to a variety of physical
systems now studied experimentally with QND measurements.Comment: 18 pages, REVTeX, 8 figure
Imprinting interference fringes in massive optomechanical systems
An interferometric scheme for the creation of momentum superposition states
of mechanical oscillators, using a quantum mirror kicked by free photons is
analyzed. The scheme features ultra-fast preparation with immediate detection
and should allow for the observation of signatures of momentum superpositions
in a massive macroscopic system at non-zero temperatures. It is robust against
thermalized initial states, displacement and movement, mirror imperfections,
and the measurements' back-actions.Comment: 4 pages, 3 figures, 7 subfigure
Random surface roughness influence on gas damped nanoresonators
The author investigates quantitatively the influence of random surface roughness on the quality factor Q of nanoresonators due to noise by impinging gas molecules. The roughness is characterized by the amplitude w, the correlation length ξ, and the roughness exponent H that describes fine roughness details at short wavelengths. Surface roughening (decreasing H and increasing ratio w/ξ) leads to lower Q, which translates to lower sensitivity to external perturbations, and a higher limit to mass sensitivity. The influence of the exponent H is shown to be important as that of w/ξ, indicating the necessity for precise control of the surface morphology.
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
Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer
We present an optomechanical displacement transducer, that relies on three
cavity modes parametrically coupled to a mechanical oscillator and whose
frequency spacing matches the mechanical resonance frequency. The additional
resonances allow to reach the standard quantum limit at substantially lower
input power (compared to the case of only one resonance), as both, sensitivity
and quantum backaction are enhanced. Furthermore, it is shown that in the case
of multiple cavity modes, coupling between the modes is induced via reservoir
interaction, e.g., enabling quantum backaction noise cancellation. Experimental
implementation of the schemes is discussed in both the optical and microwave
domain.Comment: 5 pages, 3 figures. Revised and amended versio
Quantum Signatures of the Optomechanical Instability
In the past few years, coupling strengths between light and mechanical motion
in optomechanical setups have improved by orders of magnitude. Here we show
that, in the standard setup under continuous laser illumination, the steady
state of the mechanical oscillator can develop a non-classical, strongly
negative Wigner density if the optomechanical coupling is large at the
single-photon level. Because of its robustness, such a Wigner density can be
mapped using optical homodyne tomography. These features are observed near the
onset of the instability towards self-induced oscillations. We show that there
are also distinct signatures in the photon-photon correlation function
in that regime, including oscillations decaying on a time scale
not only much longer than the optical cavity decay time, but even longer than
the \emph{mechanical} decay time.Comment: 6 pages including 1 appendix. 6 Figures. Correcte
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