933 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
Thermal noises and noise compensation in high-reflection multilayer coating
Thermal fluctuations of different origin in the substrate and in the coating
of optical mirrors produce phase noise in the reflected wave. This noise
determines the ultimate stabilization capability of high-Q cavities used as a
reference system. In particular this noise is significant in interferometric
laser gravitational wave antennas. It is shown that simple alteration of a
mirror multilayer coating may provide suppression of phase noise produced by
thermorefractive, thermoelastic, photothermal and thermoradiation induced
fluctuations in the coating.Comment: 10 pages, 5 figure
Exact solution for many-body Hamiltonian of interacting particles with linear spectrum
The exact solution of the Schr\"odinger equation for the one-dimensional
system of interacting particles with the linear dispersion law in an arbitrary
external field is found. The solution is reduced to two groups of particles
moving with constant velocities in the opposite directions with a fixed
distance between the particles in each group. The problem is applied to the
edge states of the 2D topological insulator.Comment: 4 page
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.
Observation of opto-mechanical multistability in a high Q torsion balance oscillator
We observe the opto-mechanical multistability of a macroscopic torsion
balance oscillator. The torsion oscillator forms the moving mirror of a
hemi-spherical laser light cavity. When a laser beam is coupled into this
cavity, the radiation pressure force of the intra-cavity beam adds to the
torsion wire's restoring force, forming an opto-mechanical potential. In the
absence of optical damping, up to 23 stable trapping regions were observed due
to local light potential minima over a range of 4 micrometer oscillator
displacement. Each of these trapping positions exhibits optical spring
properties. Hysteresis behavior between neighboring trapping positions is also
observed. We discuss the prospect of observing opto-mechanical stochastic
resonance, aiming at enhancing the signal-to-noise ratio (SNR) in gravity
experiments.Comment: 4 pages, 5 figure
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
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
Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations
We treat two possible phenomenological effects of quantum fluctuations of
spacetime geometry: spectral line broadening and angular blurring of the image
of a distance source. A geometrical construction will be used to express both
effects in terms of the Riemann tensor correlation function. We apply the
resulting expressions to study some explicit examples in which the fluctuations
arise from a bath of gravitons in either a squeezed state or a thermal state.
In the case of a squeezed state, one has two limits of interest: a coherent
state which exhibits classical time variation but no fluctuations, and a
squeezed vacuum state, in which the fluctuations are maximized.Comment: 21 pages, 2 figures. Dedicated to Raphael Sorkin on the occasion of
his 60th birthday. (v2: several references added and some minor errors
corrected
Schroedinger Cat States of a Nanomechanical Resonator
We present a scheme of generating large-amplitude Schr\"{o}dinger cat states
and entanglement in a coupled system of nanomechanical resonator and single
Cooper pair box (SCPB), without being limited by the magnitude of the coupling.
It is shown that the entanglement between the resonator and the SCPB can be
detected by a spectroscopic method.Comment: 1 figur
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