2,243 research outputs found
Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory
The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the PPN parameter alpha sub 2, which is related to the difference in propagation speeds for gravitational and electromagnetic waves. Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific but presumably special form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity--and standard solar system experiments cannot distinguish between the two theories
Generalized uncertainty relations: Theory, examples, and Lorentz invariance
The quantum-mechanical framework in which observables are associated with
Hermitian operators is too narrow to discuss measurements of such important
physical quantities as elapsed time or harmonic-oscillator phase. We introduce
a broader framework that allows us to derive quantum-mechanical limits on the
precision to which a parameter---e.g., elapsed time---may be determined via
arbitrary data analysis of arbitrary measurements on identically prepared
quantum systems. The limits are expressed as generalized Mandelstam-Tamm
uncertainty relations, which involve the operator that generates displacements
of the parameter---e.g., the Hamiltonian operator in the case of elapsed time.
This approach avoids entirely the problem of associating a Hermitian operator
with the parameter. We illustrate the general formalism, first, with
nonrelativistic uncertainty relations for spatial displacement and momentum,
harmonic-oscillator phase and number of quanta, and time and energy and,
second, with Lorentz-invariant uncertainty relations involving the displacement
and Lorentz-rotation parameters of the Poincar\'e group.Comment: 39 pages of text plus one figure; text formatted in LaTe
Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic
Four-wave mixing near resonance in an atomic vapor can produce relative
intensity squeezed light suitable for precision measurements beyond the
shot-noise limit. We develop an analytic distributed gain/loss model to
describe the competition of mixing and absorption through the non-linear
medium. Using a novel matrix calculus, we present closed-form expressions for
the degree of relative intensity squeezing produced by this system. We use
these theoretical results to analyze experimentally measured squeezing from a
Rb vapor and demonstrate the analytic model's utility as an experimental
diagnostic.Comment: 10 pages, 5 figure
Separable balls around the maximally mixed multipartite quantum states
We show that for an m-partite quantum system, there is a ball of radius
2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable
(unentangled) positive semidefinite matrices. This can be used to derive an
epsilon below which mixtures of epsilon of any density matrix with 1 - epsilon
of the maximally mixed state will be separable. The epsilon thus obtained is
exponentially better (in the number of systems) than existing results. This
gives a number of qubits below which NMR with standard pseudopure-state
preparation techniques can access only unentangled states; with parameters
realistic for current experiments, this is 23 qubits (compared to 13 qubits via
earlier results). A ball of radius 1 is obtained for multipartite states
separable over the reals.Comment: 8 pages, LaTe
Quantum Fluctuations of Radiation Pressure
Quantum fluctuations of electromagnetic radiation pressure are discussed. We
use an approach based on the quantum stress tensor to calculate the
fluctuations in velocity and position of a mirror subjected to electromagnetic
radiation. Our approach reveals that radiation pressure fluctuations are due to
a cross term between vacuum and state dependent terms in a stress tensor
operator product. Thus observation of these fluctuations would entail
experimental confirmation of this cross term. We first analyze the pressure
fluctuations on a single, perfectly reflecting mirror, and then study the case
of an interferometer. This involves a study of the effects of multiple bounces
in one arm, as well as the correlations of the pressure fluctuations between
arms of the interferometer. In all cases, our results are consistent with those
previously obtained by Caves using different mehods.Comment: 23 pages, 3 figures, RevTe
Equivalent efficiency of a simulated photon-number detector
Homodyne detection is considered as a way to improve the efficiency of
communication near the single-photon level. The current lack of commercially
available {\it infrared} photon-number detectors significantly reduces the
mutual information accessible in such a communication channel. We consider
simulating direct detection via homodyne detection. We find that our particular
simulated direct detection strategy could provide limited improvement in the
classical information transfer. However, we argue that homodyne detectors (and
a polynomial number of linear optical elements) cannot simulate photocounters
arbitrarily well, since otherwise the exponential gap between quantum and
classical computers would vanish.Comment: 4 pages, 4 figure
Quantum Mechanics and Linearized Gravitational Waves
The interaction of classical gravitational waves (GW) with matter is studied
within a quantum mechanical framework. The classical equations of motion in the
long wave-length limit is quantized and a Schroedinger equation for the
interaction of GW with matter is proposed. Due to its quadrapole nature, the GW
interacts with matter by producing squeezed quantum states. The resultant
hamiltonian is quite different from one would expect from general principles,
however. The interaction of GW with the free particle, the harmonic oscillator
and the hydrogen atom is then studied using this hamiltonian.Comment: 24 pages, written in REVTE
International Capital Markets and Canadian Economic Policy under Flexible and Fixed Exchange Rates, 1952-69
Standard Quantum Limits for broadband position measurement
I utilize the Caves-Milburn model for continuous position measurements to
formulate a broadband version of the Standard Quantum Limit (SQL) for
monitoring the position of a free mass, and illustrate the use of Kalman
filtering to recover the SQL for estimating a weak classical force that acts on
a quantum-mechanical test particle under continuous observation. These
derivations are intended to clarify the interpretation of SQL's in the context
of continuous quantum measurement.Comment: Replaced version: changed title, fixed algebra error at the very end,
conclusions modified accordingly. Four pages, one eps figur
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.
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