46 research outputs found
Tensor spherical harmonics on S^2 and S^3 as eigenvalue problems
Tensor spherical harmonics for the 2âsphere and 3âsphere are discussed as eigenfunction problems of the Laplace operators on these manifolds. The scalar, vector, and secondârank tensor harmonics are given explicitly in terms of known functions and their properties summarized
On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle
The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-and-phase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurementâa "back-action-evading" measurement of the real part X_1 (or the imaginary part X_2) of the oscillator's complex amplitude. In principle X_1 can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X_1 can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X_1, in which one measures position (or momentum) at half-cycle intervals. Alternatively, one can make "continuous single-transducer" measurements of X_1 by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about X_1 and reject information about X_2. Continuous single-transducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous single-transducer measurements are almost as good as perfectly coupled two-transducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice
Quantum Nondemolition Measurements of Harmonic Oscillators
The complex amplitude X1+iX2âĄ(x+ip / mÏ)e^(iÏt) of a harmonic oscillator is constant in the absence of driving forces. Although the uncertainty principle forbids precise measurements of X1 and X2 simultaneously (ÎX1ÎX2>~â / 2mÏ), X1 alone can be measured precisely and continuously ("quantum nondemolition measurement"). Examples are given of measuring systems that do this job. Such systems might play a crucial role in gravitational-wave detection and elsewhere
Tests of Lorentz violation in muon antineutrino to electron antineutrino oscillations
A recently developed Standard-Model Extension (SME) formalism for neutrino
oscillations that includes Lorentz and CPT violation is used to analyze the
sidereal time variation of the neutrino event excess measured by the Liquid
Scintillator Neutrino Detector (LSND) experiment. The LSND experiment,
performed at Los Alamos National Laboratory, observed an excess, consistent
with neutrino oscillations, of in a beam of . It
is determined that the LSND oscillation signal is consistent with no sidereal
variation. However, there are several combinations of SME coefficients that
describe the LSND data; both with and without sidereal variations. The scale of
Lorentz and CPT violation extracted from the LSND data is of order
GeV for the SME coefficients and . This solution for
Lorentz and CPT violating neutrino oscillations may be tested by other short
baseline neutrino oscillation experiments, such as the MiniBooNE experiment.Comment: 10 pages, 10 figures, 2 tables, uses revtex4 replaced with version to
be published in Physical Review D, 11 pages, 11 figures, 2 tables, uses
revtex
Search for Decay in LSND
We observe a net beam-excess of (stat) (syst) events,
above 160 MeV, resulting from the charged-current reaction of
and/or on C and H in the LSND detector. No beam related muon
background is expected in this energy regime. Within an analysis framework of
, we set a direct upper limit for this
branching ratio of at 90% confidence level.Comment: 4 pages, 4 figure
Measurements of Charged Current Reactions of on
Charged Current reactions of on have been studied using a
decay-at-rest beam at the Los Alamos Neutron Science Center.
The cross section for the exclusive reaction
was measured to be cm. The observed
energy dependence of the cross section and angular distribution of the outgoing
electron agree well with theoretical expectations. Measurements are also
presented for inclusive transitions to excited states,
and compared with theoretical expectations. The
measured cross section, cm, is somewhat
lower than previous measurements and than a continuum random phase
approximation calculation. It is in better agreement with a recent shell model
calculation.Comment: 34 pages, 18 figures, accepted to PRC, replaced with the accepted on
Measurement of electron-neutrino electron elastic scattering
The cross section for the elastic scattering reaction nu_e+e- -> nu_e+e- was
measured by the Liquid Scintillator Neutrino Detector using a mu+ decay-at-rest
nu_e beam at the Los Alamos Neutron Science Center. The standard model of
electroweak physics predicts a large destructive interference between the
charge current and neutral current channels for this reaction. The measured
cross section, sigma_{nu_e e-}=[10.1 +- 1.1(stat.) +- 1.0(syst.)]x E_{nu_e}
(MeV) x 10^{-45} cm^2, agrees well with standard model expectations. The
measured value of the interference parameter, I=-1.01 +- 0.13(stat.) +-
0.12(syst.), is in good agreement with the standard model expectation of
I^{SM}=-1.09. Limits are placed on neutrino flavor-changing neutral currents.
An upper limit on the muon-neutrino magnetic moment of 6.8 x 10^{-10} mu_{Bohr}
is obtained using the nu_mu and \bar{nu}_mu fluxes from pi+ and mu+ decay.Comment: 22 pages, 11 figure