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 measurement—a "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.

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On the measurement of a weak classical force coupled to a quantum mechanical oscillator. i. issues of principle

With the advent of high-energy-density (HED) experimental facilities, such as high-energy lasers and fast Z-pinch, pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. This has enabled the emergence of a new class of experimental science, HED laboratory astrophysics, wherein the properties of matter and the processes that occur under extreme astrophysical conditions can be examined in the laboratory. Areas particularly suitable to this class of experimental astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds and nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars.

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Experimental astrophysics with high power lasers and Z pinches

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

The adiabatic theory of charged-particle motion is developed systematically in this review. We present the essentials of the theory without giving all the analysis in detail. The general expressions for guiding-center motion and particle energy change are given, with application to the Van Allen radiation and to Fermi acceleration. It is shown that Fermi acceleration and betatron acceleration should not be regarded as distinct processes. Modifications of the nonrelativistic theory that are necessary when the particle is relativistic are discussed. Proofs are given of the invariance to lowest order of the first and second adiabatic invariants for the case of static fields. Finally, applications are made to the theory of plasmas.

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Adiabatic charged-particle motion

Some 30% of disc galaxies have a pronounced central bar features in the disc plane and many more have weaker features of a similar kind. Kinematic data indicate that the bar constitutes a major non-axisymmetric component of the mass distribution and that the bar pattern tumbles rapidly about the axis normal to the disc plane. The observed motions are consistent with material within the bar streaming along highly elongated orbits aligned with the rotating major axis. A barred galaxy may also contain a spheroidal bulge at its centre, spirals in the outer disc and, less commonly, other features such as a ring or lens. Mild asymmetries in both the light and kinematics are quite common. The authors review the main problems presented by these complicated dynamical systems and summarize the effort so far made towards their solution, emphasizing results which appear secure.

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Dynamics of Barred Galaxies

Density Waves in a Highly Flattened, Rapidly Rotating Galaxy

Theoretical Principles in Astrophysics and Relativity

The relativistic motion of a charged particle in an inhomogeneous electromagnetic field

The Character of the Equilibrium of a Compressible, Inviscid Fluid of Varying Density.

The stability of a one-dimensional weak D-type ionization front is investigated, in case the perturbations of the neutral gas and ionized gas on thie two sides of the front are isothermal. The characteristic value problem governing the complex rates of growth for the unstable modes is formulated, and the solutions for the rates of growth are obtained in the limit that the ratio of the speed of sound in the neutral gas to the speed of sound in the ionized gas tends to zero. If the radiation field associated with the front has no particular symmetry, both overstable and unstable modes occur; if the symmetry of the radiation field is such that the flux through every plane normal to the front vanishes, then all modes are simply unstable. If the radiation field has this symmetry and the condition of the front is D-critical (in the nomenclature of Kahn), the front is stable. However, even small departures of the condition of the front from D-critical will allow a substantial instability. For this reason, the stability of the critical D-type front probably- has no important consequences. The physical mechanism for the instability is considered briefly, and it is shown that the instabilitymore » is related to such well-known processes as the rocket effect of Oort and Spitzer. As a numerical example illustrating the theory, the rates of growth are computed for the instability of the boundary of an H II region illuminated by a star of early spectral type. A conclusion tentatively drawn from this example is that the instability might produce irregularities similar to bright rims and elephant trunks'' in a time comparable to the age of the H II region. (auth)« less

Peter O. Vandervoort

Papers

Density Waves in a Highly Flattened, Rapidly Rotating Galaxy

Theoretical Principles in Astrophysics and Relativity

The relativistic motion of a charged particle in an inhomogeneous electromagnetic field

The Character of the Equilibrium of a Compressible, Inviscid Fluid of Varying Density.

On the stability of ionization fronts