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 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

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges

A new traceability chain for the derivation of the farad from dc quantum Hall effect has been implemented at INRIM. Main components of the chain are two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature bridge, both operating at 1541 Hz. The bridges are energized and controlled with a polyphase direct-digital-synthesizer, which permits to achieve both main and auxiliary equilibria in an automated way; the bridges and do not include any variable inductive divider or variable impedance box. The relative uncertainty in the realization of the farad, at the level of 1000 pF, is estimated to be 64E-9. A first verification of the realization is given by a comparison with the maintained national capacitance standard, where an agreement between measurements within their relative combined uncertainty of 420E-9 is obtained.Comment: 15 pages, 11 figures, 3 table

Research into the feasibility of metal- and oxide-film capacitors

Thin film capacitors with up to twenty-two active layers have been deposited by RF sputtering. The materials were aluminum electrodes of 1200 to 1500 angstrom thickness and silica dielectric layers of 3000 to 6000 angstrom thickness. The best electrical characteristics were capacitances of nearly 0.1 microfarad for an active area of 1.25 square centimeters, dissipation factor of less than 0.01 over a frequency range of 0.5 to 100 kilohertz and energy density of approximately 70 millijoules per cubic centimeter of active deposited material at a working voltage of 40 volts. These aluminum-silica capacitors exhibit excellent electrical stability over a temperature range from -55 C to +300 C

Investigation of discrete component chip mounting technology for hybrid microelectronic circuits

The use of polymer adhesives for high reliability microcircuit applications is a radical deviation from past practices in electronic packaging. Bonding studies were performed using two gold-filled conductive adhesives, 10/90 tin/lead solder and Indalloy no. 7 solder. Various types of discrete components were mounted on ceramic substrates using both thick-film and thin-film metallization. Electrical and mechanical testing were performed on the samples before and after environmental exposure to MIL-STD-883 screening tests

Near-field scanning microwave microscope for interline capacitance characterization of nanoelectronics interconnect

We have developed a noncontact method for measurement of the interline capacitance in Cu/low-k interconnect. It is based on a miniature test vehicle with net capacitance of a few femto-Farads formed by two 20-\mu m-long parallel wires (lines) with widths and spacings the same as those of the interconnect wires of interest. Each line is connected to a small test pad. The vehicle impedance is measured at 4 GHz by a near-field microwave probe with 10 \mu m probe size via capacitive coupling of the probe to the vehicle's test pads. Full 3D finite element modeling at 4 GHz confirms that the microwave radiation is concentrated between the two wires forming the vehicle. An analytical lumped element model and a short/open calibration approach have been proposed to extract the interline capacitance value from the measured data. We have validated the technique on several test vehicles made with copper and low-k dielectric on a 300 mm wafer. The vehicles interline spacing ranges from 0.09 to 1 \mu m and a copper line width is 0.15 \mu m. This is the first time a near-field scanning microwave microscope has been applied to measure the lumped element impedance of a test vehicle

Evaluation of capacitors for space propulsion applications final progress report

Low inductance energy storage capacitors for space propulsion application

Research into the feasibility of thin metal and oxide-film capacitors Final technical report

Feasibility of producing thin metal and oxide- film capacitors with stable electrical properties in high temperature environment