## LSU Historical Dissertations and Theses

1990

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

Warren W. Johnson

#### Abstract

We designed, constructed, and tested (using two different low phase noise electrical pump generators) a cryogenic double-resonant parabridge motion transducer made out of niobium, whose electrical output was amplified by a two stage MESFET cryogenic amplifier. Most of the experimental results agreed well with the theoretical models, and we successfully measured the mechanical Brownian motion of this transducer. We were able to adjust the two electrical bridge resonant frequencies on top of each other at the pump frequency, allowing us to obtain an electromechanical coupling as high as 0.054. This high coupling, corresponding to an rms electric field strength of 1.79 $\times$ 10$\sp5$ V/m across the capacitor plates, is the highest measured so far for this class of transducers. In one case, we observed a dip in the electrical noise spectrum near the mechanical resonant frequency due to destructive interference between this noise and its "reflection" from the mechanical resonator. At the bottom of this dip, we measured, for this transducer, an equivalent displacement noise of 4 $\times$ 10$\sp{-16}$ m/$\sqrt{\rm Hz}$ with a systematic error of less than 10%. This measured equivalent displacement noise allows this parametric transducer to detect accelerations of 1.4 $\times$ 10$\sp{-8}$ m/s$\sp2$ at 929 Hz in a one Hz bandwidth. If coupled to the LSU gravitational wave antenna, a 2.3 $\times$ 10$\sp3$ kg aluminum bar, this transducer resonator of 0.27 kg would detect gravitational wave strains (h) as small as 6 $\times$ 10$\sp{-18}$. A large improvement can be achieved if we manage to obtain 50 V$\sb{\rm peak}$ across the transducer's capacitor plates with a 5 MHz crystal oscillator. In this case, we would reach an equivalent displacement noise of 2 $\times$ 10$\sp{-17}$ m/$\sqrt{\rm Hz}$, corresponding to h $\sim$ 3 $\times$ 10$\sp{-19}$. Further improvement could be obtained by the use of a DC SQUID preamplifier.

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