On some aspects of superconducting quantum interferometer optimization

A problem is considered of optimizing the following parameters of the single-junction quantum superconducting fluxmeter: 1. The full range output signal of the magnitometer ΔA. 2. The derivative of the signal characteristic
\gamma = |\frac{\partialA}{\partial\phi_{e}}|
3. The minimum detected flux change δφ For the hysteresis case (
\ell=2\piL_{R}I_{o}\phi_{o}^{-1} > 1
) the following results have been obtained. In the resistive mode (
q= wL_{R}R^{-1} < 1
) the maximum value ΔA equals (
\phi_{o/2})[\Delta_{k}Q(\piL_{R}C_{T}^{-1}]^{1/2}
where the maximum value of the function
\Delta_{k}(\ell)
is about unity, when
\ell \approx 1.5
. A satisfactory agreement has been obtained between the measured and calculated dependences of ΔA on k and C
T
parameters for the fluxmeter having a pumping frequency of about 10 MHz and the high-Q circuit. With detuning
\xi_{o}
conditioning either a triangular or trapezoidal waveform pattern, γ is as usually given by
\gamma_{o}=\frac{w}{k}\sqrt{\frac{L_{t}}{L_{R}}}
If the detuning is great and negative a signal amplitude may take a rectangular form, and γ in this case is much more larger than γ
o
. The experimentally obtained value
\delta\phi =10^{-11}
Gs.cm
²
is near enough to the known theoretical estimation. Calculations indicate that for a nonhysteresis case one may have the following formulae:
\gamma_{\max}/\gamma_{o} = l/q \gg 1
and
(\delta\phi)_{\min} \simeq 1.2 (L_{R}/\ell) (4\Delta fk_{B} T/R)^{1/2}
giving
(\delta\phi)_{\min}/(\Deltaf)^{1/2} \approx 10^{-14}
Gs.cm
²
/
\sqrt{Hz}
when
\ell \approx 1
,
L_{R}= 10^{-10}
H (not taking into account the noise of the amplifier). The magnetometers were employed to search for the electrical dipole moment of the electron in the macroscopic experiment, in low temperature paramagnetic thermometry and also to test the degree of magnetic field shielding with a hollow superconducting screen.