AURIGA: R&D project on the SQUID
The SQUID behavior is explained by a theory which is well confirmed by the
experimental data. According to this theory, the power spectral density of
the voltage noise at the SQUID output is:
SV=16kBTRS [units of voltage2/frequency: V2/Hz].
Here RS represents value of the shunt resistances included in the SQUID sensor. As this noise is linearly proportional to the SQUID working temperature and vanishes at the absolute zero, we can call it thermal noise. For a typical thin film SQUID we have RS=8 Ohm and at the working temperature of T=4.2K (typical temperature for operating a SQUID) the voltage noise is predicted to be 7.4´10-21 V2/Hz. According to the theory, this noise could be reduced by a factor up to 300 when decreasing the temperature down to 0.01 K. At this ultracryogenic temperature the energy resolution limit is set by the Quantum Mechanics and the SQUID noise could be no more reduced.
Unfortunately this simple picture is not completely true. In fact the thermal noise is not the only noise contribution: in particular, there appears to be another contribution, not negligible and often larger, which is independent of the temperature. This means that the quantum limit cannot be reached by lowering the temperature and, indeed, the effort of further cooling is not paid for. This second contribution to the noise is mainly due to the room temperature SQUID control. Going into more details, the noise is due to the solid state amplifier which follows the SQUID and amplifies the small voltage signal present at the SQUID output.
The problem of the presence of this second noise contribution, which prevents the reaching of the quantum limit, cannot be solved easily but it can be made much less dramatic by the use of a second SQUID to amplify the voltage present at the first SQUID output. The advantages of this method are:
With the usage of a two-stage SQUID amplifier we can better approach the quantum limit by lowering the working temperature. The following plot shows the experimental results we obtained at the Laboratorio di Gravitazione Sperimentale e Fisica delle Basse Temperature at the University of Trento. In the plot the noise of a two-stage SQUID amplifier operated with open input is expressed as energy resolution in terms of hbar, h= Planck's constant.
From the above plot, the advantage of the two-stage SQUID configuration is clear: the same SQUID chip used in a single-stage configuration shows a noise of 1500 hbar at 0.1 K, instead of the 35hbar measured with the two-stage configuration. These measurements show another factor limiting the SQUID performance. Below 0.35 K the measured noise differs from expectations and tends to the constant value of 35 hbar. This fact is likely due to the so-called 'hot electron effect': the electrons “heated” in the shunt resistances by the bias current do not thermalize with the phonons and make vain any further attempts to reduce the temperature.
On the basis of these results we developed a two-stage SQUID amplifier along with its electronics. In order to allow its use in the AURIGA detector, this device works with low-loss (i.e. high Q) resonant loads at the input. To this end a two-stage SQUID amplifier, strongly coupled to a resonant capacitive transducer through a low-loss impedance matching loop, was thoroughly tested in a dedicated site (the Transducer Test Facility in the AURIGA laboratory).