Quantum metrology and fundamental constants: international school at Les Houches Physics Centre, 1st to 12 October 2007.
> Highlights (291 Ko)
The cryogenic current comparator or CCC is widely used in electrical metrology as it is the most accurate device for comparing two currents. The CCCs developed at LNE are used in two applications:
The aim of this study, coupled with studies of the metrological triangle and single-electron devices, is to develop new CCCs which will make it possible to reduce uncertainties on measurements of very weak currents.
Figure 1 : Application of Ampère's Law on a closed loop path (a)
in the volume of a superconducting tube:
B.dl = 0 = µ0 . (I1 + I2 - I) → I = I1 + I2
The principle on which the cryogenic current comparator operates is based on Ampère's Law. Two wires carrying currents I1 and I2 pass through a superconducting tube (figure 1). A supercurrent I flows along the inner surface of the tube and then closes on the outer surface, so that the magnetic flux B remains at zero density inside the superconductor. This is the Meissner effect. Application of Ampère's Law on a closed loop path (a) in the volume of the tube ensures the currents are equal:
I = I1 + I2
The value of I does not depend on the positions of the conductors inside the tube. This property is at the origin of the extremely accurate gain offered by CCCs.
Figure 2 : Schematic diagram of a CCC consisting of
two coils
of N1 and N2 turns
carrying the currents
to be compared I1 and I2.
The design of a CCC is based on the principle stated above. It consists of a series of coils wound with superconducting wire (niobium-titanium) encapsulated in superconducting toroidal lead shielding which overlaps itself without any electrical contact, rather like a snake biting its own tail (see figure 2).
Consider two coils of N1 and N2 turns, carrying currents I1 and I2 respectively. Application of Ampère's Law on a closed loop path (a) in the volume of the superconducting shielding ensures the currents are equal:
I4C = N1I1 - N2I2
where I4C is the supercurrent flowing around the surface of the shielding.
The magnetic flux created by I4C is measured by means of a SQUID, a highly sensitive magnetic detector. By adjusting the current I2 so that I4C = 0, exact equality is obtained:/p>
N1I1 = N2I2
Figure 3: Diagram of an amplifier of
very weak currents based on a CCC
The CCC may be used to amplify very weak currents. The gain is exactly equal to the winding ratio N1 / N2 (see figure 3).
The very weak current to be measured, I1, is injected into the coil with N1 turns. The supercurrent I4C is detected by the SQUID via the flux transformer. The SQUID voltage response is used to counteract the current I2 circulating in the coil with N2 turns. The fall in voltage Vs due to the current I2 passing through the feedback resistance R is:
VS = R N1/N2 I1
By using a calibrated resistance (R) and an exact winding ratio N1/N2, the CCC supplies a highly accurate measurement of the current gain.
Figure 4: Two CCCs developed at LNE
The CCC currently used to amplify and measure very weak currents generated by single-electron devices consists of two coils with N1 = 20,000 and N2 = turns respectively, providing an amplification gain of 10,000. Its level of current white noise at 1 Hz is 1 Hz est de 4fA/Hz½. It is installed at 4.2 K in the helium bath of the dilution refrigerator.
Other CCCs with an amplification gain of 20,000 and 30,000 are being developed in the context of the Trimet metrological triangle project financed by the National Research Agency ANR.
Figure 5: Design of a CCC with
microlithographed tracks and 1,000-turn
coil layers connected in series
LNE recently began developing a new generation of CCCs which will apply technology used in microelectronics. Instead of using coils wound with superconducting niobium-titanium wire, the new CCCs will have layered coils where each substrate is coated with a thin layer of niobium and tracks a few microns wide are lithographed and etched. Figure 5 shows a coil produced using this technique. It consists of several coil layers, each with a specific number of turns, which are connected in series to obtain the required total number of turns.
This manufacturing technique makes it possible to produce a compact CCC with a very large number of turns. Its reasonable size will make it easier to use, and it will also be operable at a lower temperature (50 mK) as it can be installed in the middle of the dilution refrigerator, thus reducing thermal noise.
Laurent Devoille
Tel.: (33) 1 30 69 21 55
