Applied Superconductivity - Walther Meißner Institut - Bayerische ...

Section 4.5 APPLIED SUPERCONDUCTIVITY 211Summarydc-SQUID:• A dc-SQUID is formed by a superconducting loop of inductance L intersected by two Josephsonjunctions with critical currents I c .• For negligible screening parameter β L = 2LI c /Φ 0 ≪ 1, the magnetic flux Φ = Φ ext +LI cir threadingthe SQUID loop is about equal to the external flux, Φ ≃ Φ ext , and the maximum supercurrentof the SQUID varies as∣ ( ∣∣∣Is m = 2I c cos π Φ )∣ext ∣∣∣.Φ 0• For large screening parameter β L = 2LI c /Φ 0 ≫ 1, the magnetic flux Φ = Φ ext + LI cir threadingthe SQUID loop is about equal to Φ ≃ nΦ 0 , and the maximum supercurrent of the SQUIDvaries asI m s = 2I c − 2Φ extL= 2I c(1 − 2Φ extΦ 01β L)• For intermediate screening the I m s (Φ ext ) dependence has to be determined self-consistently fromthe Φ(Φ ext ) and I m s (Φ) dependences.• For negligible screening (β L ≪ 1) and strong damping (β C ≪ 1), the IVC of the dc-SQUID isgiven by√ ( ) I 2 [ (〈V (t)〉 = I c R N − cos π Φ )] 2ext.2I c Φ 0• The mechanical analogue of the dc-SQUID are two pendula attached to a twistable rubber bar.For β L ≪ 1, the rubber bar is rigid, for β L ≫ 1 the rubber bar is soft. The relative angle of thependula is determined by the applied magnetic flux: ϕ 1 − ϕ 2 = 2πΦ ext /Φ 0 .• The performance of the dc-SQUID is determined by the flux-to-voltage transfer function( H ≡∂V∣∣∂Φ ext)I=constand the equivalent flux noise or noise energyS Φ ( f ) = S V ( f )H 2 ε( f ) = S Φ( f )2L.= S V ( f )2LH 2 .The noise energy sets the energy resolution of the dc-SQUID, which should be as small aspossible for practical applications.• For optimum operation parameters (β L ≃ 1, β C ≃ 1) the noise energy of the dc-SQUID is givenby√LCε( f ) ≃ 16k B T ≃ 16√ πk B T.β C ω pBest dc-SQUIDs have a noise energy of only a few ¯h.• Since the V (Φ ext ) dependence of dc-SQUIDs is nonlinear and periodic, the SQUID usually isoperated in a flux-locked-loop, acting as a null detector.2005