Applied Superconductivity - Walther Meißner Institut - Bayerische ...

212 R. GROSS AND A. MARX Chapter 4RF-SQUID:• A rf-SQUID is formed by a superconducting loop of inductance L intersected by a single Josephsonjunction with critical current I c .• The variation of the flux Φ threading the SQUID loop as a function of the applied flux Φ ext isgiven byΦ= Φ ext− β (L,rfΦ 0 Φ 0 2π sin 2π Φ )Φ 0.• The rf-SQUID is operated by inductively coupling it to a resonant tank circuit and measuringthe voltage V T of the tank circuit (with inductance L T , resonance frequency ω rf , quality factorQ) as a function of the external flux Φ ext .• The performance of the rf-SQUID is determined by the flux-to-voltage transfer functionH≡( ∂VT∣∂Φ ext)I rf =const∣ ≃ ω rfL TMand the equivalent flux noise or noise energyS Φ ≈ (LI c) 2ε≈ω rf( πη 2 Φ 2 02L( 2πkB TI c Φ 0) 4/3+ 2πηk B T effamp) 1.ω rfIn order to make the noise energy small one has to increase the tank frequency ω rf .rf-SQUIDs have a noise energy of the order of 100¯h.Best• Since the V T (Φ ext ) dependence of rf-SQUIDs is nonlinear and periodic, the SQUID is usuallyoperated in a flux-locked-loop, acting as a null detector.SQUID Based Instruments:• SQUID based instruments usually consist of an antenna transferring an input signal into amagnetic flux threading the SQUID loop, the autonomous SQUID acting as a flux-to-voltageconverter, and the read out electronics.• Depending on the antenna, SQUIDs can be used as magnetometers, gradiometers of differentorder, susceptometers, voltmeters, ammeters, or rf-amplifiers.• The magnetic field resolution of best SQUID magnetometers are of the order of a few fT/ √ Hzat a frequency of 1 Hz.• First and higher order gradiometers are used for suppression of perturbing magnetic field fluctuationscaused by the environment.© Walther-Meißner-Institut