Cryoconference 2010 Superconducting Quantum Interference Devices for Current Sensing and Thermometry in the Millikelvin Range J.-H. Storm, J. Beyer, D.Drung,Th.Schurig Physikalisch-Technische Bundesanstalt (PTB) Abbestraße 2-12, D-10587 Berlin, Germany Outline: fundamentals SQUIDs for the mk range (Array s and two-stage SQUIDs) SQUID noise thermometry (CSMT, MFFT)
What is a SQUID? Magnetic flux Electric current Electrical voltage/current Any physical quantity convertible into flux Typical applications: Readout of transition edge sensors (TES) PTB SQUIDs B Susceptometry I Trafo M L In TES Xray microcalorimeters at NASA/GSFC
Basic SQUID bias current I B screening current U / RI 0 2 Φ A = nφ 0 U / RI 0 2 Φ A = (n/2+1/4)φ 0 U I kreis magnetic flux Φ magnetischer Fluss Φ A 1 Φ A = (n+1/2)φ 0 1 U Josephson junction working point W 0 0 0 1 2 3 4 0 1 2 I B / I 0 Φ A / Φ 0 3 4 SQUID parameter: V Φ = du/dφ I Φ = di/dφ
SQUID current sensor I IN L IN L SQ I BIAS V SQUID M IN = k L SQ L IN A figure of merit for SQUID current sensors is the coupled energy resolution: S Φ,SQUID X 1 : read-out electronics ε C = (32k B T(L SQ C) ½ +Xi)(L IN /2M² IN ) = S I L In /2 temperature input coupling limited by fabrication technology
SQUID Noise & Electronics Noise Example: U N /V Φ =Φ N I N /I Φ =Φ N 4.2K/mK SQUID U N X 1 = S Φ,Amp = S V,Amp /V² Φ +S I,Amp /I² Φ I N G Amplifier V Out 300K Single SQUID @ 4.2K S Φ,Amp 0.25pΦ² 0 /Hz S Φ,SQUID 1.2pΦ² 0 /Hz System noise is dominated by SQUID noise Single SQUID @ 300mK S Φ,Amp 0.25pΦ² 0 /Hz 0.086pΦ² 0 /Hz S Φ,SQUID System noise is dominated by electronics noise
SQUID Array Feedback Input S Φ = S Φ,SQ1 /N L IN = L IN,SQ1 N ε C = ε CSQ1 Output / SA bias N * SQUID Series Array But the electronics contribution is decreased: S Φ,Amp =S V,Amp /N²V² Φ +S I,Amp /I² Φ 50 µm Single SQUID gradiometer Single-turn input coil SQUID loop Josephson junctions SQUID-to-SQUID connection Cooling fins
SQUID Array 3 mm 3 mm Two independent 16 SQUID series arrays per chip operable at mk, well behaved V-Φ characteristics no magnetic shield in Earth's field needed integrated bias resistors 0.2 200 mω +F -F -V +V -INR +R +F -F -V +V -INR +R rf Filters Feedback Coil 1 Shunted 16-SQUID Array Bias Resistor Feedback Coil 2 Shunted 16-SQUID Array Bias Resistor -INR +IN +R -INR +IN +R S I <5 pa/ Hz @ 0.1 K L IN <3nH ε C <57h @0,1 K P Diss 1nW (per channel)
Two-stage SQUID SQ1 bias Sensor SQUID (SQ1) R Bias L Amp Φ SQ1 Input U Out /SQ Amp bias Φ Amp M Amp f 3dB = (R Bias +R SQ1 )/2π L Amp Amplifier SQUID (SQ Amp ) ε C = S Φ,SQ1 +S Φ,R Bias + S Φ,SQ Amp + S Φ,Amp (Φ Amp /Φ SQ1 )² Φ Amp /Φ SQ1 = k Amp (L Amp *L SQ AMP ) ½ R Bais /V Φ + 1/I Φ
Two-stage SQUID 3 mm single SQUID front-end, read out by SQUID array operable at mk, well behaved V-Φ characteristics 3 mm no magnetic shield in Earth's field needed "single-squid-like V/Φ- characteristics several input inductances L IN from 25 nh to 1.8 µh +FIN -FIN Z +F -F +I +FX -IFX -V +V -FQ +FQ rf Filters Intermediate Loop Bias Resistor Shunted 16-SQUID Array Amplifier Feedback Transformer Shunted SQUID with APF +IN -Q -IN +Q Unshunted 16-SQUID Array Current Limiter S I < 0,01 pa/ Hz @ 0.1K L IN = 1,05µH ε C < 8h @ 0.1K P Diss 2 nw
SQUID Thermometers primary thermometer semi-primary thermometer measures directly the thermodynamic temperature T = g(x i ) is known without other thermometers measures directly the thermodynamic temperature g(x i ) is known, x i from one reference point One of the few established approaches of primary thermometry Nyquist noise thermometry: V 2 noise= 4k B TR f
CSNT & MFFT CSNT: R N M IN MFFT: R N ( f ) M T L In T L In 4kB T M In 2 2 (1 + f / f C ) B S Φ,therm ( f ) = S Φ,therm ( f ) = 2 2 R N π f R N (f,z,d,µ,σ) f C = R N / 2π L In k T R N ( f ) 2 mm SQUID current sensor & resistor 2 noise currents driven by thermal agitation of electric charges in conductor. B field fluctuations above surface Cu, 5N8 3 mm 3x3 mm 2 SQUID gradiometer chip (380..120µm), glued onto Cu sensor
Measurement procedure Measuring of the spectral noise density (S Φ (f, T Ref )) at a known reference temperature. Measuring of the spectral noise density (S Φ (f, T Meas )) at the unknown temperature. Calculation of the unknown temperature: T = T Ref. S Φ (0Hz, T Ref ) S Φ (0Hz,T Meas ) The frequency response of the noise spectrum remains constant as long as R N =const(t)
Measurement data of CSNT & MFFT 10-8 CSNT T 2000 = 698 mk 10-8 MFFT T 2000 = 676 mk 10-9 S Φ (Φ 0 2 /Hz) 10-10 S Φ (Φ 0 2 / Hz) 10-9 T 2000 = 10 mk 10-11 10 3 10 4 10 5 f (Hz) 10-10 T 2000 = 10 mk 10 1 10 2 10 3 f (Hz) measurement speed: t Smpl,CSNT > 3.3µs t Smpl,MFFT > 430µs relative uncertainty u rel ~ 1/ N Smpl : u rel,csnt = 1% 33ms u rel,mfft = 1% 5s
Linearity of CSNT & MFFT CSNT: MFFT: T CSNT (K) T MFFT (K) T 2000 (K) T 2000 (K) slight deviation from deviations within uncertainties bath temperature below 50mK R N = const(t ) (thermal anchoring of chip/resistor) & sensor at bath temperature
Conclusions SQUID current sensors for mk applications SQUID series array coupled energy resolution ε C < 60h @0.1K, low input inductance ~ 3nH, fast and easy to use. Two stage SQUID coupled energy resolution ε C < 8h @0.1K and a compact design with several input inductances from 25 nh to 1.8 µh SQUID Noise Thermometers CSNT easy to handle, compact and fast for a temperature range from 50 mk to 4.2K MFFT easy to handle, moderately fast and highly linear down to below 10 mk. No self heating