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Current sensing noise thermometry for millikelvin temperatures using a DC SQUID preamplifier
Physica B 280 (2000) 544}545
Current sensing noise thermometry for millikelvin temperatures using a DC SQUID preampli"er Junyun Li , V.A. Maidanov, H. Dyball , C.P. Lusher *, B.P. Cowan , J. Saunders Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham, Surrey, TW20 0EX, UK Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine
Abstract We have demonstrated the performance of a current sensing noise thermometer using a low-¹ DC SQUID as the front end ampli"er. The thermometer is fast, absolute and precise and is usable over a wide temperature range below 4.2 K, in principle down to below 1 mK. We have shown that it is possible to determine absolute temperature with a precision of 1% in a measuring time of 10 sec with a noise temperature of &30 lK, and to an accuracy of better than 0.3%. The percentage precision is independent of temperature. A comparison with the He melting curve down to 24 mK is reported. 2000 Elsevier Science B.V. All rights reserved. PACS: 07.20.Mc; 07.20.Dt; 85.25.Dq Keywords: Noise thermometry; Millikelvin temperatures; DC SQUID
1. Introduction Current sensing noise thermometry using a SQUID preampli"er promises to be a fast practical approach to absolute temperature measurement from 4.2 K down to low millikelvin temperatures and, in principle, below. The method was originally introduced by Gi!ard et al. [1,2]. Since the currently available DC SQUIDs have much lower noise than the RF SQUIDs traditionally used for this form of noise thermometry a relatively large noise resistor, in the milliohm range, can be used. This requires relatively short averaging times when measuring the spectrum of noise #uctuations. Our preliminary measurements down to 1.2 K have been reported in Ref. [3], where we also give a detailed reference to the earlier work. 2. Principle of operation A sensing resistor R, whose absolute temperature ¹ is to be measured, is connected via a shielded supercon* Corresponding author. Tel.: #44-1784-443492; fax: #441784-472794. E-mail address: [email protected] (C.P. Lusher)
ducting twisted pair to the terminals of a DC SQUID, held at constant temperature (4.2 K in the present setup). The mean square current #owing in the SQUID input coil per unit bandwidth, arising from thermal (Johnson) noise in the resistor, is given by
4k ¹ 1 1I 2" , , R 1#uq
(1)
where k is the Boltzmann's constant, u the angular frequency and q"(¸ #¸ )/R, where ¸ is the input coil inductance of the DC SQUID and ¸ is any additional inductance in the input circuit. The noise temperature ¹ of the system is given by , e (2) ¹ " , , 2k q where e is the coupled energy sensitivity of the SQUID. A rough estimate for the precision in a given measuring time t is [1,2]
*¹ 2q + , (3) ¹ t
independent of temperature, so long as ¹<¹ . , The SQUID output is captured on a fast Fourier transform spectrum analyzer (Stanford SR760) and the
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 8 5 8 - X
J. Li et al. / Physica B 280 (2000) 544}545
545
data are "tted to Eq. (1) in order to extract the temperature. A commercial DC SQUID from quantum design was used to measure the noise current. This SQUID has an input coil inductance of 1.9 lH and a coupled energy sensitivity of 500 h.
3. Performance of the thermometer We have used various sensor resistors, made from copper foil, giving di!erent noise temperatures and speeds. In the "rst set of experiments (reported in some detail earlier [3]) a 0.669 m) resistor was placed in the niobium shield of the SQUID and measurements were made with the SQUID in a transport dewar at 4.2 K. Following precise measurements of the resistance and the SQUID gain, it was shown that absolute temperature (determined from Eq. (1)) could be obtained with an accuracy of better than 0.3% and with a precision of 1% in 80 s, consistent with Eq. (3). The calculated system noise temperature was &4 lK. Secondly, a 3.99 m) resistor was used, housed in a separate niobium shield connected to the mixing chamber of a dilution refrigerator. Good agreement with a calibrated germanium thermometer was obtained down to 300 mK. The noise temperature was 26 lK and in a set of measurements at 370 mK 10 s averaging time was needed for 1% precision. The next design incorporated a method for self-calibration of the SQUID gain. Fig. 1 shows excellent agreement between the current sensing noise thermometer and a He melting curve thermometer obtained down to 24 mK. In this case the resistor was 0.29 m), giving a noise temperature of 1.7 lK and a precision of 1% in 145 s. The speed can be increased, at the expense of an increase in ¹ , by using a larger resistor. We will extend , these measurements down to sub-millikelvin temperatures, enabling a determination of the He "xed points
Fig. 1. Temperature obtained from the current sensing noise thermometer versus that of a calibrated germanium thermometer above 300 mK and a He melting curve thermometer below.
(the A-transition and the solid ordering transition) and a demonstration of the viability of the technique to (100 lK.
Acknowledgements This research was supported by EPSRC (UK).
References [1] R.P. Gi!ard, R.A. Webb, J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [2] R.A. Webb, R.P. Gi!ard, J.C. Wheatley, J. Low Temp. Phys. 13 (1973) 383. [3] C.P. Lusher, V.A. Maidanov, B. Cowan, J. Saunders, Extended abstracts of ISEC'97 (Berlin) 3 (1997) 417.
Current sensing noise thermometry for millikelvin temperatures using a DC SQUID preampli"er Junyun Li , V.A. Maidanov, H. Dyball , C.P. Lusher *, B.P. Cowan , J. Saunders Millikelvin Laboratory, Department of Physics, Royal Holloway University of London, Egham, Surrey, TW20 0EX, UK Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine
Abstract We have demonstrated the performance of a current sensing noise thermometer using a low-¹ DC SQUID as the front end ampli"er. The thermometer is fast, absolute and precise and is usable over a wide temperature range below 4.2 K, in principle down to below 1 mK. We have shown that it is possible to determine absolute temperature with a precision of 1% in a measuring time of 10 sec with a noise temperature of &30 lK, and to an accuracy of better than 0.3%. The percentage precision is independent of temperature. A comparison with the He melting curve down to 24 mK is reported. 2000 Elsevier Science B.V. All rights reserved. PACS: 07.20.Mc; 07.20.Dt; 85.25.Dq Keywords: Noise thermometry; Millikelvin temperatures; DC SQUID
1. Introduction Current sensing noise thermometry using a SQUID preampli"er promises to be a fast practical approach to absolute temperature measurement from 4.2 K down to low millikelvin temperatures and, in principle, below. The method was originally introduced by Gi!ard et al. [1,2]. Since the currently available DC SQUIDs have much lower noise than the RF SQUIDs traditionally used for this form of noise thermometry a relatively large noise resistor, in the milliohm range, can be used. This requires relatively short averaging times when measuring the spectrum of noise #uctuations. Our preliminary measurements down to 1.2 K have been reported in Ref. [3], where we also give a detailed reference to the earlier work. 2. Principle of operation A sensing resistor R, whose absolute temperature ¹ is to be measured, is connected via a shielded supercon* Corresponding author. Tel.: #44-1784-443492; fax: #441784-472794. E-mail address: [email protected] (C.P. Lusher)
ducting twisted pair to the terminals of a DC SQUID, held at constant temperature (4.2 K in the present setup). The mean square current #owing in the SQUID input coil per unit bandwidth, arising from thermal (Johnson) noise in the resistor, is given by
4k ¹ 1 1I 2" , , R 1#uq
(1)
where k is the Boltzmann's constant, u the angular frequency and q"(¸ #¸ )/R, where ¸ is the input coil inductance of the DC SQUID and ¸ is any additional inductance in the input circuit. The noise temperature ¹ of the system is given by , e (2) ¹ " , , 2k q where e is the coupled energy sensitivity of the SQUID. A rough estimate for the precision in a given measuring time t is [1,2]
*¹ 2q + , (3) ¹ t
independent of temperature, so long as ¹<¹ . , The SQUID output is captured on a fast Fourier transform spectrum analyzer (Stanford SR760) and the
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 8 5 8 - X
J. Li et al. / Physica B 280 (2000) 544}545
545
data are "tted to Eq. (1) in order to extract the temperature. A commercial DC SQUID from quantum design was used to measure the noise current. This SQUID has an input coil inductance of 1.9 lH and a coupled energy sensitivity of 500 h.
3. Performance of the thermometer We have used various sensor resistors, made from copper foil, giving di!erent noise temperatures and speeds. In the "rst set of experiments (reported in some detail earlier [3]) a 0.669 m) resistor was placed in the niobium shield of the SQUID and measurements were made with the SQUID in a transport dewar at 4.2 K. Following precise measurements of the resistance and the SQUID gain, it was shown that absolute temperature (determined from Eq. (1)) could be obtained with an accuracy of better than 0.3% and with a precision of 1% in 80 s, consistent with Eq. (3). The calculated system noise temperature was &4 lK. Secondly, a 3.99 m) resistor was used, housed in a separate niobium shield connected to the mixing chamber of a dilution refrigerator. Good agreement with a calibrated germanium thermometer was obtained down to 300 mK. The noise temperature was 26 lK and in a set of measurements at 370 mK 10 s averaging time was needed for 1% precision. The next design incorporated a method for self-calibration of the SQUID gain. Fig. 1 shows excellent agreement between the current sensing noise thermometer and a He melting curve thermometer obtained down to 24 mK. In this case the resistor was 0.29 m), giving a noise temperature of 1.7 lK and a precision of 1% in 145 s. The speed can be increased, at the expense of an increase in ¹ , by using a larger resistor. We will extend , these measurements down to sub-millikelvin temperatures, enabling a determination of the He "xed points
Fig. 1. Temperature obtained from the current sensing noise thermometer versus that of a calibrated germanium thermometer above 300 mK and a He melting curve thermometer below.
(the A-transition and the solid ordering transition) and a demonstration of the viability of the technique to (100 lK.
Acknowledgements This research was supported by EPSRC (UK).
References [1] R.P. Gi!ard, R.A. Webb, J.C. Wheatley, J. Low Temp. Phys. 6 (1972) 533. [2] R.A. Webb, R.P. Gi!ard, J.C. Wheatley, J. Low Temp. Phys. 13 (1973) 383. [3] C.P. Lusher, V.A. Maidanov, B. Cowan, J. Saunders, Extended abstracts of ISEC'97 (Berlin) 3 (1997) 417.