1. Quantenelektronik 1 High sensitive bipolar- and high electron mobility transistor read-out electronics for quantum devices.  Introduction  Bipolar-transistor read-out.  PHEMT read-out  Motivation  Features and construction  Measurement setup and procedure  Results  Verification  Discussion  Summary Contents: N. Oukhanski and H.-G. Meyer

2. Quantenelektronik 2 Introduction  Already known read-out technique for quantum devices.  Bipolar-transistor read-out. Easy to match R sensor with R noise of amplifier, T N ~80 K. 1,2  FET read-out. Minimum T N ~2 K @  ~10 kHz, owing RF energy losses. 3  SQUID-amplifiers. Minimum T N ~1–5 hf/k B. Complex in tuning and setup. 4  Pseudomorphic High Electron Mobility Transistor read-out. T N  2  5 K (  2  5 hf/k B )@~20 GHz for ambient temperatures of 10  20 K. 5, 6, 7 1. N. Oukhanski, V. Schultze, R. P. J. IJsselsteijn, and H.-G. Meyer, Rev. Sci. Instrum. 74, 12, 5189 (2003). 2. N. N. Oukhanski, R. Stolz, V. Zakosarenko, and H.-G. Meyer, Physica C 368, 166 (2002). 3. P. Horowitz and W. Hill, Cambridge Univ. Press, 1989, 2nd ed. v. 2, pp. 53–66. 4. M. Muck, J. B. Kycia, and J. Clarke, Appl. Phys. Lett. 78, 967 (2001). 5. J. Bautista, J. Laskar, P. Szydlik, TDA Progress Report 42-120, 1995. 6. J.E. Fernandez, TMO Progress Report 42-135, pp.1-9, November 15, (1998). 7. I. Angelov, N. Wadefalk, J. Stenarson, E. Kollberg, P. Starski, H. Zirath, IEEE MTT-S, (2000).

3. Quantenelektronik 3 Bipolar-transistor read-out.  Main features of designed directly- coupled bipolar-transistor electronics  Input voltage white noise level is about 0.32 nV/Hz 1/2.  Flicker noise corner frequency as low as 0.1 Hz.  Current white noise level  6.5 pA/Hz 1/2.  Wide working temperature range: 77-350 K.  One-chip FLL unit solution is resistant to ambient condition, i.e. humidity, convection flows, and temperature radiation.  Very low thermal drift: 30 nV/K (from 15 to 80 0 C).  high symmetrical differential circuits for all parts of the FLL-unit used.  full design optimization using simulation with software tool of MicroSim-PSpice. Functional diagram of the read-out electronics Prototype ( left ) and integrated version of the FLL unit ( right).  Gain-bandwidth product f GBP =400 MHz.  Three point SQUID biasing possible to reduce voltage drift on the connecting wires to the SQUID.  Power consumption: 80 mW at ±1.5 V.

4. Quantenelektronik 4 Bipolar-transistor read-out.  The maximum bandwidth of 6-8 MHz was measured with several types of low- Tc dc-SQUID magnetometers and gradiometers.  Maximum slew rate is in the range 3-9 M  0 /s.  Minimum measured white flux-noise level with SQUID magnetometer of 1.2- 1.7  0 /Hz 1/2 (1-1.4 fT/Hz 1/2 ).  A maximum system dynamic range with the SQUID magnetometer is about 155 dB (  50  0 ).  Available with high frequency ac-bias technique with frequency up to 10 MHz. 1 Flux and field noise spectrum of SQUID magnetometer with sensitivity B/  =0.85 nT/  0 in three layer shielded can. Maximum system dynamic range in FLL mode 50  0. Voltage noise spectral density with respect to the input of the integrated electronics at 300 K.

5. Quantenelektronik 5 PHEMT read-out  Already known features.  Based on the AlGaAs/InGaAs/GaAs heterostructure.  Offers a high transfer coefficient in the microwave frequency range, owing to the high density and mobility of 2DEG along the layer’s heterojunctions (due to an effect of electron space confinement).  The unique noise characteristics are derived from the 2DEG’s high electron mobility, which is dependent on the electrons scattering process in heterojunctions.  Already measured noise temperatures T N  2  5K (  2  5 hf/k B )@~20 GHz for ambient temperatures of 10  20 K.  Originally, expected that the HEMTs would be unsuitable for sensitive measurements at frequencies below 100 MHz, because of the high corner frequency of the flicker noise.

6. Quantenelektronik 6 Motivation  Desirable area of application Areas, which need highly sensitive measurements, such as the characterization of qubit circuits, 8-11 bolometric measurements, 12,13 SQUIDs 2 etc., compel us to search for more sensitive readout methods and devices. The principle scheme of resonant circuit readout with PHEMT amplifier. Circuit of interest is inductively coupled to the high-Q parallel resonant circuit, with the directly involved through a short line PHEMT. 8. J.E. Mooij, T.P. Orlando, L. Levitov, Lin Tian, van der Wal, S. Lloyd, Science 285, 1036, (1999). 9. E. Il’ichev, V. Zakosarenko, L. Fritzsch, R. Stolz, H. E. Hoenig, H.-G. Meyer, A.B. Zorin, V.V. Khanin, M. Götz, A.B. Pavolotsky, and J. Niemeyer, Rev. Sci. Instr., 72, 1882, (2001). 10. E. Il’ichev, Wagner Th., Fritzsch L., Kunert J., Schultze V., May T., Hoenig H. E., Meyer H.-G., Grajcar M., Born D., Krech W., Fistul M., Zagoskin A. Appl. Phys. Lett., 80, 4184, (2002). 11. E. Ilґichev, N. Oukhanski, A. Izmalkov, Th. Wagner, M. Grajcar, H.-G. Meyer, A. Yu. Smirnov, Alec Maassen van den Brink, M. H. S. Amin, and A.M. Zagoskin, Phys. Rev. Lett. 91, 9, 097906 (2003). 12. D.-V. Anghel and L. Kuzmin, Appl. Phys. Lett. 88, 293-295 (2003). 13. L. Kuzmin, Proc. Thermal Detector Workshop, Goddard SFC, Washington DC, (2003), to be published. U G1 U G2 U G3 U SUPP G ROOM Out T=300 K T  380 mK L C R Qubit From RF generator

7. Quantenelektronik 7 Features of construction  To decrease the power consumption and improve low frequency noise performance:  We reduced the transistor’s drain voltage to 0.1 V (2 % of V ds ) and the drain current to 200  A (0.3 % of I dss ).  the first stage power dissipation was only 20  W.  All resistances in the amplifier’s signal channel were replaced by inductances.  To protect the amplifier from external and self interferences we used symmetric design.  The amplifier was thermally connected to the helium-3 pot of the commercially available refrigerator, “Heliox 2” by Oxford Instruments with temperature below 400 mK.  Two amplifier version, based on the commercial PHEMT ATF-35143, have a common layout and were assembled on a printed board of 33x13 mm 2 (see Fig. 2).  Three-stage construction is used to provide the best conditions for minimizing the input noise temperature and back-action to the tank circuit (in the first stage), maximizing the gain factor (second stage), and impedance matching to the input and output lines (first and third stage). Photo of amplifier

8. Quantenelektronik 8 Measurement setup and procedure U SUPP 50 Ohm trans. line, K 5 (f)= 0.042dB loss @ 2.5MHz 50 Ohm divider, K 4 (f)= -67.113 dB trans. coeff. @ 2.5MHz SVSV U G3 U G2 U G1 Room temperature amplifier with gain K 2 (f) T  380 mK 50 Ohm trans. line, K 1 (f)= 0.042dB loss @ 2.5MHz R IN 10 k  Network Analyser HP4396B PHEMT Amplifier, with gain K 3 (f)  Measurements with resistor at T  0.38 K  To provide a good thermal contact between the source resistor R IN and 3 He pot, a copper finger was used.  Noise temperature 3, 14  S VCOM - input voltage noise spectrum  Measurements with resonant circuit  Active resistance of resonant circuit at resonant frequency The simplified scheme of the amplifier and setup for the noise temperature measurements with resistor (a) and resonant circuit (b). L C R T  380 mK PHEMT amplifier Out (a) (b) 14. N. Oukhanski, M. Grajcar, E. Il’ichev, and H.-G. Meyer, Rev. Sci. Instrum. 74, 1145 (2003).

9. Quantenelektronik 9 Results Comparison of the voltage noise for the 1 st version of cryogenic amplifier with that for the standard room temperature design and rated parameters. Measured with resistor T N and calculated current noise S I 1/2 of 1 st amplifier version. T N MIN (R S =R N ) – estimated minimum noise temperature. Inset are the noise of tank circuit, coupled to the input of the 1 st (a) and 2 d (b) amplifier version.  1 st amplifier version with resistor  Measured minimum T N  100 mК@1-4 MHz with 10 k  input resistor.  For used in this case method 3,14 T N MIN ( R S =R N )=S V 1/2 S I 1/2 /2k B, where R S - real part of input resistance, noise resistance R N =S V 1/2 /S I 1/2, S I 1/2 =(4k B R S T N -S V ) 1/2 /R S,  estimated minimum noise temperature 3 is T N MIN  70  50 mK  50  35 hf/k B @30 MHz, R N  21k   With resonant circuit (Q=1510, f 0 =28.6 MHz, L=66 nH, C=470 pF, R S (f 0 )  18 k  )  Measured upper limit of noise temperature in optimistic case (assuming that R S (f 0 ) associated only to dissipation noise of the tank circuit and amplifier) is T N (f 0 )  55  25 mK (  40  18 hf/k B ).

10. Quantenelektronik 10 Results  Back-action noise: 15 T ba =T N -T ad Additive component T ad (measured without input source), 15 originate mainly from drain noise temperature (T d >>T  T g ), 16 back- action component T ba under the influence of drain fluctuations on the tank circuit by means of parasitic capacitor C gs.  For 1 st amplifier version T ba ~15 mK S v -measured with shorted input voltage noise. Very high sensitivity applications, where a drain current and/or voltage fluctuation can increase the gate temperature, or can decrease the decoherence time of an input signal, impose strong requirements on T ba  2 d amplifier version with resonant circuit (Q=2080, f 0 =26.77 MHz, L=177 nH, C=200 pF, R S (f 0 )=61.8 kOhm,)  Assuming R S (f 0 ) associated only to dissipation noise: T N (f 0 )  73  30 mK at ambient temperature T=370 mK  Back-action noise temperature: T ba =T N -T ad ~10 mK U G1 U SUPP L C R T  380 mK TdTd gmVgsgmVgs R ds C gs RsRs C gd R gs Drain Source Gate RgRg TgTg RdRd 15. A. Vinante, M. Bonaldi, M. Cerdonio, P. Falferi, R. Mezzena, G. A. Prodi, and S. Vitale, Classical and Quantum Gravity, 19, Is. 7, p. 1979 (2002). 16. M. W. Pospieszalski IEEE Trans. on Microwave Theory and Techniques, 37, no. 9, pp. 1340-1350 (1991). Variant of the 1 st stage with the lowest designed back-action. Simplified small-signal circuit diagram of PHEMT.

11. Quantenelektronik 11 Verification  To be convinced in our estimation we used amplifier noise model based on the definition of voltage and current noise, as S V =2k B T N R N and S I =2k B T N /R N. 17 Assuming R S (f 0 ) associated only to dissipation noise,  noise temperature: T N (f 0 )=(S VCOM (f 0 )-4k B TR S )R N /(2k B (R S 2 +R N 2 ))  (S V S I ) 1/2 /(2k B ). 17. T. Ryhanen and H. Seppa, J. Low Temp. Phys. 76, 287 (1989). SVSV SISI G L C R S R d L C R c SVSV SISI G  Suppose the worst case, when R S (f 0 ) associated with dissipation noise of common resistance (R d and R c ) and contribution of damping cold resistance from amplifier R c. Hence S I =(S VCOM -S V )/R S -4k B T/R d. Taking into account: 1.Maximum quality factor, measured between available tank circuits, with both system (Q  2040, f 0  27 MHz, C=100 pF and Q  3340, f 0  25 MHz, C=100 pF correspondingly). 2.Absence of voltage flicker noise in the working frequency range on the ceramic capacitors which we used in our resonant circuits.  The pessimistic value for the noise temperature in this case T N (f 0 )=(S V S I ) 1/2 /(2k B ): T N (f 0 )=110 mK, and 170 mK for the 1 st and 2 d variant of electronics correspondingly.

12. Quantenelektronik 12 Discussion  By taking into account tank circuit quality factor Q=2080 (2 d variant of amplifier), this setup gives us an opportunity to perform quantum level measurements with periodical signals, even if the coupling coefficient of the thank circuit to the sensor is less than 1.  It is necessary to note, that available in real condition tank circuit impedance can be far from optimum value, which can noticeably increase setup noise temperature. Measurements with Qubit, T N  270 mK, amplifier ambient temperature ~2 K 18. M. Grajcar, A. Izmalkov, E. Il'ichev, Th. Wagner, N. Oukhanski, U. Huebner, T. May, I. Zhilyaev, H.E. Hoenig, Ya.S. Greenberg, V.I. Shnyrkov, D. Born, W. Krech, H.-G. Meyer, Alec Maassen van den Brink, and M.H.S. Amin, Phys. Rev. B 69, 060501(R) (2004). 19. A. Izmalkov, M. Grajcar, E. Il'ichev, N. Oukhanski, Th. Wagner, H.-G. Meyer, W. Krech, M.H.S. Amin, Alec Maassen van den Brink, A.M. Zagoskin, Europhys. Lett., 65 (6), pp. 844–849 (2004).  The second version of the amplifier placed at temperature  2 K was successfully employed for different quantum measurements. 11, 18, 1 9  By taking into account system bandwidth f=100 MHz and rating quality factor Q  1000@30 MHz estimated available number of cannels  1000 with  f  100 kHz.

13. Quantenelektronik 13 Summary  Integrated version of direct coupled bipolar-transistor dc SQUID read-out electronics with minimum noise temperature T N =80 K is presented.  Very low thermal drift (30 nV/K) of the electronics and the low corner frequency of flicker noise (0.1 Hz) is useful for realization of long-time experiments.  Wide working temperature range of read-out electronics (77– 350 K) provides system reliability at any climatic conditions.  High slew rate (up to 9 M  0 /s) and sensitivity (0.32 nV/Hz 1/2 ), large bandwidth (6 MHz) and system dynamic range at using of long cable between the sensor and electronics (about of 1–2 meters) well suited for high-precision measurements at unshielded conditions.

14. Quantenelektronik 14 Summary and acknowledgment  Two versions of a cryogenic PHEMT amplifier designed for quantum device readout and tested at an ambient temperature  380 mK.  Noise temperature of the 1 st amplifier version is below 110  50 mK (  80  40 hf/k B )@28.6 MHz, estimated from the noise of a coupled input tank circuit with resistance R S (f 0 )  18 kOhm at the resonant frequency.  Its minimum input voltage spectral noise density is  200 pV/(Hz) 1/2 and the corner frequency of the 1/f noise is close to 300 kHz.  For the amplifier with the lowest designed back-action, the noise temperature below 170  70 mK (  150  60 hf/k B )@26.8 MHz was measured when coupled to an input tank circuit with R S (f 0 )  62 kOhm.  The amplifiers’ power consumption is in the range of 100–600  W.  The second version of the amplifier with ambient temperature  2 K was successfully employed for different quantum measurements. The authors gratefully acknowledge the discussions and help on the different stages of work of H. E. Hoenig, E. Il'ichev, V. Zakosarenko, R. Stolz, M. Grajcar, Th. Wagner, A. Izmalkov, S. Uchaikin and R. Boucher.