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Zero-Point Fluctuations Limited SIS Receiver at 500 GHz
Andrey Baryshev , Willem Luinge
SRON-Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands

Valery Koshelets, Sergey Shitov
Institute of Radio Engineering and Electronics RAS, Mokhovaya St. 11, Moscow, 103907, Russia

T.M. Klapwijk
Department of Applied Physics and Material Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

Abstract. We report on a 471 GHz quasi-optical superconductor-insulator-superconductor (SIS) receiver with an uncorrected DSB noise temperature as low as 40±3 K. The results are analyzed using a novel method which does not require the determination of the embedding impedances and hence does not suffer from numerical instabilities. Excellent agreement with theory is only found after the zero-point quantum fluctuations (ZPF) for the noise temperatures are included, demonstrating that the intrinsic noise temperature hf of the SIS mixer is given by 2kb , which is 11 K at 471 GHz.

Tn =

hf hf ) coth( 2kb 2kb T

(2)

was used to include ZPF in the description of all receiver elements. The value given by (2) deviates significantly from the physical temp erature at low temp eratures. The blackb ody calibration source noise temp eratures were also corrected using (2). The prop erties of optical elements can b e calculated as follows. The output signal of a thin transparent film placed in front of receiver can b e describ ed as T
out

SIS mixer noise temp eratures in the submm band are approaching the quantum limit [1], [2], [3]. The inclusion of ZPF is essential for a full understanding of the low system noise level. We present a full analysis of noise sources of an exp erimental SIS hetero dyne receiver at 471 GHz. The analysis is based on splitting the SIS receiver into n linear elements connected in series. The noise p ower P in a bandwidth f is represented by a noise temp erature T n = P/kb f [4]. The bandwidth f is usually determined by a narrow band filter in the if chain. The receiver gain Gsys and receiver noise temp erature Tsys can b e written as
n n

= Trad r + Tabs a + Tin (1 - r )(1 - a ),
P

where r = Pref is the p ower reflection coefficient, a = in Pabs Pin is the p ower absorption co efficient, Tabs is the film temp erature and Trad is the p ower reflected towards the receiver. For example, Trad is the room temp erature for the b eamsplitter and Trad is equal to 4.2 K corrected by (2) for the dewar window. Equation (2) was applied to both Trad and Tabs in order to include ZPF. The optical element gain and input noise temp erature can b e written as: Gi = (1 - r )(1 - a ), Ti = Trad r + Tabs a . (1 - r )(1 - a ) (3)

G

sy s

=
i=1

Gi , Tsys = T1 +
i=2

Ti n k=2

G

,
k

(1)

where Gi is gain and Ti is effective noise temp erature of the i-th element. Loss in an element is represented by Gi < 1. Values of Tsys and Gsys can b e measured by using the standard Y-factor technique and shot noise calibration of the if chain [5]. Just in front of the mixer an element unk is intro duced describing the gain (loss) Gunk and noise temp erature Tunk not explained by other known elements. The values Gunk and Tunk for one element can b e determined from (1) if the prop erties of all other elements are known. The Callen and Welton formula for noise p ower density

The values of r and a of the b eamsplitter, the dewar window and the heat filters were determined with a Michelson Fourier Transform Sp ectrometer. The unpump ed SIS junction was used for if amplifier and detector chain calibration. The SIS junction's if output p ower can b e describ ed by the shot noise formula: Tn = eRd I eV ), coth( 2kb kb T (4)

where Rd is differential resistance, V , I are bias voltage and current. The signal at the output of the if amplifier can b e describ ed as [5], [6]: T
out

=

Tin M (Rl ,Rd ) + Tiso (1 - M (Rl ,Rd )+ T
amp

G

amp

,

(5)

Submitted to Applyed Physics Letters 5 September 1998, E-mail:andrey@sron.rug.nl



where Rl is the if chain imp edance connected to the SIS junction, Tamp and Gamp are the noise temp erature and 1


the gain of if amplifier, Tiso is the temp erature of the isolator 50 load and M (Rl ,Rd ) = 1 - |Rl - Rd | |Rl + Rd |
2

(6)

is the p ower coupling co efficient. Values of Rl , Gamp , Tamp and Tiso were obtained by fitting to the exp erimental dep endance of the if output signal with bias voltage. The load imp edance Rl may not necessarily b e 50 Ohm b ecause of if wiring transformation. The bias dep endent if amplifier element Gi and Ti can b e written as Gi = G
amp

, Ti =

(1 - M (Rl ,Rd ))T Gamp

cir

+ Tamp

.

(7)

Multiple Andreev reflection [6] was ignored b ecause the subgap current for our NbAlOx Nb SIS junction is low enough. DSB mixer op eration with the calibration signal applied in lower and upp er sidebands (LSB, USB) with equal input imp edance of mixer for LSB, USB and LO path is considered. The mixer gain from [1] can b e simplified as: G
mix

= M (Z

emb

1 ,Rrf ) R 4

rf

dIdc 2 Rd M (Rd ,Rl ), dVrf
G G
M IF

(8)

G

unk

can b e derived from (1). The SIS mixer can b e describ ed without the numerically unstable calculation of the SIS junction emb edding imp edance by following the pro cedure describ ed ab ove. The analyzed receiver contains a double dip ole antenna SIS mixer with integrated tuning elements. This mixer is designed as a reference unit to measure the ultimate p erformance of the Integrated Receiver [7]. The rf design of the mixer has b een describ ed in detail in [8]. The tuning circuit consist of an end-loaded stripline connected to a double dip ole antenna via a matching stripline transformer. The Josephson effect noise was suppressed by an integrated magnetic field control line. The receiver chip (4x4x0.5 mm) was mounted on to a silicon elliptical lens. An antireflection coating was applied to the lens. A backreflector was mounted b ehind the antenna. The mixer block was mounted on the dewar cold plate b ehind a Zitex heat filter at 4.2 K, a 150 µm quartz plate heat filter at 78 K and a 15 µm thick Kapton dewar window at 295 K. A mylar b eamsplitter (6µm) was used to combine the LO signal with the calibration sources. The blackb odies at 295 K and 78K have b een used as calibration source. The SIS junction was connected to a low noise 1.5 GHz HEMT amplifier via a bias tee and isolator. A Thompson Carcinotron in the 460-500 GHz range has b een used as the LO. The NbAlOx Nb junction with an area of 1.5 µm2 and a normal resistance Rn =14 was used. The subgap over normal resistance ratio was ab out 30 for this mixer.
120 110

where Rrf is the junction input imp edance, Rd is the dynamic resistance of the pump ed I-V curve and M (a, b) is the p ower coupling co efficient from (6). According to (8) the mixer can b e split into three parts with gains: Gunk , GM , GIF . The mixer DSB conversion gain for the junction, that is p erfectly matched b oth to if and rf p orts, is describ ed by GM . The ZPF ( 2hfb ) is the effective noise k temp erature of this element. The if chain mismatch is represented by GIF . Subgap current shot noise determines the effective noise temp erature for this element (4). The rf loss due to the tuning element mismatch is represented by Gunk . All rf losses in the lens and the loss due to the receiver b eam efficiency are attributed to Gunk . For example, if the receiver b eam is partly limited by the cold (4.2K) diaphragm then the element noise temp erature Tunk could b e calculated by an expression similar to (3) having Tabs = 0 and Trad = 4.2 K corrected by (2). The imaginary part [1] of the quantum conductance is not considered in this pap er. In order to avoid this inaccuracy the bias p oint in the center of the photon step was used for the calculation. eVrf Pumping parameter = hf can b e obtained with the reasonable accuracy by fitting the measured pump ed I-V curve to the calculated one using [1]. The dynamic resistance Rd for the pump ed I-V curve can b e also measured. The junction input imp edance Rrf can b e calculated using the unpump ed I-V curve and the determined pumping level . Finaly the values for Gunk and Tunk 2

R ece ive r Noi se Te mperatu re (K)

100 90 80 70 60 50 40 30 20 10 460 465

2K H e bath t emper at ure 4.2K He bath t emper at ure

hF / k

b

hF / 2k

b

470

475

480

485

490

495

500

Frequen cy (G Hz )

FIG. 1. DSB Receiver Noise Temperature for Two He Bath Temperatures, Uncorrected for Beamsplitter

The measured uncorrected DSB receiver noise temp erature vs. LO frequency is presented in Fig. 1. The b est noise temp erature measured was 40±3 K uncorrected for the b eamsplitter at 471 GHz, that is only ab out 3 times the ZPF of 11.4 K. The p oint at 471 GHz was used for the determination of the receiver parameters. The measured unpump ed and pump ed junction I-V curves as well as the if output p ower are shown in Fig. 2. The contributions of the receiver elements calculated by the metho d


describ ed ab ove using the data from Fig. 2 are shown in Table 1. The main uncertainty for the calculated data was in the measurement of Rd . Other sources of measurements error were the uncertainty in the cold blackb ody radiator temp erature (78±2 K) and the uncertainty in measurement of the Y -factor (±0.04 dB). The low rf loss Gunk =-0.5 dB represents a go o d tuning circuit match and high b eam efficiency for the receiver. The measured noise temp erature Tunk =12 K corresp onds Trad =100 K in (3). This noise temp erature could b e attributed to 300 K background radiation accepted by part of receiver b eam even if 78 K load is in front of the receiver.

350

350

a)
300 300

I F Ou tput Pow er (K )

250 200 150 100 50

f) d) e)

250 200 150 100 50

It was not p ossible to solve (1) without taking into account ZPF in all elements of receiver. We conclude that ZPF in all receiver comp onents is a key factor limiting the receiver noise temp erature. The method prop osed ab ove is suitable for optimization of SIS receiver p erformance and allows to confirm indirectly that DSB noise temp erature of SIS heterodyne receiver is hf limited by ZPF 2kb . The quantum limited p erformance (Tsys =40 K) has b een observed at 500 GHz. All noise contributions of our receiver are understood. We would like to thank Lyudmila Filipp enko for samples fabrication, Duc Van Nguen, Hans Golstein, Heino Smit and Sjef Kikken for mechanical and electronic arrangements and Herman van de Stadt, Nick Whyb orn, Gert de Lange for helpful comments and discussion. This work is supp orted in part by Russia Program for Basic Research, Russian SSP "Sup erconductivity" and ESA contract 11/653/95/NL/PB.

Bia s Curre nt (m k A)

b)

c)
0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 5.0

Bia s Vo ltage (mV )

FIG. 2. I-V curves and if output power for SIS receiver, a) Pumped SIS Junction if Output Power for 295 K Load, b) Pumped SIS Junction if Output Power for 78 K Load, c) Unpumped SIS Junction if Output Power, d) Pumped SIS Junction I-V Curve for 295 K Load, e) Pumped SIS Junction I-V Curve for 78 K Load, f ) Unpumped SIS Junction I-V Curve TABLE I. Noise temperature Ti and gain Gi of SIS receiver elements for fLO =471 GHz and junction bias Voltage = 1.7 mV. Tf ront is the noise contribution of the element referred to the receiver input. Element name Beamsplitter Dewar input window Quartz IR filter (78K) Zitex IR filter (4.2K) rf loss element (unknown) Conversion gain (zero-point fluctuations) if mismatch if amplifier Receiver Ti (K) 7±2 4±2 2±1 1.0±0.5 12±5 11.4±0.01 3±2 5±2 Gi (dB) -0.10±0.02 -0.11±0.02 -0.10±0.02 -0.17±0.02 -0.5±0.3 -0.2±0.4 -1.1±0.4 0.0±0.4 -2.3±0.1 Tf ront (K) 7±2 4±2 2±1 1.0±0.5 13±5 14±5 5±3 8±3 54±3

[1] J.R. Tucker, M.J. Feldman, Quantum Detection at millimeter wavelengths, P.1055-1112, Reviews of Modern Physics, Vol. 57, No. 4, October 1985 [2] M.C. Gaidis, H.G. Leduc, Mei Bin, D. Miller, J.A. Stern, and J. Zmuidzinas, Characterisation of Low Noise QuasiOptical SIS Mixers for the Submil limeter Band, IEEE Transactions of Microwave Theory and Techniques, p. 1130-1139, 1996 [3] A. Karpov, J. Blondell, M. Voss, K.H. Gundlach, Four photons sensitivity heterodyne detection of submil limeter radiation with superconducting tunnel junctions, IEEE Trans on Appl. Superconductivity, Vol. 5, N 2, pp. 33043307, 1995. [4] A.R. Kerr, M.J. Feldman, S.-K. Pan Receiver Noise Temperature, the Quantum Noise Limit, and the Role of the Zero-Point Fluctuations, Eight Int Symp on Space Terahertz Technology proceedings, p. 101-111, 1997. [5] D.P. Woody, Measurement of the Noise Contributions to SIS Heterodyne Receivers, ASC'94 Proceedings, 1995 [6] P. Dieleman and T.M. Klapwijk, Shot noise beyond the Tucker theory in niobium tunnel junction mixers, Applied Physics Letters, Vol 72, Number 13, p. 1653-1655, 1998 [7] V.P. Koshelets, S.V. Shitov, L.V. Filippenko, A.M. Baryshev, H. Golstein, T. de Graauw, W. Luinge, H. Schaeffer, H. van de Stadt, First Implementation of a Superconducting Integrated Receiver at 450 GHz, Appl. Phys. Lett., Vol. 68, No. 9, pp. 1273-1275, 1996. [8] S.V. Shitov, A.B. Ermakov, L.V. Filippenko, V.P. Koshelets, W. Luinge, A.M. Baryshev, J.R. Gao, P. Lehikoinen, Recent Progress on the Superconducting Imaging Receiver at 500 GHz, Proc. of 9-th Int. Symp. on Space Terahertz Technology, 17-19 March 1998, Pasadena Hilton, Pasadena, California, USA, pp. 263-272.

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