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Josephson effectObjectivesPrincipleConservation of the voltJosephson junction arraysContactPublicationsProjets et collaborations

Focus on...Quantum metrology and fundamental constants: international school at Les Houches Physics Centre, 1st to 12October 2007.> Highlights (291 Ko)

ObjectivesThe first objective of this study is to ensure the conservation of the volt, by developing a quantum voltage standardbased on the Josephson effect and by developing and improving instruments used in the calibration chain. The secondobjective of the study is to develop research into new applications of the Josephson effect in metrology of the volt.

Principle

Fig. 1 : Josephson junctionThe Josephson effect [1] is one of the notable effects of superconductivity, a macroscopic quantum phenomenonwhich appears in certain metals at very low temperatures. In the superconducting state, electrons are attracted by eachother and form bound pairs, called Cooper pairs. The Josephson effect occurs when these pairs of electrons tunnelthrough a thin insulating barrier placed between two superconductors, the whole being called Josephson junction(Fig.1).DC Josephson effect: If no voltage is applied to the junction terminals, a direct current - a current of Cooper pairs Ij,- flows through the junction up to a critical value Ic, which depends on the geometry, temperature and magnetic field(Fig.2a). AC Josephson effect: If a direct voltage is applied to the junction terminals, the current of the electron pairscrossing the junction oscillates at a frequency which depends solely on the applied voltage V and fundamental constants(the electron charge ee and the Planck constanth) :

Conversely, if an AC voltage of frequency fa is applied to the junction terminals by microwave irradiation, the current of

Cooper pairs tends to synchronize with this frequency (and its harmonics) and a direct voltage appears at the junctionterminals. This synchronization is revealed in the current-voltage characteristics by the appearance of voltagesteps at integer multiples of the value V = (h/2e) fa. These are called Shapiro steps (Fig.2b).

The exactitude of the voltage-frequency relation V = (h/2e) f and its independence from experimental conditions(temperature, polarization current, junction materials) have been tested on many occasions with an uncertainty level of

up to 10-16 [2]. A Josephson junction therefore acts as a fundamentally accurate voltage-frequency converter. Thisis why the Josephson effect is now used for conservation of the volt. The constant of proportionality, Kj = 2e/h,between frequency and voltage is called the Josephson constant.

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Fig.2a - 2b : Current-voltage characteristicsa) When no voltage is applied to the junction terminals, a direct current flows through the junction up to Ic,. Above this value, a direct voltage develops at the junction terminals and the electron pair current IJ oscillates atfrequency f = 2e V/h ;b) Current-voltage characteristics of a Josephson junction under microwave irradiation for different microwave power:Shapiro steps

Conservation of the voltThe definition of the volt in the International System of Units (SI) is as follows: "The volt is the electromotive forcebetween two points of a conductor carrying a current of 1 ampere when the power dissipated between the two points is 1watt" [3]. Realization of the volt in the SI system rests on experiments comparing an electrostatic force with amechanical force, but the uncertainties obtained by this method are much too great to meet the requirements of moderninstrumentation. Conversely, the stability of voltage references based on the Josephson effect depends solely on

frequency stability, which can easily reach 10-12 . For this reason, National Metrology Laboratories started using the ACJosephson effect as a representation of the volt and adopted KJ, KJ-90= 483 597,9 GHz/V as a true value for the

Josephson constant , This value was accepted by international agreement at the 18th General Conference on Weightsand Measures and came into application on 1st January 1990.

Fig.4 : Josephson measurement benchIt is based on a weighted average of the KJ values obtained by SI realizations of the volt and other experimental

methods before 1990. Expressed in SI units, this value is marred by a high relative uncertainty of (4.10-7).The Josephson voltage standard is an intrinsic standard which gives a highly stable voltage reference that can bereproduced anywhere, whatever the sample.At LNE, as in most National Metrology Laboratories, we have developed a measurement system based on the Josephsoneffect (Fig. 3) in order to calibrate standard cells (or Weston cells) and Zener diode voltage references by comparisonwith Josephson junction arrays over the -10 V à +10 V range.A direct comparison of two Josephson arrays in 1994

showed that the total measurement uncertainty of the system for a voltage of 1.018V is 1.7.10-10 [4].

Josephson junction arrays

Fig. 5: Diagram of a microstrip lineintegrating several Josephson junctionsDevelopment of voltage standards based on the Josephson effect is closely linked to the advances in junctionmanufacture and nanotechnologies (nanofabrication techniques such as thin layer deposition and microlithography).These voltage standards, which at present go up to 10 V, take the form of superconducting integrated circuitscontaining thousands of Josephson junctions connected in series and integrated in a microwave transmission line (Fig.4). Each junction has a surface area of a few µm² and is only a few nanometers thick. The two major difficulties lie inthe need to ensure a great homogeneity of the critical currents Ic across the entire junction array, with no more than afew % dispersion, and a uniform power distribution across the microwave circuit (working frequencies may varybetween 1 and 80 GHz).

Equivalent diagram of the junction in a circuitIn the 1980s, it was not yet possible to manufacture overdamped Josephson junction arrays (Fig. 7) that weresufficiently uniform for easy polarization of the entire array on the same voltage step. For this reason, the first arrays -comprising several thousand junctions connected in series and rising to 1 V and later 10 V - were built withunderdamped (SIS - Superconductor-Insulator-Superconductor) Josephson junctions whose I-V characteristic ishysteretic (Fig.6). The voltage steps crossing the zero current axis made it possible to obtain quantized voltages for alarge number of junctions at zero polarization current and circumvented the problem of junction uniformity. Thesearrays present a major disadvantage, however, as the steps are highly unstable and difficult to select.Advances in nanotechnologies over the last 10 years have finally made it possible to produce arrays of several thousandnon-hysteretic junctions of SNS (Superconductor-Normal metal-Superconductor) or SINIS (Superconductor- Insulator-Normal metal-Insulator-Superconductor) type. The advantage of these arrays is that the voltage steps can be selectedprecisely and very quickly, opening up numerous applications in AC voltage. A new architecture has been developed forthese arrays, based on a distribution of Josephson junctions in binary sequences called segments (Fig. 8a). Each of thesegments irradiated at frequency f can be polarized individually on steps n = 0, ± 1, by applying a polarization current I= 0, ± Ip (Fig.8b). The output voltage of the array is the sum of the voltages developed by each segment. It rises to amaximum of ± N f / KJ-90, where N is the total number of junctions in the array. The possibility of controlling current

sources by computer turns the Josephson junction array into a fundamental precision digital/analog converter or aprogrammable array [5] paving the way for AC voltage generation (Fig. 8c) [6].

Fig. 8 :a) Architecture of binary arrays andb) I-V caracteristic of the array on steps n = 0,+/-1. Each segment irradiated at frequency f can be polarized individuallyon steps n = 0, ± 1 by applying a polarization current I= 0, ± Ip.c) Sine curve of 1.25 V amplitude and 100 Hz frequency obtained from a 1 V binary arrayReferences :[1] B.D. Josephson, Phys. Lett., 1, 251 (1962)

[2] J-S. Tsai et al., Phys. Rev. Lett.,51, 316 (1983)[3] C. A. Hamilton, Rev. Scien. Inst., 71, 3611 (2000)[4] D. Reyman et al., Metrologia 31, 35-37 (1994)[5] C. A. Hamilton, IEE Trans. Instrum. Meas., 44, 223 (1995)[6] O. Monnoye, Congrès de métrologie, Toulon, (2003)

ContactSophie DjordjevicTel : 01 30 69 21 57

PublicationsJ.P. Lo-Hive, S. Djordjevic, P. Cancela, F. Piquemal, R. Behr, C. Burroughs and H. Seppä, "Characterisation of binaryJosephson series arrays of different types at BNM-LNE and comparisons with conventional SIS arrays", IEEE T.I.M.,Special issue CPEM'2002, Vol. 52, pp. 516-520, April 2003R. Behr et al, "Analysis of different measurement set-ups for a programmable Josephson voltage standard", IEEET.I.M., Special issue CPEM'2002, Vol. 52, pp. 524-528, April 2003F. Piquemal, "Point sur les étalons électriques fondamentaux dans le système SI", Groupe de travail sur les unités debase, Académie des Sciences, 31 mars 2003J.P. Lo-Hive, D. reymann, G. Geneves, "Using 10 V Josephson voltage standards to estimate the uncertainty of Zenervoltage references as travelling standards ", IEEE T.I.M., Special issue CPEM'1998, Vol. 48, pp. 253-256, April 1999J.P. Lo-Hive, G. Genevès, "Comparaisons d'étalons de tension à effet Josephson", Bulletin du BNM, n° 111, janvier1998D. Reymann, J. P. Lohive and G. Genevès, "A Comparison of One Volt Josephson Junction Array Voltage Standardsdriven by a common Microwave source", Metrologia, 31, 35-37, 1994

Projets et collaborationsGeneration of AC voltage with programmable arraysParticipation in the European Euramet BJAPS project (Binary Josephson Array Power Standard)Participation in ANR Trimet project (Quantum metrological triangle)