Quantum interference phenomena between long Josephson junctions

Volume 109A, number 3

PHYSICS LETTERS

13 May 1985

QUANTUM INTERFERENCE PHENOMENA BETWEEN LONG JOSEPHSON JUNCTIONS ~ M. C I R I L L O 1, S. PACE, S. P A G A N O Dipartimento di Fisica, Universiti~ di Salerno, 1-84100 Salerno, Italy

and G. P A T E R N 0 Associazione EURA T O M - E N E A sulla Fusione, Centro Ricerehe Energia Frascati c.p. 65, 00044 Fraseati, Rome, Italy

Received 31 January 1985; accepted for publication 11 March 1985

A system composed of two long Josephson junctions coupled by a superconducting loop has been experimentally investigated. The results show evidence of macroscopicquantum interference when the device is current-biased both on the Josephson current and on dc current singularities.

It has recently been shown that a superconducting interferometer might exhibit resonances in the currentvoltage characteristics [1 ]. The resonant voltage is determined by the loop inductance and the junction capacitance. The current amplitude of the resonances is modulated by a magnetic flux threading the loop [2,3]. Usually these phenomena are studied on small junctions in order to minimize effects due to junction self-resonances. In the present paper we consider the case of two identical long Josephson junctions coupled by a superconducting loop. This physical system has already been investigated by mechanical analog [4] and digital computer simulations [5] because of its potential practical applications. The junctions are of the overlap type and exhibit zero-field singularities (ZFS) in the currentvoltage characteristics at voltages Vn = n ~ o C / L , where C is the electromagnetic wave velocity in the oxide barrier, L is the junction length and 40 is the flux quantum. The dependence of the current amplitude of the ZFS upon the magnetic flux coupled to the loop has been investigated. The experimental results Work partially supported by the G.N.S.M. (Italy). i Present address: National Bureau of Standards, Electromagnetic Technology Division, Boulder, CO 80303, USA. 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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b Fig. 1. Sketch of a typical sample used for the experiments: (a) side view; (b) top view. show that the step amplitudes exhibit an interference modulation similar to that observed for the maximum Josephson current. The samples investigated were interferometers with two N b - N b O x - P b Josephson junctions. Junctions patterning was defined by photolithography and chemical etching [6]. A schematic drawing of the device is reported in fig. 1. On the same substrate an overlap junction of length 2L and no loop was also 117

Volume 109A, number 3

PHYSICS LETTERS

13 May 1985

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fabricated. The magnetic field was generated either by a control line beside the interferometer or by a solenoid around the sample. Either way similar results were obtained, indicating that in both cases the magnetic field was coupled to the loop and to the junctions. In fig. 2 magnetic field dependences of the maximum Josephson current 1j, the first Fiske step 11/2 and the first SFS 11 for an interferometer are shown. The characteristic parameters for this device are: Josephson current 1j = 265/aA, Josephson penetration depth Xj = 270/am, loop area = 56 #rn 2. The loop inductance evaluated by using the expression for a square loop of the same area [7] was l 0 = 10 pH. This value is in agreement with the value 10 = 13 pH deduced from the ratio 10Ij/2¢0 evaluated from the Josephson current diffraction pattern of fig. 2a by using the general theory of superconducting interferometers [8]. The 118

dimensions of each junction were L = 300/am, W = 16.5 m, L/;kj = 1. For this device only one AFS at a voltage V = 100/aV was observed in the 1 - V curve. The voltage of the first Fiske step is V = 50/aV. From the pattern of fig. 2c it is clear that the modu. lation periodicity is the same as that of the Josephson supercurrent. This means that the physical states generating the ZFS are regularly influenced by the magnetic field threading the loop. In other words, the fluxons, or the multimode [9] oscillations, in the junctions are phase-coupled at one end. The field modulation of the first Fiske step is just the same but is out of phase with respect to the Josephson current. In fig. 3 the magnetic field dependences of the Josephson current, the first Fiske step and the first ZFS for the standard overlap junction fabricated on the same substrate are shown. In this case the long dimension is L = 620 gm, the r a t i o L/Xj = 2 and two ZFS are observed at

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Volume 109A, number 3

PHYSICS LETTERS

V= 50/aV and V = 100/aV. The voltage of the first Fiske step is V = 25/zV. In fig. 3b the first part of the pattern is missing. This is in accordance with the fact that the longer the junction the higher is the magnetic flux threshold for the appearance o f stable Fiske steps [10]. The envelopes of the maxima of the magnetic field patterns of fig. 2 are reported in fig. 4. Since they are related to the flux coupled to the junctions the curves are essentially similar to the patterns for the standard overlap junction shown in fig. 3a. In a recent paper [5] it has been shown that it is possible to couple inductively two long overlap junctions. The coupling is characterized by the parameter ~j = XjI/I 0 where l 0 is the inductance between the two long junctions and l their inductance per unit length. Numerical and analytical calculations indicate that in order to get a strong coupling the value of ~ must be o f the order o f 4/7r 2. For the device of fig. 2 the inductance per unit length was l = 12.5 × 1 0 - 9 H/m and a value o f ~ = 0.3 was deduced. It is interesting to note that an interferential behavior like that shown in fig. 2 was not clearly observable for samples for which the parameter ~ was smaller than 0.02. In conclusion we believe that the possibility of getring macroscopic quantum interference effects for self-

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13 May 1985

resonant Josephson junctions, when these are operated at resonant voltages, has been demonstrated. This represents another fairly exciting aspect of the internal dynamics of long Josephson junction devices. References [1] H.H. Zappe and B.S. Landman, J. Appl. Phys. 49 (1978) 344. [2] D.B. Tuckerman and J.H. Magerlein, Appl. Phys. Lett. 37 (1980) 241. [3] G. Paternb, A.M. Cucolo and G. Modestino, J. Appl. Phys., to be published. [4] M. Cirillo, S. Pace and B. Savo, IEEE Trans. Mag. MAG19 (1983) 1021. [5] M. Cirillo, Inductively coupled fluxon oscillator, preprint (1984). [6] V. Lacquaniti, G. Marullo and R. Vaglio, IEEE Trans. Mag. MAG-17 (1981) 812. [7] J.M. Jaycox and M.B. Ketchen, IEEE Trans. Mag. MAG-17 (1981) 400. [8] A. Barone and G. Patern6, Physics and applications of the Josephson effect (Wiley, New York, 1981) ch. 12. [9] M.P. Soerensen and R.D. Parmentier, in: LT-17, eds. U. Eckern, A. Schmid, W. Weber and H. Wihl (NorthHolland, Amsterdam, 1984) p. 707. [10] M. Cirillo, A.M. Cucolo, S. Pace and B. Savo, J. Low Temp. Phys. 54 (1984) 489.