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Stability of the zero voltage state in long Josephson junctions coupled to a microwave resonator
PHYSICA@
Physica B 194-196 (1994) 67-68 North-Holland
Stability of the Zero Voltage state in Long Josephson Junctions coupled to a Microwave Resonator P. Barbaraa,G. Costabile b, L. C a p p e t t a b and G. Carapella b ~Physics L a b o r a t o r y I, The Technical University of Denmark, DK-2800 Lyngby, Denmark bDipartimento di Fisica, Universita' di Salerno 1-84081 Baronissi (SA), Italy We are investigating the amplitude of the dc Josephson current in long Josephson junctions coupled to a stripline rf resonator by a thin film capacitor. In this experiment the junction is driven by an rf signal in the X-band and the dc critical current vs. the microwave power is recorded for different values of the external dc magnetic field. We find that the height of the dc critical current depends strongly on the relative polarities of the dc bias current and the external magnetic field. The phenomenon can be interpreted in terms of the Perturbed Sine Gordon Equation model.
The investigation of the interaction of long Josephson tunnel junctions with a resonator [1] can help to clarify [2] the basic mechanism relative to the coupling of microwaves to long junctions, which must be understood to design devices for applications [3]. For our experiment we used junctions fabricated in the N b / A 1 / A I O x / N b trilayer technology: the trilayer was deposited by rf m a g n e t r o n sputtering on silicon wafer and patterned by Reactive Ion Etching to form the geometry of the base electrode, then the area of the junction was defined by a SNAP process, and finally, after sputter cleaning, a wiring Nb film was deposited and patterned by lift-off technique so to form an overlap geometry. The junction is coupled to a stripline rf resonator by a thin film capacitor, t h a t is formed during the Nb wiring deposition as the Nb film extends through the gap between the junction and the resonator and overlaps the resonator itself, t h a t had been partially anodized by the SNAP process. The overlap area is 30 × 85/~rn 2, which produces an estimated capacity of about 3 pF. We tested several samples, t h a t all showed similar behaviour, but we report here only the results recorded from one of them. In this sample the junction dimensions are 640 × 20/zrn 2, the measured critical current Ic is 3.8 mA, the estimated current density is 55A/crn 2, wi/2r was about 17 GHz and ~j. was estimated to be about 115/zrn Therefore the electrical length of the junction I = L/)~j is about 6. The I-V characteristic of
the junction and the pattern of the critical current as a function of the magnetic field perpendicular to the long dimension were very regular. Our basic observation is that the critical current is suppressed asymmetrically in the presence of b o t h a magnetic field and microwaves, i.e., one of the two branches, positive or negative, stays larger t h a n the other while the rf amplitude is increased. In particular, one can find a field value for which the positive (or the negative} branch is totally suppressed by the rf field, while the other is only slightly reduced; then, increasing further the amplitude of the rf signal, the stable branch becomes suddenly unstable and drops abruptly to zero (Fig.l(a)). Reversing the direction of the external magnetic field, the role of the dc critical current branches is also reversed; the general features of the phenomenon are summarized in Fig. l(b). Qualitatively, the phenomenon can be understood assuming t h a t the rf signal is applied mainly at the edge of the junction strongly coupled to the resonator. When the magnetic field sums up at the irradiated edge to the dc bias, the stability of the zero voltage state is decreased, while in the opposite case, i.e., when the magnetic field affects the phase in the opposite direction with respect to the dc bias, the stability is increased. To check the validity of this picture, and also to investigate the dynamics of our sampies, we are carrying on numerical simulations
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)E0607-I
68
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Figure 1. Experimental behavior of the upper (squares) and the lower (circles) branches of the dc critical current as a function of the rf power (a) and of the magnetic field (b). In both cases the rf frequency is ~, = IO.9GHz, and the current is normalized to the m a x i m u m critical current.
based on the Perturbed Sine Gordon Equation model with boundary conditions that reflect the above interpretation, i.e., uniform magnetic field and a s y m m e t r i c irradiation. Here, for the sake of comparison, we show in Fig. 2 some numerical results t h a t indicate the agreement between the e x p e r i m e n t a l d a t a and the model. We remark t h a t the phenomenon is the most evident both in the experiment and in the simulation when the rf frequency is less than half the p l a s m a frequency. In fact, since for a long, overlap junction both a small magnetic field and a signal at a frequency lower t h a n wy are confined to a fraction of the
..~.1.~ -1.0 -0.5 0.0 0.5 1.0 1.5 Mognetic Field (A.U.)
Figure 2. Results of the numerical simulations. The meaning of the plots is the same than in Fig. 1 (a),(b). It was assumed l = 6, wrl = 0.4w3. The magnetic field and the rf power span a range that can be compared with the experimental data.
junction length near the edge, the boundary conditions play the major role. Further work on this subject is in progress. REFERENCES 2.
R.Monaco et al., Phys.Lett.A,151,195, (1990). G.Filatrella et al., J.Appl.Phys., 72, 3179,
3.
R.D.Parmentier,
1.
(1992). "Solitons
a n d L o n g Joseph-
son Junctions", in NATO ASI : The New Superconducting Electronics, Watherville Valley, NH, USA, August, 1992, [to be published].
Physica B 194-196 (1994) 67-68 North-Holland
Stability of the Zero Voltage state in Long Josephson Junctions coupled to a Microwave Resonator P. Barbaraa,G. Costabile b, L. C a p p e t t a b and G. Carapella b ~Physics L a b o r a t o r y I, The Technical University of Denmark, DK-2800 Lyngby, Denmark bDipartimento di Fisica, Universita' di Salerno 1-84081 Baronissi (SA), Italy We are investigating the amplitude of the dc Josephson current in long Josephson junctions coupled to a stripline rf resonator by a thin film capacitor. In this experiment the junction is driven by an rf signal in the X-band and the dc critical current vs. the microwave power is recorded for different values of the external dc magnetic field. We find that the height of the dc critical current depends strongly on the relative polarities of the dc bias current and the external magnetic field. The phenomenon can be interpreted in terms of the Perturbed Sine Gordon Equation model.
The investigation of the interaction of long Josephson tunnel junctions with a resonator [1] can help to clarify [2] the basic mechanism relative to the coupling of microwaves to long junctions, which must be understood to design devices for applications [3]. For our experiment we used junctions fabricated in the N b / A 1 / A I O x / N b trilayer technology: the trilayer was deposited by rf m a g n e t r o n sputtering on silicon wafer and patterned by Reactive Ion Etching to form the geometry of the base electrode, then the area of the junction was defined by a SNAP process, and finally, after sputter cleaning, a wiring Nb film was deposited and patterned by lift-off technique so to form an overlap geometry. The junction is coupled to a stripline rf resonator by a thin film capacitor, t h a t is formed during the Nb wiring deposition as the Nb film extends through the gap between the junction and the resonator and overlaps the resonator itself, t h a t had been partially anodized by the SNAP process. The overlap area is 30 × 85/~rn 2, which produces an estimated capacity of about 3 pF. We tested several samples, t h a t all showed similar behaviour, but we report here only the results recorded from one of them. In this sample the junction dimensions are 640 × 20/zrn 2, the measured critical current Ic is 3.8 mA, the estimated current density is 55A/crn 2, wi/2r was about 17 GHz and ~j. was estimated to be about 115/zrn Therefore the electrical length of the junction I = L/)~j is about 6. The I-V characteristic of
the junction and the pattern of the critical current as a function of the magnetic field perpendicular to the long dimension were very regular. Our basic observation is that the critical current is suppressed asymmetrically in the presence of b o t h a magnetic field and microwaves, i.e., one of the two branches, positive or negative, stays larger t h a n the other while the rf amplitude is increased. In particular, one can find a field value for which the positive (or the negative} branch is totally suppressed by the rf field, while the other is only slightly reduced; then, increasing further the amplitude of the rf signal, the stable branch becomes suddenly unstable and drops abruptly to zero (Fig.l(a)). Reversing the direction of the external magnetic field, the role of the dc critical current branches is also reversed; the general features of the phenomenon are summarized in Fig. l(b). Qualitatively, the phenomenon can be understood assuming t h a t the rf signal is applied mainly at the edge of the junction strongly coupled to the resonator. When the magnetic field sums up at the irradiated edge to the dc bias, the stability of the zero voltage state is decreased, while in the opposite case, i.e., when the magnetic field affects the phase in the opposite direction with respect to the dc bias, the stability is increased. To check the validity of this picture, and also to investigate the dynamics of our sampies, we are carrying on numerical simulations
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved
SSDI 0921-4526(93)E0607-I
68
0.8
0.8
"I'
(a)
(a)
B= ~ o
7
B=O.I Oouss
0.6
0.6 o
•
i
0
0
o
¢k~°%o
0.4
0.2
0.#
0.2
o
o o o
0.0
0'0-40 . . . . . . : ~ b . . . . . . -~0 . . . . . . :'tO . . . . . . . R.F POWER(dB) 06 7
(b)
P, , = O d e
. . . . . . . . .
-40
,
. . . . . . . . .
-.so
, . . ,
-2o
. . . . . . .
.
. . . . . . . .
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o
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1.0 7
(b)
P,~=OdB
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0.4
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0
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0
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0 0.0 o..--~-0.15-0.
.... I0-0.05
• . • . , ........ 0.00 0.05
~, r ~ . , , - 4 p 0.10 0.15
0.0 . . . . . . . . . . . . . . . . . . . . . . .
-I.5
a (9=urn.)
Figure 1. Experimental behavior of the upper (squares) and the lower (circles) branches of the dc critical current as a function of the rf power (a) and of the magnetic field (b). In both cases the rf frequency is ~, = IO.9GHz, and the current is normalized to the m a x i m u m critical current.
based on the Perturbed Sine Gordon Equation model with boundary conditions that reflect the above interpretation, i.e., uniform magnetic field and a s y m m e t r i c irradiation. Here, for the sake of comparison, we show in Fig. 2 some numerical results t h a t indicate the agreement between the e x p e r i m e n t a l d a t a and the model. We remark t h a t the phenomenon is the most evident both in the experiment and in the simulation when the rf frequency is less than half the p l a s m a frequency. In fact, since for a long, overlap junction both a small magnetic field and a signal at a frequency lower t h a n wy are confined to a fraction of the
..~.1.~ -1.0 -0.5 0.0 0.5 1.0 1.5 Mognetic Field (A.U.)
Figure 2. Results of the numerical simulations. The meaning of the plots is the same than in Fig. 1 (a),(b). It was assumed l = 6, wrl = 0.4w3. The magnetic field and the rf power span a range that can be compared with the experimental data.
junction length near the edge, the boundary conditions play the major role. Further work on this subject is in progress. REFERENCES 2.
R.Monaco et al., Phys.Lett.A,151,195, (1990). G.Filatrella et al., J.Appl.Phys., 72, 3179,
3.
R.D.Parmentier,
1.
(1992). "Solitons
a n d L o n g Joseph-
son Junctions", in NATO ASI : The New Superconducting Electronics, Watherville Valley, NH, USA, August, 1992, [to be published].