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Behavior of a multiple-quantum-state superconducting ring with Josephson tunnel junctions
Solid State Communications,
Vol. 11, pp. 1183—1185, 1972.
Pergamon Press. Printed in Great Britain
BEHAVIOR OF A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING WITH JOSEPHSON TUNNEL JUNCTIONS J. Wilson and R.I. Gayley Department of Physics, State University of New York, ~3uffalo, New York 14214, U.S.A. (Received 16 June 1972 by H. Suhi)
We have learned how to preselect the quantum state of a superconducting ring that has a number of possible states, and we have studied the limits of stability of these states. We find that when these limits are exceeded, two different kinds of transitions can occur.
WE HAVE been studying rings of superconducting tin that are interrupted at two points by Josephson tunnel junctions. A diagram of the specimen is shown in Fig. 1. The four electrical leads shown permit measurement of the ring critical current
MAGNETIC F~LD DIRECTION NIO8IUM WIRE
GOLD CONTACT FILM
~-..
SAPPHIRE SUBSTRATE..~~ TUNNEL
I~.(The current applied to one pair is slowly increased until a voltage is detected across the
JUNCTION TIN RING
other pair. The current at which this happens is
I
~ The tin film thickness is 2000 A, the ring diameter is about 0.5 mm, and the junctions are roughly 0.01mm on a side. The niobium wire, which is not important for the results presented 25mm. The junctions here, has a diameter of 0. show nearly ideal properties and will be the subject of a separate publication. Each junction has its own critical current of the order of 0.1 mA, and the ring inductance is about iO~H, so that the maximum supercurrent that can circulate in the ring without producing a voltage across the junctions will generate roughly 50 flux quanta. As has been discussed by Goldman et al., such a system has a number of available quantum states, each with a different circulating current and a different I,,. In agreement 1,2 with earlier wonc, we find that when the system selects a quantum state, it chooses one from a number of possibilities in an apparently random manner.
TUNNEL
JUNCTION
I
II I i I
FIG. 1. A schematic diagram of the specimen.
The superconducting tin ring was constructed in three steps. First the large semicircle and its attached leads were laid down, then the film was subjected to an oxygen glow discharge which produced a thin oxide layer, and finally the small semicircle and attached leads were deposited.
procedure for putting the ring into a preselected state. For the typical specimen, the critical currents of the two junctions differed by about 10 per cent. Because of this, the critical current
In order to examine the properties of a particular state, we have developed the following
was usually different for positive and negative applied currents. Only the state of zero circulating current was symmetric with respect to 1183
1184
A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING
current direction. An a.c. current of amplitude greater than the largest I~was applied, and its amplitude was slowly reduced. A little reflection shows that when this is done a point must be reached such that the current amplitude exceeds
0 05
I~,for either positive or negative currents, for every state except the zero circulating state. When any other state is selected, on the subsequent current cycle I~will be exceeded and the ring will leave that quantum state. Sooner or later, however, the ring will select the zero circulating current state, I~will not be reached, and the ring will remain in this state. With the quantum state now set and the a.c. current removed, the magnetic field was changed by an amount L\B, which induced a circulating current in the ring. A d.c. current was then gradually applied to measure the value of I.. The whole process was repeated, using various values for AB, resulting in the data of Fig. 2. This figure is the first of its kind for a ring with multiple quantum states. The small amount of scatter shows that our state-selection procedure was successful and also that the state was very stable. Noise did not cause transitions to other states. This find is significant because it has been suggested 1,3 that the reason that a number of different states are normally observed is because a given state is unstable. The points lie nicely on straight lines, as is expected, but there is a region of I~values in which no points are shown. In these regions the 1 0’s obtained by the above procedure seemed to be randomly distributed, and the cutoff value of I~separating the two regions was sharply defined. Below the cutoff I~,when the applied current reached the value lying on the expected line, any voltage that appeared and to was not observed. The was ringonly madetransitory a transition a new quantum state with a lower circulating current and a higher Ia.. This new I~was what was eventually observed in the measurement. The correctness of this interpretation was shown by the following experiment. After the ring was put into the zero circulating current state, ~\B was brought to some value and then returned to zero, and only then was I~measured. If the L\B increase was not enough to cross the line, i.e. AB < 6.4 mG for Fig. 2, the resulting I~,was that of the original
Vol. 11, No. 9
as
-25
-05
‘o
a9~/
-a
-
FIG. 2. Ring critical current i,, vs. field change ~ for a specific quantum state. For each point, the ring was first put into the zero circulating current state, by the procedure outlined in the text, then applied was changed by was an amount ..\B.theand finallyfield the critical current measured. In the region where no points are shown, I~could not be determined by this method because no detectable voltage appeared when the critical The lines arebedrawn to fit thecurrent points.was (Wereached. expect straight lines cause we are unable to measure the small difference between flux and fluxoid in this specimen.)
state, i.e. 0.148 mA. ~1oweverif ~B crossed the line, the L~obtained would take on random values, showing that the ring had made a transition to a new state. The possibility that rings with weak links could have two kinds of transitions, one ending in the finite d.c. voltage configuration and the other ending in a new quantum state, was recognized by others 1,4 but we now see clearly that a single ring can exhibit both kinds of behavior in a symmetric way. In fact, by numerical integration 4 of the equations thatparameters Sullivan and proposed, using the of Zimmerman our rings, we find agreement with our observations. If the critical current is exceeded when the circulating current is large, a new quantum state is selected. If the circulating current is small, both junctions are driven into the voltage configuration and a d.c. voltage appears across the ring.
.4ckrzowledgement
— We are indebted to S. Paley for designing the specirrens and assisting in their developrrent.
Vol. 11, No. 9
A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING
1185
REFERENCES 1.
GOLDMAN A.M., KREISMAN P.J., and SCALAPINO D.J., Phys. Rev. Lett. 15, 495 (1965).
2.
JAKLEVIC R.C., LAMBE J., MERCEREAU J.E. and SILVER A.H., Phys. Rev. 140A, 1628 (1965).
3.
MERCEREAU J. in Superconductivity, (Edited by PARKS R.D. p. 412.) (Marcel Dekker, New York. (1969).
4.
SULLIVAN D.B. and ZIMMERMAN J.E., Am. J. Phys. 39, 1504 (1971).
Wir haben gelernt, wie man den Quaritenzustand eines supraleitenden Rings, welcher viele mögliche Zustände hat, im Voraus bestimmt, und wir haben die Stabilitätagrenzen diesser Zust~ndeuntersucht. Wir haben gefunden, dass zwei verschiedene Arten von Ubergängen aftreten können, wenn man diese Grenzen überschreitet.
Vol. 11, pp. 1183—1185, 1972.
Pergamon Press. Printed in Great Britain
BEHAVIOR OF A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING WITH JOSEPHSON TUNNEL JUNCTIONS J. Wilson and R.I. Gayley Department of Physics, State University of New York, ~3uffalo, New York 14214, U.S.A. (Received 16 June 1972 by H. Suhi)
We have learned how to preselect the quantum state of a superconducting ring that has a number of possible states, and we have studied the limits of stability of these states. We find that when these limits are exceeded, two different kinds of transitions can occur.
WE HAVE been studying rings of superconducting tin that are interrupted at two points by Josephson tunnel junctions. A diagram of the specimen is shown in Fig. 1. The four electrical leads shown permit measurement of the ring critical current
MAGNETIC F~LD DIRECTION NIO8IUM WIRE
GOLD CONTACT FILM
~-..
SAPPHIRE SUBSTRATE..~~ TUNNEL
I~.(The current applied to one pair is slowly increased until a voltage is detected across the
JUNCTION TIN RING
other pair. The current at which this happens is
I
~ The tin film thickness is 2000 A, the ring diameter is about 0.5 mm, and the junctions are roughly 0.01mm on a side. The niobium wire, which is not important for the results presented 25mm. The junctions here, has a diameter of 0. show nearly ideal properties and will be the subject of a separate publication. Each junction has its own critical current of the order of 0.1 mA, and the ring inductance is about iO~H, so that the maximum supercurrent that can circulate in the ring without producing a voltage across the junctions will generate roughly 50 flux quanta. As has been discussed by Goldman et al., such a system has a number of available quantum states, each with a different circulating current and a different I,,. In agreement 1,2 with earlier wonc, we find that when the system selects a quantum state, it chooses one from a number of possibilities in an apparently random manner.
TUNNEL
JUNCTION
I
II I i I
FIG. 1. A schematic diagram of the specimen.
The superconducting tin ring was constructed in three steps. First the large semicircle and its attached leads were laid down, then the film was subjected to an oxygen glow discharge which produced a thin oxide layer, and finally the small semicircle and attached leads were deposited.
procedure for putting the ring into a preselected state. For the typical specimen, the critical currents of the two junctions differed by about 10 per cent. Because of this, the critical current
In order to examine the properties of a particular state, we have developed the following
was usually different for positive and negative applied currents. Only the state of zero circulating current was symmetric with respect to 1183
1184
A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING
current direction. An a.c. current of amplitude greater than the largest I~was applied, and its amplitude was slowly reduced. A little reflection shows that when this is done a point must be reached such that the current amplitude exceeds
0 05
I~,for either positive or negative currents, for every state except the zero circulating state. When any other state is selected, on the subsequent current cycle I~will be exceeded and the ring will leave that quantum state. Sooner or later, however, the ring will select the zero circulating current state, I~will not be reached, and the ring will remain in this state. With the quantum state now set and the a.c. current removed, the magnetic field was changed by an amount L\B, which induced a circulating current in the ring. A d.c. current was then gradually applied to measure the value of I.. The whole process was repeated, using various values for AB, resulting in the data of Fig. 2. This figure is the first of its kind for a ring with multiple quantum states. The small amount of scatter shows that our state-selection procedure was successful and also that the state was very stable. Noise did not cause transitions to other states. This find is significant because it has been suggested 1,3 that the reason that a number of different states are normally observed is because a given state is unstable. The points lie nicely on straight lines, as is expected, but there is a region of I~values in which no points are shown. In these regions the 1 0’s obtained by the above procedure seemed to be randomly distributed, and the cutoff value of I~separating the two regions was sharply defined. Below the cutoff I~,when the applied current reached the value lying on the expected line, any voltage that appeared and to was not observed. The was ringonly madetransitory a transition a new quantum state with a lower circulating current and a higher Ia.. This new I~was what was eventually observed in the measurement. The correctness of this interpretation was shown by the following experiment. After the ring was put into the zero circulating current state, ~\B was brought to some value and then returned to zero, and only then was I~measured. If the L\B increase was not enough to cross the line, i.e. AB < 6.4 mG for Fig. 2, the resulting I~,was that of the original
Vol. 11, No. 9
as
-25
-05
‘o
a9~/
-a
-
FIG. 2. Ring critical current i,, vs. field change ~ for a specific quantum state. For each point, the ring was first put into the zero circulating current state, by the procedure outlined in the text, then applied was changed by was an amount ..\B.theand finallyfield the critical current measured. In the region where no points are shown, I~could not be determined by this method because no detectable voltage appeared when the critical The lines arebedrawn to fit thecurrent points.was (Wereached. expect straight lines cause we are unable to measure the small difference between flux and fluxoid in this specimen.)
state, i.e. 0.148 mA. ~1oweverif ~B crossed the line, the L~obtained would take on random values, showing that the ring had made a transition to a new state. The possibility that rings with weak links could have two kinds of transitions, one ending in the finite d.c. voltage configuration and the other ending in a new quantum state, was recognized by others 1,4 but we now see clearly that a single ring can exhibit both kinds of behavior in a symmetric way. In fact, by numerical integration 4 of the equations thatparameters Sullivan and proposed, using the of Zimmerman our rings, we find agreement with our observations. If the critical current is exceeded when the circulating current is large, a new quantum state is selected. If the circulating current is small, both junctions are driven into the voltage configuration and a d.c. voltage appears across the ring.
.4ckrzowledgement
— We are indebted to S. Paley for designing the specirrens and assisting in their developrrent.
Vol. 11, No. 9
A MULTIPLE-QUANTUM-STATE SUPERCONDUCTING RING
1185
REFERENCES 1.
GOLDMAN A.M., KREISMAN P.J., and SCALAPINO D.J., Phys. Rev. Lett. 15, 495 (1965).
2.
JAKLEVIC R.C., LAMBE J., MERCEREAU J.E. and SILVER A.H., Phys. Rev. 140A, 1628 (1965).
3.
MERCEREAU J. in Superconductivity, (Edited by PARKS R.D. p. 412.) (Marcel Dekker, New York. (1969).
4.
SULLIVAN D.B. and ZIMMERMAN J.E., Am. J. Phys. 39, 1504 (1971).
Wir haben gelernt, wie man den Quaritenzustand eines supraleitenden Rings, welcher viele mögliche Zustände hat, im Voraus bestimmt, und wir haben die Stabilitätagrenzen diesser Zust~ndeuntersucht. Wir haben gefunden, dass zwei verschiedene Arten von Ubergängen aftreten können, wenn man diese Grenzen überschreitet.