Superconducting Josephson Junctions

Josephson junctions are superconducting devices that are capable of generating voltage oscillations of extraordinarily high frequency, typically 1O —10 cycles 

Although quantum mechanics is required to explain the origin of the Josephson effect, we can nevertheless describe the dynamics of Josephson junctions in classical terms. Josephson junctions have been particularly useful for experimental studies of nonlinear dynamics, because the equation governing a single junction is the same as that for a pendulum In this section we will study the dynamics of a single junction in the overdamped limit. In later sections we will discuss underdamped junctions, as well as arrays of enormous numbers of junctions coupled together. 

As a 22-year-old graduate student, Brian Josephson (1962) suggested that it should be possible for a current to pass between the two superconductors, even if there were no voltage difference between them. Although this behavior would be impossible classically, it could occur because of quantum mechanical tunneling of Cooper pairs across the junction. An observation of this Josephson effect was made by Anderson and Rowell in 1963. 

Incidentally, Josephson won the Nobel Prize in 1973, after which he lost interest in mainstream physics and was rarely heard from again. See Josephson (1982) for an interview in which he reminisces about his early work and discusses his 

Equation (1) implies that the phase difference increases as the bias current 1 increases. 

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However, in all other respects, flows on the circle are similar to flows on the line, so this will be a short chapter. We will discuss the dynamics of some simple oscillators, and then show that these equations arise in a wide variety of applications. For example, the flashing of fireflies and the voltage oscillations of superconducting Josephson junctions have been modeled by the same equation, even though their oscillation frequencies differ by about ten orders of magnitude ... 

The system in Example 6.6.3 is closely related to a model of two superconducting Josephson junctions coupled through a resistive load (Tsang et al. 1991). For further discussion, see Exercise 6.6.9 and Example 8.7.4. Reversible, nonconservative systems also arise in the context of lasers (Politi et al. 1986) and fluid flows (Stone, Nadim, and Strogatz 1991 and Exercise 6.6.8). 

This section deals with a physical problem in which both homoclinic and infinite-period bifurcations arise. The problem was introduced back in Sections 4.4 and 4.6. At that time we were studying the dynamics of a damped pendulum driven by a constant torque, or equivalently, its high-tech analog, a superconducting Josephson junction driven by a constant current. Because we weren t ready for two-dimensional systems, we reduced both problems to vector fields on the circle by looking at the heavily overdamped limit of negligible mass (for the pendulum) or negligible capacitance (for the Josephson junction). 

The superconducting quantum interference device (SQUID) is formed from a superconducting loop containing at least one Josephson junction. Basically, a SQUID amplifier converts an input current to an output voltage with a transresistance of the order of 107 V/A. The input noise is of the order of 10-11 A/(Hz)1/2. The bandwidth of the SQUID amplifier can be up to 80kHz. The dynamic range in 1 Hz bandwidth can be 150dB. 

Fig. 1. Special equipment required to fabricate low-temperature superconducting junctions. Josephson junctions are comprised of aluminum oxide sandwiched between layers of niobium. These trilayer devices are considered vital to the very-high-speed signal processing demands of next-generation computers, radar, and communication systems. Shown in illustration is scientist Dr. Joonhee Kang. (Westinghouse Electric Corporation)...

Fig. 3. Scientist Donald L. Miller holds an integrated circuit chip comprising a high-resolution superconducting analog-to-digital converter. The one-square-cen timeter chip, known as a counting converter, holds promise as an unprecedented combination of high resolution and low power consumption, as needed in future air traffic control radar and infrared space-tracking applications. The 12-bit circuit (Josephson junction) has a resolution of 1 part in 40CK). (Westinghouse Electric Corporation)...

For example, a single FCV on a narrow place of a superconducting micro bridge can play the role of a Josephson junction (Fig5b). The scheme of a thin-film dc-SQUID is shown in Fig.5c. The hole of the SQUID is formed by a FCV with a diameter of 100 microns and two Josephson junctions are formed by two FCV s with smaller diameter. 

In 1962 a postgraduate student, Brian Josephson, working in the University of Cambridge, and later to win a Nobel Prize, predicted that Cooper pairs should be able to tunnel through a thin (approximately 1 nm) insulating barrier from one superconductor to another with no electrical resistance [46]. This quantum tunnelling was confirmed by experiment and is known as the Josephson effect . The superconducting electronic devices exploit Josephson junctions. 

An application of Josephson junctions is in superconducting quantum interference devices (SQUIDS). Figure 4.61 shows two Josephson junctions passing a current with a magnetic induction B, through the ring of area A. 

Fig. 4.61 Two Josephson junctions comprising a superconducting quantum interference device (SQUID).

The Josephson junction is one such ultrafast superconducting switching device. Josephson junctions, which until recently operated only at liquid-helium temperature, are traditionally made of niobium-tin or niobium-germanium and are really simple connections between superconductors. They can do everything vacuum tubes and transistors do, but a lot faster. 

But let s return to Josephson junctions for a moment. Even though a computer made of these incredible instruments has not yet been built, the junctions themselves, as we have said, are in use, fabricated of conventional superconducting materials. They are also beginning to appear in devices run by the new superconducting ceramics. 

Josephson junction A superfast, superconducting electronic switch based on the Josephson effect. 

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