By using the nonlinearity of the system parameters, the driving energy can be transferred to the signal energy, and the amplification can be realized. But parametric amplification also has a significant short board - it can only amplify the signal in a very narrow range near the driving frequency (half). Imagine that when we swing, if we change the rhythm of our body position and the frequency of swing oscillation are inconsistent, we will know. With the development of science and technology, we have found a new and more ideal non-linear circuit element, Josephson junction. With the help of the zero resistance characteristic of superconductor, we can construct a parametric amplifier whose noise is close to or even beyond the quantum limit. The "second spring" of parametric amplifier will come. After that, the more extreme quantum measurement technology has ushered in the "third spring" of parametric amplifiers, which has made great achievements in the field of quantum computing.
Author: Innocent (quantum computing practitioners)
The second spring of parametric amplifier is the discovery and application of Josephson junction. Josephson junction is a sandwich structure composed of two superconductors separated by a thin insulating layer. This insulating layer is very thin, only a few nanometers. At this time, the superconducting wave function will have the opportunity to spread to the other side of the insulating layer, and interfere with the superconductor on the other side. This is the Josephson effect.
*Note: in a broad sense, this is only the form of tunnel junction. Josephson junction can be other forms. For the convenience of explanation, this most classical form is adopted here.
Josephson effect was discovered by a college student named Josephson. After the establishment of BCS theory, a famous micro theory of superconductivity, Josephson, a college student, intuitively believed that Cooper pairs, the "basic particles" that make up superconductive condensates, can also tunnel like electrons. Based on this assumption, he quickly obtained the relationship between the tunneling current and the phase difference of superconductors at both ends of the tunneling barrier, as well as the relationship between the change of the phase difference and the voltage, which are respectively called Josephson current relationship and voltage relationship, or the DC Josephson effect and the AC Josephson effect. The combination of these two effects makes the current voltage relationship of Josephson junction show complex nonlinear behavior. At the same time, in the case of small current (i.e. the current flowing through Josephson junction is less than its critical current), it has no energy loss, which makes it very useful in the circuit.
When I first started, I did a device application called "squid". This device is the most sensitive magnetic detector known. For this kind of detector and its application, I will not see the following table for the moment, but allow single circuit decomposition. We just say its core component is Josephson junction. Now Google and IBM are working on the superconducting quantum computer, the core component of which is Josephson junction. The "C3" plan led by the United States and the superconducting computer led by Professor Wang Zhen of Shanghai Institute of microsystems in China, the core component of which is Josephson junction. Of course, the core element of Josephson parametric amplifier is Josephson junction.
a) A Josephson junction, b) representation of Josephson junction in circuit, c) equivalent circuit diagram of Josephson junction. Josephson junction is equivalent to an inductance, but its equivalent inductance can change with the phase difference, or even can be negative.
Combining Josephson current relation with voltage relation, we find that a Josephson junction can be equivalent to an inductance in a circuit. This inductance value is related to the phase difference on the junction. It is a non-linear inductance. What's more, this inductance can also be negative! This is the main reason for the abundant and complex dynamics of Josephson junction. The story of using varactor diodes to construct parametric amplifiers has been mentioned in the last part. It also mentions that there are two parameters L and C in LC oscillation circuit. Well, now we have nonlinear devices with variable inductance! We can use Josephson junction to replace, or partially replace, the inductance in LC - oscillation circuit, introduce nonlinearity, and make parametric amplifier!
Josephson parametric amplifier
In the 1970s and 1980s, there was only a very low additional noise in theory, and Josephson oscillation frequency was just in the range of 1-100ghz, which is the favorite frequency band of military radar. Therefore, people had a strong motivation to develop a parameter amplifier based on Josephson effect, which is simply called Josephson parametric amplifier (JPA).
However, the research and development process is not smooth. Limited by the lack of refrigeration technology at that time, and the immaturity of Josephson junction preparation and material technology *, although JPA was made and amplification was seen, the noise performance was not satisfactory, and it was not stable, and it was easy to have unexplained oscillations. So soon, there are fewer and fewer researchers engaged in this field. In addition, the clumsiness of the refrigerator can't match the "reality" of the semiconductor amplifier completely, which is difficult to be compared with the military. Such research is gradually silent. However, the research in this period laid the theoretical foundation of JPA, and also accumulated a lot of experimental experience, resulting in a number of relevant literature, which is ready for the "third spring" of the later parametric amplifier. (for the development of refrigeration technology, please refer to "in the silence close to absolute zero, is there such a big killer as quantum computing hidden? 》）
*Note: the most popular one in that era was the Josephson junction with lead as superconductor. The biggest disadvantage of this kind of knot is its instability.
In entering the next part (also the most difficult part to understand)