AC Josephson Effect

A comparison between theory and experiment for the fine structure intervals in helium holds the promise of providing a measurement of the fine structure constant a that would provide a significant test of other methods such as the ac Josephson effect the and quantum Hall effect. The latter two differ by 15 parts in 108 and are not in good agreement with each other [59]. 

To compare the theory of ae with experiment, it is necessary to know the value of a, which has been measured in diverse branches of physics. Currently best values of a, with relative standard uncertainty of 1 x 10-7 or less, are those based on the quantum Hall effect [32], the ac Josephson effect [25], the neutron de Broglie wavelength [33], the muonium hyperfine structure [34,35], and an absolute optical frequency measurement of the Cesium >1 line [36] ... 

Josephson110 Effect. If two superconductors are separated by a thin layer (<3 nm for an insulator, several micrometers for a metal), then both a DC Josephson effect and an AC Josephson effect can occur. In the DC Josephson effect, a supercurrent can bridge the layer by quantum-mechanical tunneling, but there is a change in phase, which can be detected. It is very sensitive to magnetic fields indeed the supercurrent has the form f = f0 sin (O/O0)/ 7i(/0), where I0 depends on the temperature and the structure of the junction. If a DC potential V is applied across a Josephson junction, then the AC Josephson effect creates a response at a frequency... 

The RF SQUID is based on the AC Josephson effect, uses only one Josephson junction, and is less sensitive than the DC SQUID, but is cheaper and easier to manufacture its SQUID is inductively coupled to a resonant tank circuit. Depending on the external magnetic field, as the SQUID operates in the resistive mode, the effective inductance of the tank circuit changes, thus changing the resonant frequency of the tank circuit. These frequency measurements can be easily done, and thus the losses that appear as the voltage across the load resistor in the circuit are a periodic function of the applied magnetic flux with a period of 0. 

If a Josephson junction is irradiated with microwaves of frequency /, the I-V behavior shows a series of steps, called Shapiro steps, as shown in Figure 30.32. These steps correspond to supercurrents across the junction when the condition for the absorption of microwave photons is satisfied (this is called the ac Josephson effect). Similar behavior is seen when we expose the junction to a magnetic field. How Josephson junctions can be used to detect very small magnetic fields is described in Chapter 33. 

The first of the macroscopic quantum effects to be demonstrated was the ac Josephson effect, whereby 2e/h is established via the invariant ratio nV/V for irradiation at frequency V and noting the n th step voltage, V. This has been a powerful tool in the service of electrical measurements. The history, which has been well reviewed by Petley, shows a rapid evolution from laboratory curiosity through a significant determination of a to the role of maintenance of the operational unit of voltage [16]. Incidentally, the early history of this area of work is an instance in which electrical metrology made a distinct impact on atomic physics. It will be recalled that a key issue of the early 1960 s was the discrepancy between values of a obtained from fine-structure measurement and those deduced from hyperfine structure. This story is well told in the widely known summary, due to Taylor,... 

MG Wicks, PR Haycocks, T Hori. AC Josephson effect in superconducting niobium nitride tunnel junctions at up to 2.5 THz. Electron Lett 26 610, 1990. 

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As we explore the interaction of cold-atom systems with microwave and terahertz radiation, we find that they have some unique properties as detectors. A comparison with superconductor-based detectors such as SQUlDs is instractive. Because of the third law of thermodynamics, i.e., a system in a single quantum state has zero entropy, the response of a SQUID is almost free of thermal noise. But an additional properly of SQUIDs is that they exhibit the phenomenon of coherence, i.e., wave interference, which leads to entirely new effects, e.g. the AC and DC Josephson effects. Cold atom clouds share this behavior, as we will discuss below. 

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