Josephson frequency

Parker and Langenberg [6]. An important feature of the Josephson frequency-voltage measurements is their complete independence from geometry. It is precisely this fact which has permitted refinement to reach its present level near 0.01 ppm and there appears no obvious obstacle to further improvement. 

Ideally a standard cell is constmcted simply and is characterized by a high constancy of emf, a low temperature coefficient of emf, and an emf close to one volt. The Weston cell, which uses a standard cadmium sulfate electrolyte and electrodes of cadmium amalgam and a paste of mercury and mercurous sulfate, essentially meets these conditions. The voltage of the cell is 1.0183 V at 20°C. The a-c Josephson effect, which relates the frequency of a superconducting oscillator to the potential difference between two superconducting components, is used by NIST to maintain the unit of emf. The definition of the volt, however, remains as the Q/A derivation described. 

In this section we calculate the Josephson current between the S layers of a FSFSF structure. We assume again that the thickness of the F layers dp is much larger than In this case the Josephson coupling between the S layers is due to the long range part of the TC. Therefore the supercurrent in the transverse direction is unusual, since it is caused by the triplet component of the condensate that is odd in frequency and even in momentum. 

Thus, if the condition dp is fulfilled the Josephson coupling between neighboring S layers is only due to the TC. Therefore in this case a new type of superconductivity may arise in the multilayered structures with non-collinear magnetizations. The supercurrent within each S layer is caused by the SC, whereas the supercurrent across the layers is caused by the triplet condensate, which is odd in the frequency iv and even in the momentum. 

Examples of the observational equations are given in Table 2. In that table, r H and vb are transition frequencies in hydrogen and deuterium such as those given in Table 3 below, Kj is the Josephson constant, which is characteristic of the Josephson effect, and Rk is the von Klitzing constant, which is characteristic of the quantum Hall effect. Note that Ex(riLj)/h is proportional to cRoo and independent of h, hence h is not an adjusted constant in these equations. 

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... 

Thus the Josephson junction can be an excellent DC voltage-to-microwave-frequency converter the factor ine/h is approximately equal to 3 x 1014Hz. 

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. 

Some escajje processes of interest are affected by external forces a typical situation is escapie in the presence of a radiation field whose frequency is close to resonance with the well motion. Experimental examples are molecular photodissociation in condensed phases, photodesorption, and microwave-induced transitions in Josephson junctions. To describe such processes within the Kramers theory one needs to analyze the effect of an additional periodic force in Eq. (2.1) (or its non-Markovian counterpart). 

It is worthwhile to note that the charged Bose gas trapped in the double well potential Ua of Eq. 50 behaves as an inverted Josephson junction (N-S-S-N). The super-current, which accompanies the matter wave coherence, is induced between the degenerate resonance states of the adjacent wells at the frequency of the tunnel splitting A response time, as is typical of tunnel junctions (whose frequency cutoff is much smaller than the vibrational frequency even for nano junctions). The coherent oscillations of the Josephson current can be observed by virtue of their slow frequency A V which is robustly controlled by the bias voltage. 

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 ... 

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

Before analyzing (4), we mention some typical parameter values for Josephson junctions. The critical current is typically in the range I I /zA- 1 mA, and a typical voltage is I R 1 mV. Since le/h 4,83 x 10 " Hz/V, a typical frequency is on the orderof lO" Hz. Finally, a typical length scale for Josephson junctions is around 1 (im, but this depends on the geometry and the type of coupling used. 

The Josephson effect is the phenomenon in which two superconducting materials weakly coupled through a non-superconducting interface show a sharp increase in conductance of current flowing from one of the superconductors to the other if radiation of a suitable frequency is applied to the interface. The relation between the voltage difference between the two superconductors Uj and the frequency / of the applied radiation for which there is an increase in current is given by... 

The existence of a relativistic temperature-dependent contribution to the chemical isomer shift was pointed out independently by Pound and Rebka [6] and by Josephson [7]. The emitting or absorbing atom is vibrating on its lattice site in the crystal. The frequency of oscillation about the mean position is of the order of 10 per second, so that the average displacement during the Mossbauer event is zero. However, there is a term in the Doppler shift which depends on v, so that the mean value is non-zero. 

Josephson effect - The tunneling of electron pairs through a thin insulating layer which separates two superconductors. When a potential difference is applied to the superconductors, an alternating current is generated whose frequency is precisely proportional to the potential difference. This effect has important applications in metrology and determination of fundamental physical constants. 

This list includes, in particular, some of the experimental results mentioned in the introduction high-precision transition frequencies in hydrogen, between the IS and 2S levels [7], and other measurements between levels with n up to 12 (see, e.g., [21]). Other examples of included measurements are the electron g-factor [22], and the Josephson constant Kj [3, p. 28]. 

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. 

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