Superconducting quantum interference device (SQUID) and its application in science and engineering. A presentation Submitted by

Transcription

1 Superconducting quantum interference device (SQUID) and its application in science and engineering. A presentation Submitted by S.Srikamal Jaganraj Department of Physics, University of Alaska, Fairbanks, Ak

2 Content Abstract 3 1. Introduction 3 2. Macroscopic quantum interference.4 3. Superconducting quantum Interference device (SQUID) SQUID microscopy or magnetometer SQUID electronics Summary Reference.. 8 2

3 Abstract I like to present a topic on SQUID which is basically derived from Josephson s junction. SQUIDs have very bright applications in science and technology. Recently numerous scientific publications were found based on its sensitivity in detecting week magnetic field, high speed switching circuits and in quantum computation. Though SQUIDs can be extremely small (in the order of 10 9 ) it requires cryogenic cooler setup to maintain the low temperature. Nevertheless hunting High T c superconducting material is still a hot research field in solid state physics. Being in Advance stage there has been large increasing interest for fabrication and designing of SQUIDS. In this presentation I will mainly focus on introduction to Josephson junction and how useful it is in the field of science and technology. 1. Introduction In 1962, Brian Josephson proposed a novel behavior of superconductor called Josephson junction. Josephson junction is a junction of two superconducting material separated by a thin insulating layer. This sandwich starts conducting when cooper fig1.1 pairs from both the metal layers tunnel through insulators. Here cooper pairs means pair of electrons at T<T c. The wave function of this pair is exactly like the wave function of free particle having opposite spin and equal and opposite momentum [2]. This pair condensation named after American physicist Leen Cooper is one of the basis for development of BCS theory of superconductivity[1]. These electron pairs behaves like bosons and responsible for the flow of electrons through the insulating layer with phase difference φ. There exist two types, one is DC (in the absence of electric and magnetic field) and another one is AC (applied DC across the junction) Josephson Effect depending upon the type of current that flows between the junctions. When a DC voltage is applied across a Josephson junction it produces a current with oscillating frequency J = J 0 sin[ (0) (2eVt / h)]. 1.1 Thus we can calculate e / h with very high accuracy because voltage and frequency ω = 2eV / h can be determined precisely [1]. 3

4 2. Macroscopic quantum interference One of the Powerful applications of Josephson junction is that leads to invention of SQUID. When two Josephson junctions are coupled together parallel in the presence of DC magnetic field will result in maximum super current to show interference effect as a function of magnetic field intensity. The Interference occurs due to the tunneling cooper electrons form both the end of the junction say J 1 and J 2 and corresponding current say I 1 and I 2 respectively. One can imagine this interference of electrons analogous with the quantum interference of light in the double slit experiment. The total supercurrent I 1 and I 2 are not in phase when a small magnetic field is applied. As a result there exists interference between I 1 and I Superconducting quantum Interference device (SQUID) From the fig.2.1 you see insulators at the position YZ and XW are the superconducting material. For applied magnetic small field B Perpendicular to the plane of the ring produces a cooper pairs of electron along the path ZXY and YWZ. Thus a small current I is induced and that induced I is sufficient enough to cancel the magnetic flux B according to the Lenz s law but the critical current of the superconductor-insulator link prevent this. The total magnetic flux that passes through a superconductor ring may be assumed only in quantized value, Integral multiples of the flux quantum 2π hc / q [1]. That is the total change in phase between current I and the applied magnetic field B around the closed Loop can be written as ( φ) = [( φ) ] I + [( φ) ] B 3.1 where 4πm r r [( φ) ] I = Js dl 3.2 hn c ie and 4

5 4πe r r [( φ) ] B = A dl 3.3 h c Where J r is current density, A r is the magnetic vector potential anddl r is line element along the closed loop. By applying stokes theorem we get m r r m r r Φ ' = J dl + B ds n s ie 2e this integral gives h Φ =n e thus Φ 0 =πh / e which is equal to 2.07X10-15 Wb. There is no quantization condition from external source, so that superconducting Φ sc must adjust itself appropriately in order that Φ assume a quantized value [1]. Φa Ic = 2i c cosπ 3.6 Φ 0 I c is critical measuring current and i c is critical current. Hence circulating supercurrent has a periodic dependence on the magnitude of the applied magnetic field, with a period of variation ofφ 0.The plot describes the behavior of measuring current vs. the applied magnetic field [3]. So detecting this circulating current can leads us to the measurement of very small B or in other words we can take 1fT as a nominal resolution of the SQUID. 4. SQUID microscopy or magnetometer The typical ultimate field sensitivity of the SQUID microscope is given by the SQUID flux noise divided by the effective pickup area. For typical value [4] of Φ 0 2 flux noise of, a pickup area of ( 7µ m) corresponding to an effective Hz 5

6 T 2 noise of, where as a pickup area of (mm 1 ) corresponding to an Hz T effective field noise of. In the case of scanning SQUID microscope Hz the pickup coil is few millimeter and it can be classified by the temperature in which the SQUID and the sample are placed. Basically of two types one with low temperature either in a common vacuum space or in a cryogenic fluid. And in the second one the SQUID is placed in between Cryogenic reservoir and the room temperature. Depending up on the samples both microscopes has their own advantages [4]. The images are just the translation of magnetic field that scanned over a surface of sample. So the images are usually false-color or grey scale images. In the above figure Dr.J.R.Kirtley [4] has used a Squid microscope to scan a Josephson vortex in La-Sr and in some organic crystal when the temperature was lowered through T c. At the temperature close to T c the bright part in the Figure 4.1 spreads out. Threshold for SQUID is 1x10-15 Magnetic field of heart is 50,000 ft Magnetic field of brain is a few ft. 6

7 5. SQUID electronics SQUIDs are solid state device like transistors and resistors. Usually SQUID are operated in the presence of magnetic field and it produces a frequency in the order of several MHz for few micro volts when applied across the junctions. So it can be used like an amplifier. NIST have demonstrated experimentally with identical input coils connected in series with 100-SQUID arrays producing very large bandwidth about 100 MHz. In analogy with LCR circuits when a dc SQUID is connected to inductance L and shunt resistor R a relaxation oscillation are produced. SQUIDs are also used in constructing Quantum logic gates [6]. This is just because of its quantum mechanical character. 6. Summary Ac and Dc Josephson device is a solid state device extremely sensitive to applied magnetic field. When two Josephson junction is coupled parallel to form Superconducting Quantum interference Device or SQUID. It can measure voltage and magnetic field to very high accuracy in the order of femto scale. Though the research in this field is considered to be advance stage, the refrigeration issue is still the major obstacle for application of low T c superconducting device outside laboratory environment. This might be achieved with extensive computer control. 7

8 7. References [1]. Charls Kittel, introduction to solid state physics, eight edition, John weley & sons [2]. A thesis by John Blands, mossbauer spectroscopy and magnetometry study of magnetic multilayer and oxides [ [3]. H.Matsumoto, T.Koyama, M,Machida, Electromagnetic waves in Single and Multi-Josephson Junction. Physica C, 468 (2008), 654. [4].J.R.Kirtley, SQUID microscopy for fundamental studies, Physica C, 368, 55-65, [5]. Applied Superconductivity, Application of High temperature SQUIDs, Vol. 3, No.7-10, pp.368, [6]. A.Ekert, P.hayden, H.Inamori basic concepts in quantum computation, University of Oxford, UK, Feb 1,