SQUID and Josephson Devices

1. 1 SQUID and Josephson Devices By : Yatin Singhal

2. 2 Overview What is SQUID? Theory SQUID. Josephson effect : DC effect AC effect Inverse AC effect. Cooper pairs. Applications of SQUID and Josephson devices.

3. 3 Facts about SQUID Superconducting quantum interference device is a mechanism used to measure extremely week signals. Detect change of 100 billion times weaker signal than that moves a compass needle. Have been used to measure the magnetic field in mouse brain to test whether there might be enough magnetism to attribute their navigational ability to an compass. Threshold for SQUID: 10-14 T Magnetic field of heart:10-10 T Magnetic field of brain: 10-13 T Superconducting quantum interference device is a mechanism used o measure extremely week signals, such as changes in the human body’s electromagnetic energy field.. How it does that we will talk about it in the nest slide. Squids have been used to measure the magnetic fields in mouse brains to test whether there might be enough magnetism to attribute their navigational ability to an internal compass. Some energy field of humans are ----Superconducting quantum interference device is a mechanism used o measure extremely week signals, such as changes in the human body’s electromagnetic energy field.. How it does that we will talk about it in the nest slide. Squids have been used to measure the magnetic fields in mouse brains to test whether there might be enough magnetism to attribute their navigational ability to an internal compass. Some energy field of humans are ----

4. 4 SQUID The superconducting quantum interference device (SQUID) consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. The device may be configured as a magnetometer to detect incredibly small magnetic fields -- small enough to measure the magnetic fields in living organisms. Working--: If a constant biasing current is maintained in the SQUID device, the measured voltage oscillates with the changes in phase at the two junctions, which depends upon the change in the magnetic flux. Counting the oscillations allows you to evaluate the flux change which has occurred. A radio frequency (RF) SQUID is made up of one Josephson junction, which is mounted on a superconducting ring. An oscillating current is applied to an external circuit, whose voltage changes as an effect of the interaction between it and the ring. The magnetic flux is then measured. A direct current (DC) SQUID, which is much more sensitive, consists of two Josephson junctions employed in parallel so that electrons tunneling through the junctions demonstrate quantum interference, dependent upon the strength of the magnetic field within a loop. DC SQUID’s demonstrate resistance in response to even tiny variations in a magnetic field, which is the capacity that enables detection of such minute changes. The superconducting quantum interference device (SQUID) consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions. The device may be configured as a magnetometer to detect incredibly small magnetic fields -- small enough to measure the magnetic fields in living organisms. Working--: If a constant biasing current is maintained in the SQUID device, the measured voltage oscillates with the changes in phase at the two junctions, which depends upon the change in the magnetic flux. Counting the oscillations allows you to evaluate the flux change which has occurred. A radio frequency (RF) SQUID is made up of one Josephson junction, which is mounted on a superconducting ring. An oscillating current is applied to an external circuit, whose voltage changes as an effect of the interaction between it and the ring. The magnetic flux is then measured. A direct current (DC) SQUID, which is much more sensitive, consists of two Josephson junctions employed in parallel so that electrons tunneling through the junctions demonstrate quantum interference, dependent upon the strength of the magnetic field within a loop. DC SQUID’s demonstrate resistance in response to even tiny variations in a magnetic field, which is the capacity that enables detection of such minute changes.

5. 5 Material used for construction of SQUID SQUIDs are usually fabricated from either a lead alloy (with 10% gold or indium) and/or niobium. often consisting of the tunnel barrier sandwiched between a base electrode of niobium and the top electrode of lead alloy. More recently developed "High Temperature" SQUIDS are made of a substance called YBCO (chemical formula YBa2Cu3O7-x), Most SQUIDs are fabricated from lead or pure niobium. The lead is usually in the form of an alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed. The base electrode of the SQUID is made of a very thin niobium layer, formed by deposition, and the tunnel barrier is oxidised onto this niobium surface. The top electrode is a layer of lead alloy deposited on top of the other two, forming a sandwich arrangement. More recently developed "High Temperature" SQUIDS are made of a substance called YBCO (chemical formula YBa2Cu3O7-x), and are cooled by liquid nitrogen which is cheaper and more easily handled than liquid helium. They are less sensitive than conventional "Low Temperature" SQUIDS but many applications do not require the extreme sensitivity of the LT SQUID.Most SQUIDs are fabricated from lead or pure niobium. The lead is usually in the form of an alloy with 10% gold or indium, as pure lead is unstable when its temperature is repeatedly changed. The base electrode of the SQUID is made of a very thin niobium layer, formed by deposition, and the tunnel barrier is oxidised onto this niobium surface. The top electrode is a layer of lead alloy deposited on top of the other two, forming a sandwich arrangement. More recently developed "High Temperature" SQUIDS are made of a substance called YBCO (chemical formula YBa2Cu3O7-x), and are cooled by liquid nitrogen which is cheaper and more easily handled than liquid helium. They are less sensitive than conventional "Low Temperature" SQUIDS but many applications do not require the extreme sensitivity of the LT SQUID.

6. 6 SQUID devices The great sensitivity of the SQUID devices is associated with measuring changes in magnetic field associated with one flux quantum. One of the discoveries associated with Josephson junctions was the flux is quantized in units The basic principle of operation is closely linked to flux quantization. This is the phenomenon that the favored states for a loop of superconductor are those where the flux inside is a multiple of the flux quantum. The basic principle of operation is closely linked to flux quantization. This is the phenomenon that the favored states for a loop of superconductor are those where the flux inside is a multiple of the flux quantum.

7. 7 Josephson Junction A Josephson junction is a type of electronic circuit capable of switching at very high speeds when operated at temperatures approaching absolute zero. The ability of certain materials to conduct electric current with practically zero resistance. The Josephson effect is a term given to the phenomenon of current flow across two superconductors separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting oxide barrier—is known as a Josephson junction; The flow of current between the superconductors in the absence of an applied voltage is called a Josephson current, and the movement of electrons across the barrier is known as Josephson tunneling. Two or more junctions joined by superconducting paths form what is called a Josephson interferometer. The Josephson effect is a term given to the phenomenon of current flow across two superconductors separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting oxide barrier—is known as a Josephson junction; The flow of current between the superconductors in the absence of an applied voltage is called a Josephson current, and the movement of electrons across the barrier is known as Josephson tunneling. Two or more junctions joined by superconducting paths form what is called a Josephson interferometer.

8. 8 Operation of junction Assume Hamiltonian for the system can be written as a sum of two Hamiltonians H = H0+ HT where: H0 = normal Hamiltonian for 2 isolated superconductors HT = tunneling Hamiltonian So, this is "right" for tunneling links only. Two superconductors separated by a thin insulating layer can experience tunneling of Cooper pairs of electrons through the junction. The Cooper pairs on each side of the junction can be represented by a wave function similar to a free particle wave function. Two superconductors separated by a thin insulating layer can experience tunneling of Cooper pairs of electrons through the junction. The Cooper pairs on each side of the junction can be represented by a wave function similar to a free particle wave function.

9. 9 Josephson Equations Consider the very simple example of two, identical superconductors separated by a thin insulator. (Typically about 1nm is sufficiently thin). Assume junction is sufficiently large in the x and y direction to ignore edge/boundary effects, and thick enough in z. The governing equations are: The basic equations[2] governing the dynamics of the Josephson effect are where U(t) and I(t) are the voltage and current across the Josephson junction, f(t) is the phase difference between the wave functions in the two superconductors comprising the junction, and Ic is a constant, the critical current of the junction. The critical current is an important phenomenological parameter of the device that can be affected by temperature as well as by an applied magnetic field. The physical constant, is the magnetic flux quantum, the inverse of which is the Josephson constant.The basic equations[2] governing the dynamics of the Josephson effect are where U(t) and I(t) are the voltage and current across the Josephson junction, f(t) is the phase difference between the wave functions in the two superconductors comprising the junction, and Ic is a constant, the critical current of the junction. The critical current is an important phenomenological parameter of the device that can be affected by temperature as well as by an applied magnetic field. The physical constant, is the magnetic flux quantum, the inverse of which is the Josephson constant.

10. 10 DC Josephson Effect No Magnetic field: A current flows, nut no voltage drop, up until the critical current. Past the critical current, normal single electron tunneling is dominant. With magnetic field: Current is: Critical current depends on various properties of the junction , including geometery , material , etc. With no magnetic field This refers to the phenomenon of a direct current crossing the insulator in the absence of any external electromagnetic field, owing to tunneling. Critical current: under magnetic field write on board I = Ic[ sin( @/@ 0 )/(@ /@ 0 )] This DC Josephson current is proportional to the sine of the phase difference across the insulator, and may take values between - Ic and Ic. Critical current depends on various properties of the junction , including geometery , material , etc. With no magnetic field This refers to the phenomenon of a direct current crossing the insulator in the absence of any external electromagnetic field, owing to tunneling. Critical current: under magnetic field write on board I = Ic[ sin( @/@ 0 )/(@ /@ 0 )] This DC Josephson current is proportional to the sine of the phase difference across the insulator, and may take values between - Ic and Ic.

11. 11 With no magnetic field, static potential: Integrating equation for ? : We can substitute into our other equation and get : From this, we get a time varying current with frequency AC Josephson Effect Apply voltage, not current, across the jucntion With a fixed voltage UDC across the junctions, the phase will vary linear with time and the current will be an AC current with amplitude Ic and frequency 2e/h UDC. This means a Josephson junction can act as a perfect voltage-to-frequency converter. Apply voltage, not current, across the jucntion With a fixed voltage UDC across the junctions, the phase will vary linear with time and the current will be an AC current with amplitude Ic and frequency 2e/h UDC. This means a Josephson junction can act as a perfect voltage-to-frequency converter.

12. 12 AC Josephson Effect With varying potential: Do similar analysis as static potential case. It turns out that this has dc component but when qVo/wh = n (where n= integer) Dc current has spikes at regularly values of Vo Total current has steps at these points.

13. 13 If the phase takes the form f(t) = f0 + n?t + asin(?t), the voltage and current will be The DC components will then be Inverse AC Josephson Effect We can infer Hence, for distinct DC voltages, the junction may carry a DC current and the junction acts like a perfect frequency-to-voltage converter. We can infer Hence, for distinct DC voltages, the junction may carry a DC current and the junction acts like a perfect frequency-to-voltage converter.

14. 14 Electron pairs coupling over range of hundreds of nanometers are called cooper pair. These coupled electron can take character of boson and condense into ground state. Cooper pair The behavior of superconductors suggests that electron pairs are coupling over a range of hundreds of nanometers, these have orders of magnitude larger than the lattice spacing. Called Cooper pairs, these coupled electrons can take the character of a boson and condense into the ground state. This pair condensation is the basis for the BCS theory of superconductivity. The effective net attraction between the normally repulsive electrons produces a pair binding energy on the order of mille-electron volts, enough to keep them paired at extremely low temperatures. Boson Definition: any of a class of elementary particles not subject to the exclusion principle that have spins of zero or an integral number, as photons or mesons. A composite atom can also be referred to as a boson or bosonic atom if the sum of the spin states of all of its subcomponents are 0 or an integral number. The behavior of superconductors suggests that electron pairs are coupling over a range of hundreds of nanometers, these have orders of magnitude larger than the lattice spacing. Called Cooper pairs, these coupled electrons can take the character of a boson and condense into the ground state. This pair condensation is the basis for the BCS theory of superconductivity. The effective net attraction between the normally repulsive electrons produces a pair binding energy on the order of mille-electron volts, enough to keep them paired at extremely low temperatures. Boson Definition: any of a class of elementary particles not subject to the exclusion principle that have spins of zero or an integral number, as photons or mesons. A composite atom can also be referred to as a boson or bosonic atom if the sum of the spin states of all of its subcomponents are 0 or an integral number.

15. 15 Applications Magneto encephalography (MEG) Applications of MEG include mapping Somatosensory and motor cortices. Foetal Examination: SQUID are used to measure the minute magnetic fields generated by baby’s heart MEG is a non-invasive method of recording minute magnetic fields emanating from the brain. The MEG device is also known as a Neuromagnetometer. It consist of a multi-million dollar helmet-like instrument which is placed around the subject's head. The helmet is made up of 2 probes or dewars which each contain 37 SQUIDs. The SQUIDS are kept cool by bathing the magnetic detector coils at a temperature of -269 degrees Celcius and the device works by picking up the tiny magnetic fluxes from the brain and using them to induce small currents in the coils. Every single quantum of magnetic field is enough to produce a measurable current in the coil. The current in the coil then induces a magnetic field in the SQUID. illustrates the data typically achieved from MEG. The areas where responses are strongest are quite clear… SQUIDs are used to measure the minute magnetic fields generated by the baby's heart. Generally we require sensitive and reliable low Tc SQUIDs which are cooled at liquid helium temperature. This finding follows the ability to distinguish the mother's heartbeats from the baby's. Such an application allows diagnosis of foetal heart conditions in a matter of minutes and gives generally a higher quality than the present ultrasound methods. This makes possible early detection of heart ailments which could lead to life-saving treatment during or immediately after the pregnancy. It works through a SQUID-based sensor which is placed around the mother's abdomen. It has the added advantages that the data is unaffected by foetal fat, that it has a higher resolution than an electrocardiogram and is gives more sensitivity at a deeper depth. Separate measurements can be performed on twins and an electrocardiogram can be achieved as soon as the 20th week of the pregnancy. MEG is a non-invasive method of recording minute magnetic fields emanating from the brain. The MEG device is also known as a Neuromagnetometer. It consist of a multi-million dollar helmet-like instrument which is placed around the subject's head. The helmet is made up of 2 probes or dewars which each contain 37 SQUIDs. The SQUIDS are kept cool by bathing the magnetic detector coils at a temperature of -269 degrees Celcius and the device works by picking up the tiny magnetic fluxes from the brain and using them to induce small currents in the coils. Every single quantum of magnetic field is enough to produce a measurable current in the coil. The current in the coil then induces a magnetic field in the SQUID. illustrates the data typically achieved from MEG. The areas where responses are strongest are quite clear… SQUIDs are used to measure the minute magnetic fields generated by the baby's heart. Generally we require sensitive and reliable low Tc SQUIDs which are cooled at liquid helium temperature. This finding follows the ability to distinguish the mother's heartbeats from the baby's. Such an application allows diagnosis of foetal heart conditions in a matter of minutes and gives generally a higher quality than the present ultrasound methods. This makes possible early detection of heart ailments which could lead to life-saving treatment during or immediately after the pregnancy. It works through a SQUID-based sensor which is placed around the mother's abdomen. It has the added advantages that the data is unaffected by foetal fat, that it has a higher resolution than an electrocardiogram and is gives more sensitivity at a deeper depth. Separate measurements can be performed on twins and an electrocardiogram can be achieved as soon as the 20th week of the pregnancy.

16. 16 Applications Further Applications of Josephson Devices Magnetic Sensors Gradiometers Oscilloscopes Decoders Analogue to Digital converters Samplers Oscillators Microwave amplifiers Sensors for biomedical, scientific and defense purposes Digital circuit development for Integrated circuits Microprocessors Random Access Memories (RAM’s) Further Applications of Josephson Devices Josephson devices are continuing to find more and more applications. Such applications include Magnetic Sensors Gradiometers Oscilloscopes Decoders Analogue to Digital converters Samplers Oscillators Microwave amplifiers Sensors for biomedical, scientific and defense purposes Digital circuit development for Integrated circuits Microprocessors Random Access Memories (RAM’s) Further Applications of Josephson Devices Josephson devices are continuing to find more and more applications. Such applications include Magnetic Sensors Gradiometers Oscilloscopes Decoders Analogue to Digital converters Samplers Oscillators Microwave amplifiers Sensors for biomedical, scientific and defense purposes Digital circuit development for Integrated circuits Microprocessors Random Access Memories (RAM’s)

17. 17 References http://en.wikipedia.org/wiki/SQUID http://hyperphysics.phy-astr.gsu.edu/hbase/solids/squid.html Steven T. Ruggiero, David A. Rudman, Superconducting Devices. New York: McGraw-Hills, 1975. Barone A, Paterno G. Physics and Applications of the Josephson Effect. New York: John Wiley & Sons; 1982. http://whatis.techtarget.com/definition/0,,sid9_gci816722,00.html http://en.wikipedia.org/wiki/Josephson_junction http://hyperphysics.phy-astr.gsu.edu/hbase/solids/squid.html#c3 http://www.abdn.ac.uk/physics/case/squids.html

18. 18 Questions? Comments?