Lecture: April 3, 2019

Macroscopic Quantum Phenomenon

• (1) Superconductivity

• (2) Quantization of Resistance

• (3) Bose Einstein Condensation

• Lasers

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Superconductivity

Nobel Prizes:

(1) Heike Kamerlingh Onnes (1913): Experimental Discovery of Superconductivity: About

4 degrees Kelvin (-452 degrees Fahrenheit, -268 degrees Celsius),

(2) John Bardeen, Leon N. Cooper, and J. Robert Schrieffer (1972), ”for their jointly

developed theory of superconductivity, usually called the BCS-theory”

(3) Georg Bednorz and K. Alex Mller (1987) - High Temperature Superconductivity: 30

degrees Kelvin.

( Latest : about 92 degrees K

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion

of magnetic fields occurring in certain materials when cooled below a characteristic critical

temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911

in Leiden.

Two important properties of superconductors: (1) Zero Resistance, so they conduct without

heating the wires (2) Repel Magnetic Field

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Applications:

Two important applications are in MRI and particle accelerators. This is because

superconductors give us very powerful electromagnets.

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Superconducting magnet: An electromagnet made from coils of superconducting wire. They

must be cooled to very low temperatures during operation.

In its superconducting state the wire has no electrical resistance and therefore can conduct

much larger electric currents than ordinary wire, creating intense magnetic fields.

Superconducting magnets can produce greater magnetic fields than all but the strongest

non-superconducting electromagnets and can be cheaper to operate because no energy is dissipated

as heat in the windings.

The most widely used application for superconductors is an MRI machine commonly found in

hospitals. Only a superconductive system could allow the energy required to generate a magnetic

field that powers an MRI, which can be anywhere from 2,500 times to 10,000 times the strength

of Earths magnetic field, to be economical.

Another important application is in particle accelerators, like the kind used in CERNs Large

Hadron Collider (LHC) or its proposed Future Circular Collider.

If the MRI machine sounds powerful, the LHC is an absolute beast. Sending trillions of

particles around 27km of tunnels at speeds close to the speed of light, keeping the particle beam

stable and moving along the precise path requires a magnetic field of immense power, more than

100,000 times the Earths magnetic field. This requires an enormous amount of energy, the kind

that superconducting coils can provide.

The Future of Superconductivity

There is a lot we donot know about superconductive materials, and we are developing new

applications for superconductors every day.

The hope is to one day use superconductivity in power transmissions, which would

dramatically reduce energy costs around the world. Mag-lev trains, which use superconductivity

to hover a train car above the rail, thereby eliminating friction that might slow a train down, may

be the future of transportation.

Who knows? Maybe one day we will have electronics that utilize superconductors to give us

smartphones that only need to be charged once a month or more.

Its anyones guess, but with the rapid advances in our technology, well all likely see

superconductivity in our lives as a regular feature sooner rather than later.

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QUANTUM HALL EFFECT

Resistance R of some sheets of material, in a magnetic field assumes quantized values that

depend on charge of the electron and Planck constant.

Conductance = 1Resistance

= ne2

h, n = 1, 2, 3....

• Why is the resistance quantized

• Why is this quantization observed with extreme precision ( better than one part in billion )

• Why is the conductivity independent of geometry of the sample and impurities in the

sample ??

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Nobel Prizes:

(1) Von Klitzing in 1980, who was at the time a Heisenberg fellow at the University of

Wrzburg

(2) Robert Laughlin, 1990 ( For theoretical work on fractional quantum Hall effect )

(3) David Thouless for theoretical explanation of Quantum Hall Effect.

This mysterious phenomenon was explained by David Thouless described theoretically, using

TOPOLOGY and was awarded Nobel prize in 2016.

<https://www.nobelprize.org/prizes/physics/2016/

prize-announcement/>

Bose Einstein Condensate

Macroscopic Number of Bosons at very low temperature form a new kind of quantum state

that exists in lowest possible quantum state.

This state was first predicted, generally, in 1924-25 by Satyendra Nath Bose and Albert

Einstein.

On June 5, 1995 the first gaseous condensate was produced by Eric Cornell and Carl Wieman

at the University of Colorado at Boulder NIST-JILA lab, in a gas of rubidium atoms cooled to 170

nanokelvin.

Shortly thereafter, Wolfgang Ketterle at MIT demonstrated important BEC properties. For

their achievements Cornell, Wieman, and Ketterle received the 2001 Nobel Prize in Physics.

BEC is a new state of matter where particles loose their identity as de-Broglie wave length of

different particles overlap. Such a state of matter is a quantum mechanical state whose properties

can be tamed.

Nobel Prizes:

The Nobel Prize in Physics 2001 was awarded jointly to Eric A. Cornell, Wolfgang Ketterle

and Carl E. Wieman ”for the achievement of Bose-Einstein condensation.

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APPLICATIONS: They have applications in clock precision, new type of lasers and sensors

and also exploring new phenomena in physics.

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