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Home , Douglas Osheroff, Ivar Giaever, Olli Lounasmaa

Superconductors & Related Achievements Concepts of in Physics through Concept Mapping Contents Chapter 1 : Introduction 1.1 What is Learning? 1.2 Concept Mapping 1.3 Concept Mapping in Present Context Chapter 2 : Concepts of Nobel Laureates through Concept Mapping 2.1 Matter at Low Temperature : Concepts of for the year 1913 2.1.1. Introduction 2.1.2. Achievement of Low Temperatures by Kamerlingh Onnes 2.1.3. Effects of Low Temperature 2.1.4. 2.2 The Theory of Liquid : Concepts of Nobel Prize in Physics for the year 1962 2.2.1. Introduction 2.2.2. New State of Liquid Helium 2.2.3. Properties of Superfluid according to Landau 2.2.4. Properties of Helium-3 2.3 Theory of Superconductivity : Concepts of Nobel Prize in Physics for the year 1972 2.3.1. Introduction 2.3.2. Principle of Superconductivity 2.3.3. Superconductivity due to Cooper Pairs 2.3.4. Applications of Superconductors 2.4 Tunnelling in Superconductors : Concepts of Nobel Prize in Physics for the year 1973 2.4.1. Introduction 2.4.2. Laws of Modern Physics 2.4.3. Initial Discovery of Tunnelling Effect 2.4.4. Superconductor on the basis of Tunnelling Effect 2.4.5. 2.4.6. Applications of Tunnelling Effect 2.4.7. Applications of Josephson Effect 2.5 Helium II - The Superfluid : Concepts of Nobel Prize in Physics for the year 1978 2.5.1. Introduction 2.5.2. Helium II - The Superfluid 2.6 High Temperature Superconductivity - Concept of Nobel Prize in Physics for the year 1987 2.6.1. Introduction 2.6.2. Meissner Effect 2.6.3. High Temperature Superconductor 2.7 in Helium-3 : Concept of Nobel Prize in Physics for the year 1996 2.7.1. Introduction 2.7.2. Quantum Fluids 2.7.3. Isotopes of Helium 2.7.4. Properties of Helium-4 2.7.5. Properties of Helium-3 - Under Normal Conditions 2.7.6. Properties of Helium-3 - Under Special Conditions 7.7. in Helium-3 2.7.8. Superfluidity in Helium-3 2.7.9. Properties of Superfluidity in Helium-3 2.7.10. Application of Superfluidity in Helium-3 2.8 Development of Methods to Cool and Trap Atoms with Laser Light : Concepts of Nobel Prize in Physics for the year 1997 2.8.1. Introduction 2.8.2. Principle of Optical Molasses 2.8.3. Slowing down Atoms with Photons 2.8.4. Doppler Cooling and Optical Molasses 2.8.5. Magneto Optical Trap 2.8.6. Zeeman Slower 2.8.7. Optical Lattice 2.8.8. Formation of Dark State 2.8.9. Velocity Distribution at Recoil Temperature 2.8.10. Applications Round the Corner 2.9 Bose Einstein Condensation in Dilute Gases : Concepts of Nobel Prize in Physics for the year 2001 2.9.1. Introduction 2.9.2. Nobel Laureates of 2001 2.9.3. Types of Particles

2.9.4. New State of Matter - Bose Einstein Condensation 2.9.5. Super Atom 2.9.6. Magneto Optical Trap to exceed Doppler Limit 2.9.7. Evaporative Cooling of Alkali Atoms 2.9.8. Reality of Bose Einstein Condensation (BEC) 2.9.9. Prospects of Bose Einstein Condensation Chapter 3 : Conclusion 3.1 Effectiveness of Concept Mapping CHAPTER 1 INTRODUCTION 1.1 What is learning? Every branch of human activity has made rapid progress like discovery of Windows XP, Cloning in animal and human physiology and embracing technology in various fields like banking, communication, industries, education etc.The changes in many fields are reflected in education, where, the knowledge is not merely imparted, but makes the learner apply it in various situations. Knowledge in our minds is specifically defined as a hierarchical structure of concepts, in which inclusive concepts occupy a portion at the apex of the structure and subsume progressively less inclusive and more highly differential subconcepts and factual data. Acquisition of knowledge is the learning of organized information. According to Ausubel, the most important single factor influencing learning is what the learner already knows. Thus meaningful learning results when a person consciously and explicitely ties new knowledge to relevant concepts they already possess. Rote learning on the other hand results, when new knowledge is arbitrarily incorporated into the cognitive structure. That is the material is not linked with existing concepts in cognitive structure and form ‘discrete and isolated traces’. Knowledge in various fields is acquired to enrich ones life by making use of the technological advances. Science Education will generally impart knowledge in such a way that students will learn what they are taught and transfer what they have learnt to a more complex situation. Since superconductors and related achievements have wide range of applications in various fields, I thought a better understanding of above concepts would be more useful. Hence in this book, the concepts of superconductors and related achievements ( concepts of Nobel Laureates of Physics ) are explained through Concept Mapping, a strategy which enhances meaningful learning. 1.2 Concept Mapping The Concept Map is a device for representing the conceptual structures of a subject discipline in a two dimensional form. It is a technique for representing knowledge in graphs. Knowledge graphs are networks of concepts. Networks consist of nodes and links. Nodes represent concepts and links represent the relations between concepts. Concept Maps organize knowledge into a hierarchical structure in which subordinate concepts are subsumed under superordinate concepts. Rote learning would be just a series of propositions that are memorized, but not related to each other. With mapping, new concepts and propositions are connected into a whole existing relevant framework. Therefore, a Concept Map may be defined as a schematic device for representing a set of meanings embedded in a framework of propositions which enhances meaningful learning. 1.3 Concept Mapping in Present Context In this book, the concepts of superconductors and related achievements for which Nobel Prizes have been awarded are expressed through Concept Maps. Simple explanations precede the Concept Maps and I am sure the reader will enjoy going through the book and get enriched in knowledge. CHAPTER 2 Concepts of Nobel Laureates through Concept Mapping 2.1 Matter at Low Temperature : Concepts of Nobel Prize in Physics for 1913 2.1.1 Introduction The Dutch was awarded the Nobel Prize in physics for 1913 for his investigations on the properties of matter at low temperatures which led to the production of liquid helium. Initially he was interested in Vanderwaal's theory of gases, according to which all gases behave in the same way when the units of pressure, temperature and volume are adapted to account for weak forces of attraction between molecules. By studying the gases at low temperatures, Kamerlingh Onnes believed that important information could be obtained to verify the conformity of substances. The following Concept Maps would illustrate how he investigated the properties of substances at low temperatures, and paved way for the discovery of superconductor. 2.1.2. Achievement of Low Temperatures by Kamerlingh Onnes The name of the scientist, Kamerlingh Onnes who has achieved low temperatures, occupies the apex of the Concept Map 1. The first branch deals with his field of specialization, cryogenics, to study the properties of substances at low temperatures.The second branch indicates that hydrogen was liquefied in 1906 and the third branch denotes that helium was liquefied in 1901 at 4 K. The last branch deals with low temperatures achieved by him at 1.38 K and 1.04 K respectively using liquid helium. Hence the most general concept, the name of the scientist, is followed by progressively more specific and less inclusive concepts arranged in hierarchical manner.

2.1.3. Effects of Low Temperature The most general concept, the name of the scientist ( Kamerlingh Onnes ) is at the apex of the Concept Map 2. The first branch deals with his achievement, low temperature for studying properties of substances. The next branch indicates that random motion of molecules will be minimum at low temperature. The third branch indicates the investigations of various fields like absorption spectra of elements, phosphorescence of various compounds, viscosity of liquefied gases and magnetic properties of substances.

2.1.4. Superconductivity In the third Concept Map, the first segment deals with the discovery of superconductivity, where electrical resistance of certain metals vanishes at low temperature. The second segment mentions the theory, which explains superconductivity. The third segment mentions the Nobel Prize won by the scientist for his investigation on properties of matter at low temperature. The last segment mentions the applications of superconductivity to various fields. . 2.2 The Theory of Liquid Helium : Concepts of Nobel Prize in Physics for the Year 1962 2.2.1 Introduction Lev Davidovich Landau was awarded the Nobel Prize in Physics for 1962 for his investigtion on condensed matter i.e. matter in the and liquid state. In 1937 he joined the Institute for Physical Problems in Moscow run by famous physicist Kapitsa. Together they performed interesting experiments on liquid helium.They found that natural helium when cooled to 2 degrees above 0 K exhibited strange properties. The Concept Maps presented in this section illustrate the New State of Matter, its Properties, and Isotope of Helium (Helium-3) and its Properties at very Low Temperatures. His theories of liquid helium are an achievement of great and profound importance. 2.2.2 New State of Liquid Helium The scientist Kapitsa liquefied and cooled natural helium to about 4 degrees above 0 K. He found that when it was further cooled to about 2 degrees, it was transformed into a new state known as superfluid, having strange properties as it can flow through fine capillaries and slits not done by other liquids. In this Concept Map the most general concept natural helium is followed by less general more specific ones like liquefaction, the temperature of occurrence, new state, its name and behaviour arranged in hierarchical manner.

2.2.3. Properties of Superfluid according to Landau In the Concept Map 2, the scientist explains the superfluid state by considering quantized state of motion of whole liquid instead of single state of atom. In the second segment, he explains the excited states of liquid by motion of fictive particles called quasi particles. The third segment deals with mechanical properties of quasi particles, confirmed by scattering of neutrons in liquid helium. The last segment deals with the discovery of waves in liquid helium, which he termed as second sound.

2.2.4. Properties of Helium-3 This Concept Map deals with isotopes of helium atom namely helium-4 and Helium-3. Helium-3 has properties different from helium-4, and has many similarities with superfluid of helium-4. These properties are valid at very low temperature less than 1/10 of degree from 0 K and Landau predicted a new wave propagation called zero sound.

2.3 Theory of Superconductivity : Concepts of Nobel Prize in Physics for the year 1972 2.3.1 Introduction , Professor of Electrical Engineering & Physics at the University of Illinois, Leon N. Cooper, Professor of Physics at Brown University and , Professor of Physics at the University of Pennsylvania were awarded the Nobel Prize in Physics for 1972 for their jointly developed theory of superconductivity, usually called the BCS theory. The phenomenon of superconductivity was initially discovered by Kamerlingh Onnes. But the explanation was successfully given by the above scientists based on interaction between the and crystal lattice leading to formation of Cooper Pairs. The following Concept Maps illustrate the Principle of Superconductors i.e. the Formation of Cooper Pairs and the Applications of Superconductors. The applications of superconductors have confirmed the validity of the theoretical concepts and ideas developed by Bardeen, Cooper and Schrieffer. 2.3.2. Principle of Superconductivity The Concept Map under this section deals with superconductivity, which has zero electrical resistance. But the mechanism remained a mystery till Bardeen, Cooper and Schrieffer explained the phenomenon due to interaction between electrons and crystal lattice.

2.3.3. Superconductivity due to Cooper Pairs The second Concept Map under this section deals with Superconductivity due to Cooper Pairs. Bardeen, Cooper and Schrieffer explained superconductivity with the coupling of electrons to the vibrations of crystal lattice. The coupling of electrons lead to formation of bound pairs of electrons called Cooper Pairs, which are strongly coupled to each other to form complex collective pattern. In this state a fraction of conduction electrons are coupled together to form superconducting state leading to structure of correlated many- state. In this superconducting state, single pair of electrons is not broken, without perturbing all others and hence requires a large amount of energy that must exceed a critical value.

2.3.4. Applications of Superconductors The Concept Map under this section deals with Superconductors explained by Bardeen, Cooper and Schrieffer. The theory proposed by them is known as BCS theory. The first segment deals with remarkable properties of superconductors by means of correlated many-electron state. The second segment deals with the new effects predicted by BCS theory, which stimulated activity in theoretical and experimental research like quantum mechanical tunnelling, magnetic flux quantization and Josephson effects. . 2.4 Tunnelling in Superconductors : Concepts of Nobel Prize in Physics for the year 1973 2.4.1 Introduction Leo Ekasi (USA), (USA) and Brian D. Josephson (UK) were jointly awarded the Nobel Prize in Physics for 1973 for their discoveries regarding tunnelling phenomena in . The Concept Maps illustrate the Nature of Particles and the Laws that govern them, the Tunnelling Effect of Electrons, Explanation of Superconductors on the basis of Tunnelling Effect, Josephson Effect, Applications of Tunnelling Effect and Josephson Effect. The discoveries of these have a close relation. The pioneering work by Ekasi in 1958 provided the foundation for Giaever’s work in 1960 on tunnelling in superconductors, which in turn paved way for the discovery of Josephson Effect. Their discoveries have opened up new area for research and have led to an increasing number of important technical applications. 2.4.2. Laws of Modern physics The Concept Map under this section explains the behaviour of electrons, which according to quantum mechanics behave like wave, described by solution of wave equation. The electrons with wave nature can penetrate a barrier causing tunnelling effect, which is forbidden for classical objects.

2.4.3. Initial Discovery of Tunnelling Effect Leo Ekasi and Ivar Giaever studied tunnelling effect. Leo Ekasi explained the tunnelling effect in solids that led to discovery of electronic device called tunnel diode. Ivar Giaever demonstrated tunnelling of electrons through a sandwich with an extremely thin oxide layer surrounded with metal either in superconducting state on both sides or in normal state on one side and in superconducting state on the other side.

2.4.4. Superconductor on the basis of Tunnelling Effect Ivar Giaever demonstrated tunnelling of electrons and explained the existence of in a superconductor, which is one of key predictions of BCS theory. He also developed a method into accurate spectroscopy to study the properties of superconductors.

2.4.5. Josephson Effect obtained a new calculation of current, flowing through a barrier leading to a new phenomenon called Josephson Effect. It implies that super current can flow through the barrier even with zero applied voltage across the barrier. It also implies that fixed voltage would cause alternating current to flow through the barrier with a frequency in the microwave region.

2.4.6. Applications of Tunnelling Effect Leo Ekasi, Ivar Giaever and Brian D. Josephson won the Nobel Prize in Physics for 1973 for their discoveries regarding tunnelling phenomena in solids. Their discovery led to development of electronic devices namely tunnel diodes, tunnel detectors, tunnel transistors and some forms of lasers.

2.4.7. Applications of Josephson Effect Josephson Effect by Brian D.Josephson led to revision of values of fundamental constants. It also led to the development of new method to measure voltage. The new interferometry developed by above effect helped development of variety of experimental tools of increased range, sensitivity and precision.

2.5 Helium II: The Superfluid-Concepts of Nobel Prize in Physics for the year 1978 2.5.1 Introduction In 1978 the Nobel Prize in Physics was awarded in two equal parts. One part of the Nobel Prize was awarded to Professor Leontivitch Kapitsa, USSR for his basic inventions and discoveries in the area of low temperature physics. The Concept Map Superfluid illustrates the production and properties of superfluid. Kapitsa’s discoveries, ideas and new techniques have been basic to the modern expansion of the science of low temperature physics. 2.5.2. Helium II - The Superfluid Piotr Leontevitch Kapitsa constructed a new device, which cooled the gas by periodic expansion. The new device was used for producing liquid helium which, when exposed to temperature less than 2.3 K above 0 K changed into unusual form and was termed Helium II. Helium II had great internal mobility and vanishing viscosity and hence was termed as superfluid. Kapitsa's experiments on properties of Helium II indicated a macroscopic quantum state with zero entropy i.e. with perfect atomic order. Hence it was termed as quantum fluid.

2.6 High Temperature Superconductivity : Concept of Nobel Prize in Physics for the year 1987 2.6.1 Introduction The Nobel Prize in Physics for 1987 was awarded jointly to Dr.Johannas George Bednorz and Professor Dr.Karl Alexander Muller both researchers at the I.B.M. Zurich Research Laboratory for their important breakthrough in the discovery of superconductivity in ceramic materials. Superconductivity has been known since 1911, which arises when a superconducting material is cooled to a fairly low critical temperature. Bednorz and Muller abandoned the conventional materials and produced a ceramic material which would become superconductor at much higher temperature i.e. 12 degrees above 0 K. The Concept Maps presented in this section explain the Meissner Effect and High Temperature Superconductor (HTSC). Bednorz and Muller stand out clearly as discoverers of this specific superconductivity. They have inspired other scientists to work with related materials which have become superconductors and hence transition temperatures more than 90 degrees above 0 K were reached during the first few months of 1987 in the , China, Japan and Europe. 2.6.2. Meissner Effect George Bednorz and Alex Muller were awarded the Nobel Prize in Physics for 1987 for their discovery of superconducting materials. The superconducting materials, when cooled to low critical temperature produce superconductivity where electric current flows with no resistance. During superconductivity, Meissner Effect occurs where magnetic field cannot, or can only partly, penetrate the material.

2.6.3. High Temperature Superconductor Bednorz and Muller abandoned superconductors of conventional materials and used oxides, which apart from containing oxygen include copper and one or more of rare earth metals. The copper atoms present in the material transport electrons, which interact strongly with surrounding crystal than in normal electrical conductors. They also added barium to crystal of lanthanum copper oxide to produce ceramic materials of HTSC (High Temperature Super Conductor), which are chemically stable.

2.7 Super Fluidity in Helium-3 : Concept of Nobel Prize in Physics for the year 1996 2.7.1. Introduction The Nobel Prize in Physics for 1996 was awarded to Professor David M.Lee, USA, Professor Douglas D.Osharoff, USA, and Professor Robert C.Richardson, Cornell University USA, for their discovery of superfluidity in helium-3. Nine Concept Maps illustrate the Quantum Fluid, Isotopes of Helium and their Properties, Phase Transition in Helium-3, Superfluidity in Helium-3, Properties and Applications of Superfluidity. By studying the phenomenon of superfluidity in helium-3 the scientists have paved way for better understanding of matter at low temperatures. 2.7.2. Quantum Fluids Classical physics cannot explain superfluidity occurring in liquid helium when temperature approaches absolute zero (-273.150 C), since atoms lose their randomness and move in co-ordinated manner in each movement. This behaviour would cause liquid to lack all inner friction. Hence it would make liquid to over flow a cup, flow through very small holes and exhibit non-classical effects. Hence the behaviour of superfluidity can be explained on the basis of quantum mechanics.

2.7.3. Isotopes of Helium Helium exists in two forms with fundamentally different properties. They are Helium-4 and Helium-3. Helium-4 has even number of particles and hence termed as bosons. It is commonest and its nucleus has 2 protons and 2 neutrons surrounded by electron shell with 2 electrons. Helium-3 occurs in very small fraction and its nucleus has 2 protons and 1 neutron. Since it has odd number of particles it is termed as fermion. The nucleus of Helium-3 is also surrounded by electron shell with 2 electrons.

2.7.4. Properties of Helium-4 Helium-4 obeys Bose Einstein statistics. Under certain circumstances it condenses in the state that possesses least energy, causing phase transition known as Bose Einstein condensation. When temperature comes closer to 0 K, it causes superfluidity, which is a Bose Einstein Condensate of Helium atom and is explained by and .

.2.7.5. Properties of Helium-3 : Under Normal Conditions Helium-3 obeys Fermi Dirac statistics. It is not normally condensable in the lowest energy state. It cannot cause superfluidity even though it can be liquefied at temperature above 0 K.

2.7.6. Properties of Helium-3 : Under Special Conditions Helium-3 can be condensed in a complicated manner as proposed in BCS theory for superconductivity in metals. The electrons in cooled metals combine in twos to form Cooper Pairs and behave as bosons undergoing Bose Einstein condensation to form Bose Einstein Condensate. Thus Helium-3 can be condensed in a complicated manner combining superfluidity of Helium-4 and superconductivity in metals.

2.7.7. Phase Transition in Helium-3 studied the pressure inside a sample containing a mixture of liquid Helium-3 and solid Helium-3 ice. The sample was subjected to increase in external pressure for about 40 minutes followed by decrease in external pressure. He observed the changes in slope of the curve ( drawn between pressure and time ) and noted the temperatures confirming phase transition of Helium-3 and the existence of superfluid.

2.7.8. Superfluidity in Helium-3 of Helsinki University of Technology confirmed the superfluid nature of new liquid Helium-3. He confirmed the superfluid nature by measuring the damping of an oscillating string placed in sample and found the damping diminished by a factor of 1/1000 when the surrounding liquid underwent phase transition to the new state. This phenomenon showed the absence of inner friction i.e. viscosity.

2.7.9 Properties of Superfluidity in Helium-3 The superfluid nature of new liquid Helium-3 was found to exhibit atleast three different phases, where one of them occurs only if the sample is placed in magnetic field. It is found that the superfluid nature of new liquid Helium-3 is anisotropic. It resembles properties of liquid crystals, has different properties in different spatial directions, which does not occur in Classical Physics. The superfluid rotating at a speed exceeding critical value produces microscopic vortices. They were studied using optic fibres to observe how they affect surface of rotating Helium-3 at temperature of 1/1000 degree from 0 K.

2.7.10. Applications of Superfluidity in Helium-3 Superfluidity in Helium-3 where phase transition occurs have been studied to test cosmic strings formed in the universe. The cosmic strings might have arisen due to rapid phase transition occurred within fraction of a second after big bang. Neutrino induced nuclear reactions were performed to heat superfluid Helium-3 which when cooled formed balls of vortices which are prescribed to correspond to the cosmic strings.

2.8 Development of Methods to Cool and Trap Atoms with Laser Light: Concepts of Nobel Prize in Physics for the Year 1997 2.8.1.Introduction The Nobel Prize in Physics for 1997 was awarded jointly to Professor , Stanford University, USA, Professor Claude Cohen Tannoudgi, France, and Dr.William D.Phillips, USA for development of methods to cool and trap atoms with laser light. Nine Concept Maps are presented in this section. They illustrate Optical Molasses, Slowing Down of Atoms with Photons, Doppler Cooling and Magneto Optical Trap, Zeeman Slower, Optical Lattice, Distribution of velocity at Recoil Temperature, Formation of Dark State and Applications Round the Corner. The Nobel Laureates have developed several methods of using laser light to cool gases to the 1 µK range and keeping the chilled atoms floating or captured in different kinds of ‘atomic traps’. The new methods of investigation developed by them have formed the basis for the discovery of Bose Einstein Condensation in atomic gases. A start has been made on the design of atomic interferometer and atomic lasers which may be used in the future to manufacture very small electronic components. 2.8.2. Principle of Optical Molasses The scientists Steven Chu, Cohen-Tannoudgi and William D. Phillips developed methods to cool gases to micro kelvin range by keeping chilled atoms floating in different atomic traps. The laser light functions as thick liquid or optical molasses where atoms are slowed down. The different methods developed by scientists led to design of precise atomic clocks to be used in space navigation and accurate determination of position.

2.8.3. Slowing Down Atoms with Photons Light is made up of photons. These photons can transfer its momentum during collision to atoms which absorb one of photons if they have right energy. The atom takes its energy and momentum and is slowed down somewhat. The atom during collision, after extremely short time emits photons which have momentum and give atom a small recoil velocity, which decreases after many absorption and emission of photons.

2.8.4. Doppler Cooling and Optical Molasses Steven Chu and his co-workers devised a method where sodium atoms form a beam in vacuum, stopped by opposite laser beam and then was subjected to intersection of 6 laser beams. The six laser beams were opposed in pairs and arranged in three directions at right angles to each other. At the junction of intersection of laser beams the sodium atoms were met by photons of right energy and pushed back into area where six laser beams intersected and the atoms move as in thick liquid called Optical Molasses. At the junction of intersection of six laser beams, the temperature was about 240 µK and millions of chilled atoms were formed. These atoms travel with a speed of 30 cm/s, which agreed with Doppler limit of critical value. At the point of intersection of six laser beams, light in all beams got red shifted compared with colour absorbed by stationary sodium atoms.

2.8.5. Magneto Optical Trap Doppler cooling does not capture atoms due to gravity since Optical Molasses is crossed in about one second. Hence the scientists used MOT (Magneto Optical Trap) involving six laser beams as in previous experiment along with two magnetic coils giving slightly varying magnetic field. The beams intersect with minimum area and the slightly varying magnetic field affect characteristic energy levels of atoms known as Zeeman Effect. This effect develops a force greater than gravity and draws atoms into middle of trap for experimental studies.

2.8.6. Zeeman Slower William D. Phillips and his co-workers used magnetic fields in slowing down and stopping atoms into slow atomic beam. They used Zeeman Slower, which is a coil with varying magnetic field. Along its axis, the atoms are retarded by opposite laser beam. Thus Zeeman Slower stopped and captured sodium atoms in pure magnetic trap where temperature is very low.

2.8.7. Optical Lattice William D. Phillips and his co-workers showed the recoil velocity an atom gains when it emits a photon corresponds to a temperature known as recoil temperature. For sodium atom, the recoil temperature is 2.4 µK and for heavier cesium atom it is 0.2 µK. The scientists finally showed that with suitable laser settings the atoms that are trapped group at regular intervals in space forming Optical Lattice. This occurs when the distance separating atomic grouping is one light wavelength.

2.8.8. Formation of Dark State Doppler Cooling was used by Claude Cohen Tannoudji and is set by recoil velocity of an atom since slowest atoms also continue to absorb and emit photons. This gives atom a small speed and hence the gas has temperature. But Tannoudji used Doppler Cooling to convert slowest atoms to Dark State where atoms do not absorb photons, and are made to neglect all photons in Optical Molasses making it possible to achieve lower temperature.

2.8.9. Velocity Distribution at Recoil Temperature Claude Cohen Tannoudgi used Doppler Cooling and showed that the method functions in one, two and three dimensions. He used helium atom whose recoil limit is 4 µK. In the first experiment he used two opposite laser beams and one dimensional velocity distribution was achieved yielding half the recoil temperature. In the second experiment he used four laser beams and two dimensional velocity distribution was achieved yielding 0.25 µK which is 16 times less than recoil temperature. In the third experiment he used six laser beams and achieved a temperature of 0.18 µK where helium atoms crawl with the speed of about 2 cm/s.

2.8.10. Applications Round the Corner Laser Cooling and capture of neutral atoms led to atomic fountain. In the atomic fountain, laser cooled atoms are sprayed up from a trap like jets of water. The atoms turn at the top of trajectory and start falling and when they are subjected to microwave pulses, are almost stationary. At this stage atoms' inner structure can be sensed that led to the development of precision atomic clocks and formed the basis for discovery of Bose Einstein Condensation in atomic gases.

2.9 Bose Einstein Condensation in Dilute Gases : Concepts of Nobel Prize in Physics for the Year 2001 2.9.1.Introduction The Nobel Prize in Physics for 2001 was awarded jointly to Carl E.Wiemann, University of Colorado, USA, Eric A.Cornell, National Institute of Standards and Technology ( NIST) Colorado, USA, and , Massachusetts Institute of Technology, USA, for achievement of Bose Einstein Condensation in dilute gases of alkali atoms for early fundamental studies of the properties of the condensates. In this section eight Concept Maps are developed to illustrate the Scientists who were awarded Nobel Prize for 2001, Bose Einstein Condensation, the concept of Super Atom,Various Techniques involved in producing Low Temperature and finally the Prospects of Bose Einstein Condensation. Bose Einstein Condensation in dilute gases offers rich possibilities for studies of fundamental quantum mechanical processes, precision measurement technology and superfluidity properties. Rewarding applications of BEC in lithography, nano technology and holography appear to be just round the corner. 2.9.2. Nobel Laureates of 2001 Three American scientists namely Carl E. Wiemann, Eric A. Cornell and Wolfgang Ketterle were awarded the Nobel Prize in Physics for 2001. The award was given for achievement of Bose Einstein Condensation in dilute gases of alkali atoms and for studies of properties of condensates.

2.9.3. Types of Particles Matter consists of atoms, which rotate about their axis, hence have spin described by spin quantum number. The atoms (elements) are termed as bosons if the spin quantum number is integer and fermions if the spin quantum number is half integer.

2.9.4. New State of Matter : Bose Einstein Condensation We have already seen that based on the spin quantum number, atoms can be classified into fermions and bosons. Fermions avoid one another, hence cannot appear in the same quantum state, leading to high state of energy. But bosons at low temperature obey principles of quantum mechanics, gather in one and same quantum state with lowest energy known as Bose Einstein Condensation.

2.9.5. Super Atom Particles of micro cosmos governed by Quantum Mechanics move slowly at low temperature due to kinetic theory of gases. These particles have wave nature of matter and for dense gas of cold atoms, the wavelength is of the order of distance between atoms. At this stage the atoms can sense one another, co-ordinate leading to coherent matter as in the case of laser. The coordination of atoms (cold atoms) with one another led to the formation of Super Atom as whole complex is described by single wave as in single atom.

2.9.6. Magneto Optical Trap to exceed Doppler Limit The principle governing cooling is the exchange of momentum between photons and atoms. Head on collision takes place between photon and atom with atom in its flight. Cooling leads to reduction in speed of atoms reaching a limit known as Doppler limit. This limit can be overcome when cooled atoms are held together known as atom traps produced by combination of laser beam and magnetic fields known as Magneto Optical Trap.

2.9.7. Evaporative Cooling of Alkali Atoms D. Kleppner and T.I Greytak used evaporative cooling to reduce the temperature of the medium, where the fastest atoms leave the community reducing the average temperature of the medium. Evaporative cooling is achieved in atom traps where atoms are kept in place by magnetic dipole forces. The attractive force can be turned into repelling force if atomic magnetic poles are reversed. This is accomplished by radio frequency field where rapid atoms move high at the edge of the potential well where magnetic field and conversion frequency for pole switching is high. Thus the cooling effect is achieved by radio frequency field initially by applying a high frequency and gradually lowering it to skim off the hot atoms.

2.9.8. Reality of Bose Einstein Condensation (BEC) Evaporative cooling to drive fastest atoms was achieved initially by applying high frequency and gradually lowering it. Cornell and Wiemann in June 1995 adopted the method to achieve a condensation limit in Rb87. Ketterle used sodium atoms and reduced the atom loss at the centre of the trap by focussing powerful laser beam since it kept atoms away from loss area. Atom loss at the centre of the trap should be avoided, where magnetic field is zero and spontaneous pole switching is possible. This is achieved by rotating the magnetic field rapidly to prevent atom from pouring out of the trap. This evaporative cooling finally led to BEC by introducing laser cooling in a magneto optical trap and transfer to a purely magnetic trap at 20 nK where 2000 atoms remained in sample.

2.9.9. Prospects of Bose Einstein Condensation Bose Einstein Condensation in dilute gases offers rich possibility of studies of quantum mechanical processes. BEC with Rb85 led to resemblance of supernova (bosenova). Bose Einstein Condensation of fermions at extremely low temperature reveal future possibility of atomic pair formation and superfluidity properties. Stimulating conditions similar to white dwarf arises where outward pressure arises due to repulsive nature of fermions in a degenerate atomic gas. Bose Einstein Condensation may lead to applications in lithography, nano technology and holography. . CHAPTER 3 CONCLUSION 3.1 Effectiveness of Concept Mapping Knowledge is stored in our minds in a kind of hierarchical or holographic structure. Since the various concepts of Nobel Laureates of Physics are expressed through Concept Mapping, which stores the presentation of concepts in hierarchical manner, the learning is made easier, faster and more meaningful. Since it enhances meaningful learning and increases the retention I am sure, the reader would not have faced any difficulty in interpreting the maps and would be enriched in knowledge. References Books & Journal Articles Andal R. (1990). Concept Mapping in Learning Physical Science and its Relation to Scholastic Performance, Cognitive Ability, Attitude Towards Concept Mapping and Science Interest Among Ninth Standard Students. Unpublished Doctoral Dissertation, University of Madras. Edmondson Katherine M. (1995). Concept Mapping for the Development of Medical Curricula. Journal of Research in Science Teaching. 32 (07),777-793 Heinze-Fry, Jane Ann, (1987). Evaluation of Concept Mapping as a Tool for Meaningful Education of College Biology Students. Dissertation Abstracts International, 48 (01), 95. Heinze- Fry, Jane A. and Joseph D. Novak, (1990). Concept Mapping Brings Long Term Movement Toward Meaningful Learning. Science Education. (74), 461-480. Jaya Thilakan, V. Concept Mapping as a Strategy for Teaching Zoology at Higher Secondary Level. Unpublished Doctoral Dissertation, Bharathidasan University. Kumuda, G. A Comparative Study on the Effects of Traditional Lecture Method and Concept Mapping Strategies of Teaching on Achievement in Physics of Higher Secondary Students . Unpublished Doctoral Dissertation, University of Madras. Nisbet, John, and Janet Shucksmith, (1988).Learning Strategies. London: Routledge. Novak, Joseph D. and D.Bob Gowin, (1984). Learning How to Learn. England. Cambridge Uniersity Press. Novak, Joseph D. (1990).Concept Mapping : A Useful Tool for Science Education. Jouanal of Research in Science Teaching. 27 (10), 937-949. Wallace, Josephine, D. and Joel J. Mintzes, (1990). The Concept Map as a Research Tool Exploring Conceptual Change in Biology. Journal of Research in Science Teaching . 27 (10), 1033-1052. (Press Release from following websites of Nobel Prize in Physics are used.) http://www.nobel.se/laureates/physics-1913.html http://www.nobel.se/laureates/physics-1962.html http://www.nobel.se/laureates/physics-1972.html http://www.nobel.se/laureates/physics-1973.html http://www.nobel.se/laureates/physics-1978.html http://www.nobel.se/laureates/physics-1987.html http://www.nobel.se/laurea3tes/physics-1996.html http://www.nobel.se/laureates/physics-1997.html http://www.nobel.se/laureates/physics-2001.html