Lecture: April 20, 2020 REVIEW OF LAST LECTURE: <https://www.nobelprize.org/prizes/physics/2016/ prize-announcement/> 1 FIG. 1: Cartoon diagram: It is the number of holes in the wave function that determine quantization. FIG. 2: Theoretical model, known as Hofstadter butterfly that predicts all possible quantization of resistance. Horizontal axis is magnetic field and vertical axis is energy 2 Bose Einstein Condensate Video: <https://www.youtube.com/watch?v=nAGPAb4obs8> 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. Identity Crisis 3 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 Prize: 2001:Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman APPLICATIONS: (1) In clock precision 4 The accuracy of an atomic clock depends on two factors: the first is temperature of the sample atoms - colder atoms move much more slowly, allowing longer probe times, the second is the frequency and intrinsic linewidth of the electronic or hyperfine transition. Higher frequencies and narrow lines increase the precision. (2)New type of lasers and sensors (3) Exploring new phenomena in physics. You can engineer artificial crystals with no defects.... LASERS <https://www.youtube.com/watch?v=eQQeSUvgmJE> The laser was not discovered from a single breakthrough by one individual, but from a series of developments. Albert Einstein in 1917 presented the concept of stimulated emission, which was later experimentally verified. The maser, a precursor to the laser, was developed in 1954 by Charles Townes and independently verified by Nicolay Basov and Alexandr Prokhorov. Townes and Arthur Schawlow published an important paper on the theory of the laser in Physical Review in 1958, which led to the first patent for a laser awarded in March 1960, followed by the first demonstration of a working laser two months later by Theodore Maiman at Hughes Research Lab. Can you make lasers with electrons??? 5.