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Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 3 Bose Gas & Bose-Einstein Condensate Bose – Einstein Statistics 1924 1894 - 1974 1879 - 1955 Bose letter to Einstein June 4, 1924 SN Bose, Zeit f Phys v26, 178 (1924); v27, 384 (1924) The Historical Development of Quantum Theory, Jagdish Mehra and Helmut Rechenberg, p569 (2001); Writings on physics and philosophy by W Pauli, Charles Paul Enz, K. vMeyenn, R. Schlapp, p. 94 (citation of Bose papers) Inclusive vs Exclusive Bosons in a Box Standing Wave Eigenfunction L L L At T > 0 Probability of Occupancy Probability of Occupancy Fermion Classical limit Boson Large E or Bose-Einstein Distribution for spin-0 bosons fugacity E=0 Positive octant Bose-Einstein Condensate Bose-Einstein Distribution for spin-0 bosons or fugacity Riemann Zeta function varies monotically from z = 0 to z = 1 For small z At high temperatures At crit ical Tc Critical Temperature Crude estimate of Tc for He4 You can check that this gives a Tc value of 3.17 K, to be compared with the experimentally observed value of 2.18 K J.C. Davies group (Cornell) http://www.iranika.ir/articles%20page/mohandesi/mechanic.superfluids1.htm Bose-Einstein Condensate Term The number of zero energy bosons per unit volume University of Stuttgart measurement of BEC of Chromium atoms http://www.pi5.uni-stuttgart.de/news/050303/news050303.html Bose-Einstein Condensate Nobel Prize in Physics 2001 Cornell – Wieman experiment: Cooling two thousand Rubidium-87 atoms to below 170 nK using combination of laser cooling and magnetic evaporative cooling. Ketterle (MIT) experiment Cooled some hundred times more atoms (Na23) , and was able to demonstrate quantum mechanical interference between two BEC. Magnetic Evaporative Cooling For a visual applet on Magnetic Evaporative Cooling Go to http://www.colorado.edu/physics/2000/atomic_lab.html For a visual applet on Laser Cooling of Atoms Go to http://www.colorado.edu/physics/2000/atomic_lab.html Ketterle experiment http://online.itp.ucsb.edu/plecture/ketterle/oh/45.html Nobel Prize in Physics 1997 Transition Temperature Douglas Osheroff 1945 - Nobel Prize in Physics 1997 2 Polarization states Photon Gas Photon energy N is a function of temperature At equilibrium, fugacity, z, rises to maximum value of 1 Pressure By comparing with the equation for U, we find that the pressureenergy relation for the photon gas is Or Phonon Gas ! (k) = ! (k + 2¼n=a) http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6730Physics-for-Solid-State-ApplicationsSpring2003/8A2B76D2-7D99-445BB511-EDFA06C0482B/0/lecture12c.pdf Speed of sound in solid Peter Debye 1884 – 1966 Verh. Deut. Phys. Ges. 15, 678-689 (1913) Low Temperature Limit Low Temperature Limit Specific Heat of Solid at low temperature High Temperature Limit Dulong Petit Law http://web.mit.edu/6.730/www/ST04/Lectures/Lecture12.pdf