Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang
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Transcript of Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang
Graduate Lecture Series29 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 EinsteinJune 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
L
L
L
Standing Wave Eigenfunction
At T > 0
Probability of Occupancy
Fermion
Boson
Probability of Occupancy
Classical limit
Large E
Bose-Einstein Distribution
for spin-0 bosons
or
fugacity
Positive octant
E=0
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 critical 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
400 nK
200 nK
50 nK
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 appleton
Magnetic Evaporative Cooling
Go tohttp://www.colorado.edu/physics/2000/atomic_lab.html
For a visual appleton
Laser Cooling of Atoms
Go tohttp://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
Douglas Osheroff
1945 -
Transition Temperature
Nobel Prize in Physics 1997
Photon Gas2 Polarization states
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 pressure-energy relation for the photon gas is
Or
Phonon Gas
! (k) = ! (k+2¼n=a)http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-730Physics-for-Solid-State-ApplicationsSpring2003/8A2B76D2-7D99-445B-B511-EDFA06C0482B/0/lecture12c.pdf
Speed of sound in solid
Peter Debye
1884 – 1966
Verh. Deut. Phys. Ges. 15, 678-689 (1913)
Low Temperature Limit
Specific Heat of Solid at low temperature
Low Temperature Limit
High Temperature Limit
Dulong Petit Law
http://web.mit.edu/6.730/www/ST04/Lectures/Lecture12.pdf