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Bose Einstein Condensation. In Diluted Gas. Condensed Matter II –Spring 2007 Davi Ortega. Summary. From counting to a new state of matter Indistinguishability of particles Counting indistinguishable particles Einstein’s conclusion = New State Some properties - PowerPoint PPT Presentation
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Bose Einstein Condensation
Condensed Matter II –Spring 2007Davi Ortega
In Diluted Gas
Summary
• From counting to a new state of matter– Indistinguishability of particles– Counting indistinguishable particles– Einstein’s conclusion = New State– Some properties
• BEC in Dilute Gases and Liquid Helium• Experiments to achieve the BEC.• News
Statistics of Idea Gas• Two Particles Gas: A and B.
Classical Bosons:Can occupy the same level
Indistinguishable ParticlesFermions:
Cannot occupy the same level
Distinguishable ParticlesAverage number of occupationfor each energy state
(Boson Case)
1)](exp[1
n
Some Theory
Particle in a 3D box:2
2222
22
)(2
L
CmL zyx
Calculating explicitly the total number:
12/3
)(2/3
22 l
lB
leTmkVN
More Theory
1
2/32/3
22 l
cB lTmkVN
But what happens now if I let at this temperature the density n V of the substance increase(e.g., by isothermal compression) to even higher values?
I claim that in this case a number of molecules which always grows with the total density makes a transition to the 1. quantum state (state without kinetic energy)… … The claim thus asserts that something similar happens as when isothermally compressing a vapor beyond the volume of saturation. A separation occurs; a part “condenses”, the rest remains a “saturated ideal gas”. (Einstein, 1925).
Two more useful results
331
2/3
)(...612.2
)( cc
l
TT
l
VN
The order of the de Broglie wavelenght is the same as the volume ocupied by the
ensemble
2/3
0 1cTTNN
Number of the particles that falls to the “condensate” state
An Last statement
This whole theory assume non interacting particles: Schrödinger Equation
Interacting Particles: Gross-Pitaeviski Eq.
)()()()(2
2
int2
2
RERRNVRVM NtrapR
Achievements
• 1938 – Pyotr Kapitsa John Allen and Don Misener: Helium 4
• 1995 – Eric Cornell and Carl Wieman: Rb87: Pure BEC.
• 1995 – Wolfgang Ketterle Na23. (4 months later)
Liquid He vs. Diluted Gas
• Strong Interactions in He qualitatively changes the nature of transition.
• Diluted Gas– Pure Condensate state
• Liquid Helium– Zero Viscosity– And other strange properties.
How to make a BEC ?
• Heat the atoms: 600 K (gas)• Confine them in a beam• Decelerate the beam• Trap the atoms (Magneto Optical Trap)• Magnetic Trapping (avoid atoms recoil by
spontaneous emission and random absorption)
• Evaporative Cooling
Famous Picture
Any other way ?!
YES
Michael ChapmanAll Optical BEC
Current Research
• BEC achieved in several atoms.• Strange Properties:
– Superfluidity– Slowing of light
• Wave-like phenomena in atoms.– Interference between two condensates.
• Atom Laser– Coherent Matter Waves