Transcript Bose Einstein Condensation

Bose Einstein Condensation
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
• BEC in Dilute Gases and Liquid Helium
• Experiments to achieve the BEC.
• News
Statistics of Idea Gas
• Two Particles Gas: A and B.
Distinguishable Particles
Classical
Indistinguishable Particles
Average number of occupation
Fermions:
for each
energy state
Bosons:
(Boson
Case)
Can occupy
the same
level Cannot occupy the same level
n 
1
exp[ (   )]  1
Some Theory
Particle in a 3D box:
 2 2
 
2
2
2
 
( x  y  z )  C 
2
2mL
 L
2
Calculating explicitly the total number:
 mkBT 
N V
2 
 2 
3/ 2 

l 1
e
l (   )
l
3/ 2
More Theory
 mkBTc 
N V
2 
 2 
3/ 2 
3 / 2
l

l 1
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

3 / 2
l

N
2.612...
l 1


3
V
 (Tc )
 (Tc )3
  T 3 / 2 
N 0  N 1    
  Tc  
The order of the de Broglie
wavelenght is the same as
the volume ocupied by the
ensemble
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
2
 2M  R  Vtrap ( R)  NVint ( R)  ( R)  EN ( R)


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 Chapman
All 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