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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

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Bose einstein condensation

Bose Einstein Condensation

In Diluted Gas

Condensed Matter II –Spring 2007

Davi Ortega


  • 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

Average number of occupation

for each energy state

(Boson Case)

Statistics of Idea Gas

  • Two Particles Gas: A and B.

Distinguishable Particles

Indistinguishable Particles


Cannot occupy the same level


Can occupy the same level


Some theory
Some Theory

Particle in a 3D box:

Calculating explicitly the total number:

More theory
More Theory

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
Two more useful results

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
An Last statement

This whole theory assume non interacting particles: Schrödinger Equation

Interacting Particles: Gross-Pitaeviski Eq.


  • 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
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
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

Any other way
Any other way ?!


Michael Chapman

All Optical BEC

Current research
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