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Bose-Einstein Condensation. Student: Miaoyin Wang Instructor: Elbio Dagotto Class: Solid State II, 2010, Spring Semester Institution: Department of Physics, University of Tennessee, Knoxville. 0. Structure of Presentaton. Bosons and Bose-Einstein Distribution

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Bose-Einstein Condensation

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Bose-Einstein Condensation

Student: Miaoyin Wang

Instructor: Elbio Dagotto

Class: Solid State II, 2010, Spring Semester

Institution: Department of Physics,

University of Tennessee, Knoxville

0. Structure of Presentaton

  • Bosons and Bose-Einstein Distribution

  • Bose-Einstein Condensation

  • Experiment Realization of BEC

  • Summary

1. Bosons & Bose-Einstein Distribution


Q: How to distinguish one object from another?

- Think of daily life object

-Think of microscopic particles

1. Bosons & Bose-Einstein Distribution

Bosons vs Fermions

Bosons – integer spin / no Pauli exclusion

Fermions – half integer spin / Pauli exclusion

Fermions - 1 wayBosons – 10 ways


1. Bosons & Bose-Einstein Distribution

Bose-Einstein Distribution

For N identical bosons with M available quantum states, there are

ways that the particle can be distributed.

For quantum states with different energies:

1. Bosons & Bose-Einstein Distribution

Bose-Einstein Distribution

Consider an ideal gas model for bosons,

we have

The entropy of the gas is

S=kB ln W

Thus we can apply Lagrange multipliers

1. Bosons & Bose-Einstein Distribution

Bose-Einstein Distribution

Finally, after some calculation, we get

for each energy shell and thus

Bose-Einstein Distribution

2. Bose-Einstein Condensation (BEC)

Observe the equation:

>= 0

>= 0

>= 1


2. Bose-Einstein Condensation (BEC)

Since f(E) is a distribution, it also fulfills

Suppose there is a temperature that

(we are not sure about it!)

Have a try


2. Bose-Einstein Condensation (BEC)

What will happen below Tc?

Where do the particles go?

: (



keeps it constant

There is no

Total number


Bose-Einstein Condensation

2. Bose-Einstein Condensation (BEC)

Where do the particles go?

3. Experimental BEC

How Tc changes upon n?

To achieve BEC, one can either decrease the temperature or increase the particle density.

A temperature-density phase diagram will help a lot!

3. Experimental BEC

Difficulty to achieve BEC

BEC before it is forbiddened!

Make Time BEC << Time thermal equilibrium

3. Experimental BEC

So: have to do it in a hurry

- Pulsed laser beam as detector

- Magneto-Optical Trap (MOT)

Also: make thermal equilibrium time scale larger

- Choice of atoms – Rubidium 87

Still: very very cold!

- MOT cooling

- Cool by expand

3. Experimental BEC


Normal method




3. Experimental BEC

Result: velocity distribution data






3. Experimental BEC

Anisotropy of the data

Due to

Heisenberg Uncertainty Principle (h~x*p)


Anisotropy of the space distribution

3. Experimental BEC

Other type of BEC in Experiment

  • Superfluid

    ~Helium-4 @ 2.17K

    ~only about 8% of the atoms accumulate in ground state - not a “pure” BEC.

  • Fermions

    ~extremely low temperature

    ~must “pair up” to form compound particles (like molecules or Cooper pairs) that are bosons.

  • Magnons

    ~ a BEC transmission temperature at room temperature

    ~achieved by pumping the magnons into the system and form a high density n

4. Summary

  • BEC is predicted early and achieved tens of years later, inspiring a lot of related technologies.

  • BEC in lab is very fragile. Extremely low temperature and density is required.

  • BEC can be useful in very basic physics.

  • It can also be used in ultra-sensitive measurements. (Think of laser)

5. References

[1] Superconductivity, Superfluids and Condensates, J.F.Annett, ISBN 7-03-023624-1

[2] Thermodynamics and Statistical Mechanics, Zhicheng Wang, ISBN 7-04-011574-3

[3] Levi, Barbara Goss (2001). "Cornell, Ketterle, and Wieman Share Nobel Prize for Bose–Einstein Condensates". Search & Discovery. Physics Today online.

[4] Bose-Einstein Condensation, Wikipedia,

[5] M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell (1995). "Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor". Science 269 (5221): 198–201.

[6 ] S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm (2003). "Bose–Einstein Condensation of Molecules". Science 302 (5653): 2101–2103

[7] Demokritov, S.O.; Demidov, VE; Dzyapko, O; Melkov, GA; Serga, AA; Hillebrands, B; Slavin, AN (2006). "Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping". Nature 443 (7110): 430–433

Thank you!

Student: Miaoyin Wang

Instructor: Elbio Dagotto

Class: Solid State II, 2010, Spring Semester

Institution: Department of Physics,

University of Tennessee, Knoxville

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