Ultracold Quantum Gases

Aristeu Lima

Free University of Berlin

BEC-Group FU-Berlin

Outline of the talk

• Brief historic remarks

BEC-Group FU-Berlin

Outline of the talk

• Brief historic remarks

• Bose-Einstein condensation (BEC)

BEC-Group FU-Berlin

Outline of the talk

• Brief historic remarks

• Bose-Einstein condensation (BEC)

• BCS theory of superconductivity

BEC-Group FU-Berlin

Outline of the talk

• Brief historic remarks

• Bose-Einstein condensation (BEC)

• BCS theory of superconductivity

• BCS-BEC crossover

BEC-Group FU-Berlin

Outline of the talk

• Brief historic remarks

• Bose-Einstein condensation (BEC)

• BCS theory of superconductivity

• BCS-BEC crossover

• Spinor Fermi gases

BEC-Group FU-Berlin

Historical remarks• 1924: S. N. Bose and the bosons

BEC-Group FU-Berlin

Historical remarks• 1924: S. N. Bose and the bosons

• 1924: A. Einstein

BEC-Group FU-Berlin

Historical remarks• 1924: S. N. Bose and the bosons

• 1924: A. Einstein

• 1926: E. Fermi and the fermions

BEC-Group FU-Berlin

Historical remarks• 1924: S. N. Bose and the bosons

• 1924: A. Einstein

• 1926: E. Fermi and the fermions

• 1957: J. Bardeen, L. N. Cooper, and J. R.SchriefferMicroscopic Theory ofSuperconductivity

BEC-Group FU-Berlin

Historical remarks• 1924: S. N. Bose and the bosons

• 1924: A. Einstein

• 1926: E. Fermi and the fermions

• 1957: J. Bardeen, L. N. Cooper, and J. R.Schrieffer

• 1995: E. A. Cornell, C. E. Wieman, and W.Ketterle

BEC-Group FU-Berlin

Bose-Einstein Condensation

BEC-Group FU-Berlin

Bose-Einstein Condensation

BEC-Group FU-Berlin

Bose-Einstein Condensation

BEC-Group FU-Berlin

Bose-Einstein Condensation

BEC-Group FU-Berlin

Bose-Einstein Condensation

• Laser cooling and Trapping (Nobel 1997)

BEC-Group FU-Berlin

Bose-Einstein Condensation

• Laser cooling and Trapping (Nobel 1997)

• Evaporative cooling (Nobel 2002)

BEC-Group FU-Berlin

Bose-Einstein Condensation

• Laser cooling and Trapping (Nobel 1997)

• Evaporative cooling (Nobel 2002)

BEC-Group FU-Berlin

Bose-Einstein Condensation

• Laser cooling and Trapping (Nobel 1997)

• Evaporative cooling (Nobel 2002)

• Condensed elements

BEC-Group FU-Berlin

BCS superconductivity• Bardeen, Cooper and Schrieffer: Nobel Prize

1972

BEC-Group FU-Berlin

BCS superconductivity• Universality of the energy gap

BEC-Group FU-Berlin

BCS-BEC crossoverBose agglomerate versus Fermi sea

BEC-Group FU-Berlin

BCS-BEC crossoverBose agglomerate versus Fermi sea

BEC-Group FU-Berlin

BCS-BEC crossoverMolecules and Cooper Pairs

BEC-Group FU-Berlin

Spinor Fermi gasesZeeman Populations Internal Energy

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

16NσN

-

δ/F

σ = 3/2

σ = 1/2

σ = −1/2

σ = −3/2

0.2 0.4 0.6 0.8 1 1.2 1.4

0.8

0.9

1.1

1.26 ENEF

-

δ

Interaction Free

Contact Interaction

Thomas-Fermi Radii Expansion

0.2 0.4 0.6 0.8 1 1.2 1.4

0.2

0.4

0.6

0.8

1

1.26

Rσ(δ)RTF

-

δ

σ = 3/2

σ = 1/2

σ = −1/2

σ = −3/2

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6nσ(x, y, t)t = 2s

t = 1s

t = 0

Proceedings of Path Integrals: Trends andPerspectives BEC-Group FU-Berlin

Spinor Fermi gases: Expansion

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6nσ(x, y, t)t = 2s

t = 1s

t = 0

BEC-Group FU-Berlin

Outlook

BEC-Group FU-Berlin

Thanks• DAAD German Academic Exchange Service

BEC-Group FU-Berlin

Thanks• DAAD German Academic Exchange Service

• DFG-Priority Program SPP 1116: Interactions inUltra-Cold Atomic and Molecular Gases

BEC-Group FU-Berlin

Thanks• DAAD German Academic Exchange Service

• DFG-Priority Program SPP 1116: Interactions inUltra-Cold Atomic and Molecular Gases

• Cold atoms group FU-Berlin

BEC-Group FU-Berlin

Laser Cooling

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BEC-Group FU-Berlin

Evaporative cooling

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BEC-Group FU-Berlin