# Presentation: 787630

## Slide 1

## Physics and Astronomy Dept.

**Physics and Astronomy Dept.**

**Kevin Strecker, Andrew Truscott, Guthrie Partridge, and Randy Hulet**

**Observation of Fermi Pressure in Trapped Atoms:  The Atomic White Dwarf Star**

## Quantum Gases

- Quantum regime   n3   1

- Identical particles!

-   Gas phase  *n*  1012 cm-3
-   Low temperature  *T*  100 nK
-     1 m

## Exchange Symmetry

- Bosons

- Symmetry with respect to particle exchange

- 12(**r****1**,**r****2**)  +12(**r****2**,**r****1**)

- S. Bose, 1924
- A. Einstein, 1924-5

- Multiple state occupation

## Vortices
Solitons
Atom laser
Atom wave guides
Nonlinear atom optics
Superfluidty

**Solitons**
**Atom laser**
**Atom wave guides**
**Nonlinear atom optics**
**Superfluidty**

- Bose-Einstein Condensation

## Bose-Einstein Condensation in an Almost Ideal Gas

- Tc =  (N/1.2)1/3

## Slide 7

## Exchange Symmetry

- Fermions

- Symmetry with respect to particle exchange

- 12(**r****1**,**r****2**)  -12(**r****2**,**r****1**)

- Obey Pauli Exclusion Principle

- E. Fermi, Feb. 1926
- P.A.M. Dirac, Aug. 1926

## E. Fermi, Rendiconti Accademia Nazionale dei Lincei (2/2/26)

## Slide 10

## P.A.M. Dirac,

- Proc. Roy. Soc.
- (8/26/26)

## Slide 12

## and it comes in 2

- nuclear spin states!

## Lithium:  Non-identical Twins

- 7Li
- 3 e’s, 3 p’s, 4 n’s
- 	= 10 spin-1⁄2 particles
- 	  Boson
- 94% abundance

- 6Li
- 3 e’s, 3 p’s, 3 n’s
- 	= 9 spin-1⁄2 particles
- 	  Fermion
- 6% abundance

## Fermions - The Next Frontier

- Quantum Degenerate Fermi Gases
- 40K:  Demarco and Jin, *Science ***285**, 1703 (1999)
- 6Li:  Truscott *et al.* (Rice), *Science* **291**, 2570 (2001)
- 6Li:  Schreck *et al.* (Paris), *Phys. Rev. Lett*. **87**,
- 	080403 (2001).

-   Current status:  T  0.25 TF

## Methods

- Laser cooling  *T*  100 K
- Atom trapping
-                                                *n*  1012 cm-3
-                                                *N*  109  106
- Evaporative cooling
-                                                *T * 100 K   100 nK
-                                                -wave spin-flips
- Optical imaging

## Laser Cooling

**Momentum is imparted to an atom when it scatters                            light from a laser**
**Can slow or stop atoms in a beam**
**Trapped and cooled to**
******K temperatures**

## Evaporative Cooling

- Spin flip ‘hot’ atoms at edge of trap
- Collisions re-thermalize distribution
-  colder
-  denser

- E

-  f(E)

-  Remove tail

- Re-thermalize

## Sympathetic Cooling of 6Li

-   Pauli principle forbids s-wave interactions between
-     identical fermions

- Use both 6Li and 7Li

## Dual Source Apparatus

- 7Li/ 6Li

- Zeeman
- Slower

- Cloverleaf
- Trap

- Require vacuum pressure ~ 10-11 Torr

- Oven

## Slide 21

## Imaging

- CCD

- Mirror

- Compound
- lens

-  -scope

- Zoom
- lens

## Sympathetic Cooling

**7****Li**** ****(Bosons)**

**T = 240 nk**

**T = 510 nk**

**T = 810 nk**

**6****Li ****(Fermions)**

**T/T****F**** = 1.0**

**T/T****F**** = 0.56**

**T/T****F**** = 0.25**

- Truscott *et al.*, *Science* **291**, 2570 (2001)

## Axial Profiles

- Truscott *et al.*, *Science* **291**, 2570 (2001)

## Fermi Pressure in Trapped Atoms

- Truscott *et al.*, *Science* **291**, 2570 (2001)

## Fermi Pressure

- Fermi pressure is result of Pauli Exclusion Principle
- Stabilizes white dwarf and neutron stars against gravitational collapse

- EF ~ *n*1/3  (non-relativistic)
- Egrav ~ *n*1/3
- Balance:  Chandrasekar limit  for white dwarf stars (1931)

## Possible Experiments

- Boson/Fermion mixture
- Phase separation
- Superfluid probe

- Degenerate Fermi gas
- BCS phase transition to a gaseous superfluid
- 	6Li has an enormous attractive interaction

## BCS Transition in 6Li?

- Cooper pairing
- Superconductivity
- Superfluidity 3He
- Dilute gas? – tunable interactions

- For *s*-wave pairing,   Tc  TF exp(-1/kF|*a*|)
- For 2H, *a* = -4      Tc = 1 fK @ 1019 cm-3
- Leggett (1980)
- For 6Li, *a* = -1100      Tc = 30 nK @ 1012 cm-3
- Stoof (1996)
- Induced interactions (fermi/fermi or bose/fermi) mod. Tc
- Heiselberg et al. (2000)

## Cooper Pairing in 6Li

*S*-wave pairing symmetry forbidden between identical atoms
- 	 Create *incoherent* mixture of two states

- Stoof *et al.*, PRL **76**, 10 (1996)

## Slide 30

## Slide 31

## Slide 32

## Detecting Cooper Pairs

- Light scattering sensitive to
- normal component, i.e.  <> <>
- pair correlation fcn.  <- +> <- +>+
- but rF ~ (EF / 1⁄2m2)1⁄2 ~ 50 m   normal component
-          rp ~ 1 / kF ~ 0.2 m               pair correlation length
- Experiment:
- Zhang, Sackett, and Hulet, PRA **60**, 504 (1999)
- Also, Ruostekoski, PRA **60**, R1775 (1999)

-    << EF    no significant change in density

## Detecting Superfluidity

- Superfluids in anisotropic traps exhibit a “scissors” mode oscillation when displaced
-  Guery-Odelin and Stringari (theory)
-  Marago *et al.* (expt with BEC)