1. Experiments with Trapped Potassium Atoms Robert Brecha University of Dayton

2. Outline Basics of cooling and trapping atoms Fermionic and bosonic atoms - why do we use potassium? Parametric excitation and cooling Sympathetic cooling and BEC

3. Co-workers and Affiliations Giovanni Modugno – LENS Gabriele Ferrari – LENS Giacomo Roati – Università di Trento Nicola Poli – Università di Firenze Massimo Inguscio – LENS and Università di Firenze

4. In the Lab at LENS

5. Motivations for Trapping Atoms Fundamental atomic physics measurements Condensed matter physics with controllable interactions (“soft” condensed matter) Tabletop astrophysics – collapsing stars, black holes, white dwarfs Quantum computing

6. Atomic Cooling Laser photons Physics2000 Demo

7. Cooling Force Random emission directions  momentum kicks  retarding force Force = (momentum change per absorbed photon)  (scattering rate of photons) (Depends on intensity, detuning, relative speed) Force is not position-dependent  no permanent trapping

8. Laser Cooling and Trapping Magnetic Field Coils (anti-Helmholtz) Circularly polarized laser beams

9. Far Off-Resonance Trap (FORT) One disadvantage of MOT – presence of magnetic fields; only certain internal states trappable Solution – Use all-optical method Laser electric field induces an atomic dipole Interaction potential of dipole and field:

10. FORT Trapping Potential Standing-wave in z-direction, Gaussian radially Oscillation frequencies: 450  K

11. Fermions vs. Bosons Spin-1/2Integer spin State-occupation limitedGregarious Do not collide* Collide

12. Fermions vs. Bosons Bosonic ground-state occupation fraction Fermionic occupation probabilities Ensher, et al., PRL 77, 4984 (1996)

13. Potassium Three isotopes: 39 K (93.26%)  boson 40 K (0.01%)  fermion 41 K (6.73%)  boson

14. Potassium Energy Levels

15. FORT Experimental Schematic MOT: 5 × 10 7 atoms T ~ 60  K FORT: 5 × 10 5 atoms T = 80  K Absorption beam

16. Absorption Image from FORT N =  ×    atoms n = 5 ×    cm -3 T = 50 – 80  K dT/dt = 40  K/s  r = 2  × 1 kHz  a = 2  × 600 kHz U 0 = 300 - 600  K 450  K

17. Elastic Collisions  =  p /2  n    cm  a t = 169(9)a 0  = 10(3) ms

18. Inelastic Collisions

19. Frequency Measurements “Parametric Excitation” Driving an oscillator by modulating the spring constant leads to resonances for frequencies 2  0 /n. 00 Here we modulate the dipole-trap laser by a few percent

20. Parametric Resonances 2a2a 1.8  a

21. Parametric Heating... and Cooling 2a2a 1.8  a T ex = 10 ms  = 12 % T ex = 2 ms  = 12 %

22. Trap Anharmonicity

23. Cooling by Parametric Excitation Selective excitation of high-lying levels  forced evaporation Occurs on a fast time-scale Independent of internal atomic structure  works on external degrees of freedom Somewhat limited in effectiveness

24. The New Experiment

25. Transfer Tube - MOT1 to MOT2

26. Sympathetic Cooling Use “bath” of Rb to cool a sample of K atoms Goal 1 – Achieve Fermi degeneracy for 40 K atoms Goal 2 – (After #1 did not seem to work) Achieve Bose-Einstein condensation for 41 K

27. Some Open Questions Do K and Rb atoms collide? (What is the elastic collisional cross-section?) Do K and K atoms collide? Is the scattering length positive (stable BEC) or negative (unstable BEC at best)

28. Some Cold-Collision Physics Scattered particle wavefunction is written as a sum of “partial waves” with l quantum numbers. For l > 0, there is repulsive barrier in the corresponding potential that inhibits collisions at low temperatures. For identical particles, fermions have only l-odd partial waves, bosons have only l-even waves.  Identical fermions do not collide at low temperatures.

29. Rubidium Energy Levels 87 Rb F´= 3 F´= 2 F´= 1 F´= 0 F = 1 F = 2 6835 MHz 267 MHz 157 MHz 72 MHz 780 nm (4×10 8 MHz)

30. Rubidium Ground-State Apply a B-field: m F = 2 F = 1 F = 2 6835 MHz m F = -1 “Low-field-seeking states”

31. BEC Procedure Trap 87 Rb, then 41 K in MOT1 Transfer first Rb, then K into MOT2 Now have 10 7 K atoms at 300  K and 5×10 8 Rb atoms at 100  K Load these into the magnetic trap after preparing in doubly-polarized spin state |F=2,m F =2> Selective evaporative cooling with microwave knife Check temperature (density) at various stages (a destructive process)

32. QUIC Trap Figure by Tilman Esslinger, ETH Zurich

33. QUIC Trap Transfer Figure by Tilman Esslinger, ETH Zurich Quadrupole field Magnetic trap field

34. Microwave “Knife” (Link to JILA group Rb BEC)

35. Rb K Temperature and Number of Atoms

36. Potassium BEC Transition (Link to JILA group Rb BEC) A BC

37. Optical Density Cross-section Thermal Mixed Condensate

38. Absorption Images Rb density remains constant K density increases 100x

39. Elastic Collisional Measurements Return to parametric heating (of Rb) and watch the subsequent temperature increase of K. Determined from absorption images

40. Elastic Collisional Measurements Ferrari, et al., submitted to PRL Temperature dependence of elastic collision rate (Is a >0 or is a < 0?) Potassium temperature after parametrically heating rubidium

41. Double Bose Condensate

42. Future Directions