1. Degenerate Quantum Gases on a Chip Dept. Of Physics, University of Toronto Prof: Joseph Thywissen Post Docs: Seth Aubin Stefan Myrskog Ph.D. Students: Marcius Extavour M.Sc. Students:Lindsay LeBlanc Undergrads:Barbara Cieslak Ian Leroux Research Technologist:Alan Stummer

2. Outline Quantum Gases – Bosons ( 87 Rb) + Fermions ( 40 K) Laser Cooling Magnetic Traps Chip Traps Evaporative/Sympathetic Cooling Outlook science! BEC / DFG thermal atoms magnetic traps evap. cooling MOT  psd 10 -13 110 -6 10 5

3. Bose-Einstein Condensation Phase transition occurs in a gas of particles, when the deBroglie wavelength becomes comparable to the inter-particle separation. d Phase-Transition Evolution governed by the GP equation (NLSE) T=0

4. Degenerate Fermi Gas Unlike bosons, identical fermions are not allowed to occupy the same state. EFEF No phase transition, so quantum behaviour gradually emerges Data from Randy Hulet T=0

5. Laser Cooling Atoms v Doppler shifted to lower frequency Doppler shifted to higher frequency Closer to resonance Slightly below resonance Doppler Cooling (Optical Molasses) F(N) V(m/s) a~10 4 m/s 2 Temperature Limit T D ~140 μK

6. Magneto-Optical Trapping m=1 m=0 m=-1 z E z B ~10 G/cm Spatial trapping accomplished by adding a magnetic gradient I Add Anti-Helmholtz coils

7. The System Spectroscopy and Laser Stabilization X 4 (2 for Rb, 2 for K) Amplification New Focus Vortex lasers Stabilized to ~ 300 kHz ~ 7 mW output 780 nm767 nm Rb 1 Rb 2 K1K1 K2K2 Optical Fiber TOPTICA Amplifier ~900 mW D 10 9 atoms 30 μK 600 μm radius DCWP

8. Imaging Data collection performed in 2 ways Fluorescence Imaging: Absorption Imaging CCD Camera CCD Camera Beer’s Law w/o atomswith atoms Divided image MicroPix 10 bit Firewire

9. Magnetic Trapping of Neutral Atoms For an atom in a state having total angular momentum F where. For an atom in the arbitrary hyperfine state.so that B  Interaction between external magnetic field and atomic magnetic moment:

10. Magnetic Trapping of Neutral Atoms Since, atoms in states having are magnetically trappable in magnetic field minima. min. B min. U Q: Given that a central B(r) results in a confining potential U(r), how can such a magnetic field geometry be generated?

11. Anti-Helmholtz Coils quadrupole (linear) magnetic trap

12. Optical Pumping Move atomic population into a single internal magnetic sublevel for improved magnetic trapping efficacy. F = 9/2 m F = 9/2 m F = 7/2 m F = -9/2 … U r m F = 9/2 m F = 7/2 m F = 5/2

13. Microtraps for Neutral Atoms  -traps Coils B’10 4 - 10 5 G/cm with I=2A Need I ~ 10 5 A for comparable B’ B’’100 G/cm 2 with I=2A Need I ~ 10 5 A for comparable B’’ UHVP ~ 10 -9 torr OK P ~ 10 -11 torr Atom #10 4 - 10 6 (“small” traps) 10 6 -10 8 (“large” traps) + + + -

14. Infinite Wire and External Bias Infinite current-carrying wire, into page at (x=0,z=0) I I = 2 A B bias = 150 G z 0 = 27  m atoms confined in 2D here

15. 3D Confinement based on Biot-Savart-type calculations with finite wire segments quadrupole “U trap”harmonic “U trap”

16. Orsay Chip gold conductors (yellow) on SiO 2 -coated Si wafer wire widths from 20 to 460  m wire heights of 7  m 16 mm 28 mm

17. Magnetically Trapped Atoms Macro. magnetic trap g N ~ 10 6, T ~ 100  K microchip trap atoms

18. Stack physical support of atom chip in UHV chamber (macor clamps) electrical connections heat-sinking atom-dispensers

19. Evaporative Cooling Remove most energetic (hottest) atoms Wait for atoms to rethermalize among themselves Wait time is given by the elastic collision rate k elastic = n  v Macro-trap: low initial density, evaporation time ~ 10-30 s. Micro-trap: high initial density, evaporation time ~ 1-2 s.

20. 1. Evaporate atoms  remaining atoms get colder.  N atoms decreases. 2. Atoms are less energetic  Atoms stay closer to trap center.  Volume decreases. 3. If n=N atoms /Volume increases then atoms undergo runaway evaporation. Runaway Evaporation Phase space density: Typically, 999 out of 1000 atoms are evaporated for 1 BEC atom.

21. RF evaporation  RF frequency determines energy at which spin flip occurs.  We use a DDS to generate RF at 10 kHz – 200 MHz.  Chip wire serves as RF B-field source. In a harmonic trap:

22. Pulse Timing Control Sequencer Direct Digitial Synthesizer (DDS) chip

23. The problem with Fermions In traps with very low temperatures, If, then two atoms must scatter as an s-wave:  s-wave is symmetric under exchange of particles: as T  0:  Identical Bosons undergo s-wave scattering.  Identical Fermions cannot scatters as s-waves.  identical Fermions do not scatter (i.e. interact).

24. Sympathetic Cooling Problem: Cold identical fermions do not interact (cannot rethermalize)  No evaporative cooling Solution: add non-identical particles  s-wave scattering permitted We cool our fermionic 40 K atoms sympathetically with an 87 Rb BEC. 2 possibilities: 1.Evaporate 40 K and 87 Rb mixture simultaneously. 2.Evaporate 87 Rb only, while 40 K cools through thermal contact.

25. What does an Ultra-Cold Fermi gas look like? BECDFG Hulet group, Rice University: Science 291, 2570 (2001).

26. Condensed Matter Physics Applications 1.BCS Cooper pairing in an ultra-cold fermi gas.  no clean signature yet. 2.Quantum simulation of the Fermi-Hubbard model.  not solved numerically or analytically.  proposed model for high-T c superconductors. 3. Low dimensional system.  1-D Fermi gas: Luttinger-Tomonaga liquid  1-D Bose gas: Tonks gas. Optical lattice for Fermi- Hubbard model.

27. Interferometry Applications of Degenerate Fermions 1.Atomic Clocks (temporal interferometer -- exp(i  t) )  DFG significantly reduces collision shift (clock shift). 2. Spatial interferometers – exp(ikz): k=2  mv/h 780 nm photon: k=8  10 6 m -1, 87 Rb at 1 m/s: k=1.4  10 9 m -1 BEC Good: Heisenberg limited momentum spread. Bad: large density dependent atom-atom interactions. DFG Good: Vanishing atom-atom interactions. Less good: small momentum spread.

28. Other Experiments 1. Atomic lifetime increase 2. Fermion Evaporation After excitation, the states into which the atom can decay/recoil are limited due to Pauli blocking.  Lifetime increases.  Linewidth narrows. RF cut n n

29. Outlook Current Status:  40 K and 87 Rb laser frequency and amplification set-up.  39 K MOT, 87 Rb MOT.  87 Rb quadrupole magnetic trap.  87 Rb transported to chip.  87 Rb loaded into chip U-trap. Next Steps:  load chip Z-trap, RF evaporation, BEC.  40 K MOT, DFG.

30. Group Members Marcius ExtavourLindsay LeBlanc Ian Leroux Barbara Cieslak Joseph Thywissen Seth Aubin Stefan Myrskog Alan Stummer