Ultra-Cold Matter Technology Physics and Applications

1. Ultra-Cold Matter Technology Physics and Applications Seth A. M. Aubin University of Toronto, Canada June 15, 2006 NRC, Ottawa

2. Outline • Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases • Physics  Past: 40K-87Rb cross-section.  Present: Matter-wave interferometry.  Future: Constructing larger quantum systems.

3. mK μK nK p p p x x x What’s Ultra-Cold Matter ? • Very Cold  Typically nanoKelvin – microKelvin  Atoms/particles have velocity ~ mm/s – cm/s • Very Dense … in Phase Space Different temperatures Same phase space density Higher phase space density

4. Quantum mechanics requires p  fundamental unit of phase space volume Dp x Dx Boltzmann régime Quantum régime Ultra-cold Quantum Mechanics  Quantum physics is important when Equivalent: deBroglie wavelength ~ inter-particle separation

5. NBEC Ni 1 Ni Ei EF Ei Quantum Statistics Bosons Fermions • anti-symmetric multi-particle wavefunction. • ½-integer spin: electrons, protons, neutrons, 40K. • probability of occupying a state |i> with energy Ei. • symmetric multi-particle wavefunction. • Integer spin: photons, 87Rb. • probability of occupying a state |i> with energy Ei.

6. How do you make ULTRA-COLD matter? Two step process: 1. Laser cooling  Doppler cooling  Magneto-Optical Trap (MOT) 2. Evaporative cooling  Magnetic traps  Evaporation

7.  Atom’s frame Lab frame, after absorption v-vrecoil m/s2 87Rb:  = - I = Isat • Absorb a photon  atom gets momentum kick. • Repeat process at 107 kicks/s  large deceleration. • Emitted photons are radiated symmetrically  do not affect motion on average Vrecoil = 6 mm/s m/s Vdoppler ~ 10 cm/s Doppler Cooling Lab frame v

8. Magneto-Optical Trap (MOT) Problem: Doppler cooling reduces momentum spread of atoms only.  Similar to a damping or friction force.  Does not reduce spatial spread.  Does not confine the atoms. Solution: Spatially tune the laser-atom detuning with the Zeeman shift from a spatially varying magnetic field. B,  z ~10 G/cm ~14 MHz/cm

9. Magneto-Optical Trap (MOT)

10. 10-13 10-6 1 PSD thermal atoms Laser cooling quantum behavior ??? Magneto-Optical Trap (MOT) ~ 100 K

11.  B Magnetic Traps Interaction between external magnetic field and atomic magnetic moment: For an atom in the hyperfine state Energy = minimum |B| = minimum

12. Iz Micro-magnetic Traps • Advantages of “atom” chips: • Very tight confinement. • Fast evaporation time. • photo-lithographic production. • Integration of complex trapping potentials. • Integration of RF, microwave and optical elements. • Single vacuum chamber apparatus.

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

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

15.   B B RF RF Evaporation In a harmonic trap: • RF frequency determines energy at which spin flip occurs. • Sweep RF between 1 MHz and 30 MHz. • Chip wire serves as RF B-field source.

20. Outline • Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases • Physics  Past: 40K-87Rb cross-section.  Present: Matter-wave interferometry.  Future: Constructing larger quantum systems.

21. 10-13 10-6 1 105 PSD thermal atoms MOT magnetic trapping evap. cooling BEC Evaporation Efficiency Bose-Einstein Condensation of 87Rb

22. RF@1.660 MHz: N=1.4x105, T<Tc RF@1.725 MHz: N = 6.4x105, T~Tc RF@1.740 MHz: N = 7.3x105, T>Tc 87Rb BEC

23. RF@1.660 MHz: N=1.4x105, T<Tc RF@1.725 MHz: N = 6.4x105, T~Tc RF@1.740 MHz: N = 7.3x105, T>Tc Surprise! Reach Tc with only a 30x loss in number. (trap loaded with 2x107 atoms)  Experimental cycle = 5 - 15 seconds 87Rb BEC

24. “Iceberg” BEC Fermi Sea Fermions: Sympathetic Cooling Problem: Cold identical fermions do not interact due to Pauli Exclusion Principle.  No rethermalization.  No evaporative cooling. Solution: add non-identical particles  Pauli exclusion principle does not apply. We cool our fermionic 40K atoms sympathetically with an 87Rb BEC.

25. 104 104 104 102 102 102 100 100 100 105 105 105 106 106 106 107 107 107 Cooling Efficiency 102 102 102 104 104 104 106 106 106 108 108 108 Sympathetic Cooling

26. Below TF 0.9 TF 0.35 TF • For Boltzmann statistics and a harmonic trap, • For ultra-cold fermions, even at T=0,

27. Fermi Boltzmann Gaussian Fit First time on a chip ! S. Aubin et al. Nature Physics2, 384 (2006). Pauli Pressure

28. Outline • Intro to Ultra-cold Matter  What is it ?  How do you make it ?  Bose-Einstein Condensates  Degenerate Fermi Gases • Physics  Past: 40K-87Rb cross-section.  Present: Matter-wave interferometry.  Future: Constructing larger quantum systems.

29. What’s Special about Ultra-cold Atoms ? • Extreme Control: • Perfect knowledge (T=0). • Precision external and internal control with magnetic, electric, and electromagnetic fields. • Interactions: • Tunable interactions between atoms with a Feshbach resonance. • Slow dynamics for imaging. • Narrow internal energy levels: • Energy resolution of internal levels at the 1 part per 109 – 1014. • 100+ years of spectroscopy. • Frequency measurements at 103-1014 Hz. • Ab initio calculable internal structure.

30. Past: Surprises with Rb-K cold collisions

31. Collision Rates Rb-Rb Rb-K Sympathetic cooling should work really well !!! Naïve Scattering Theory Sympathetic cooling 1st try: • “Should just work !” -- Anonymous • Add 40K to 87Rb BEC  No sympathetic cooling observed !

32. Evaporation 3 times slower than for BEC Experiment: Sympathetic cooling only works for slow evaporation

33. TK40(K) Cross-Section Measurement Thermalization of 40K with 87Rb

34. Rb-K Effective range theory Rb-K Naïve theory Rb-Rb cross-section What’s happening?

35. Present: Atom Interferometry

36. D1 Mach-Zender atom Interferometer: Measure a phase difference () between paths A and B. D2 ABcan be caused by a difference in length, force, energy, etc … Path A Path B Atom Interferometry IDEA: replace photon waves with atom waves.  atom photon Example: 87Rb atom @ v=1 m/s  atom  5 nm. green photon  photon  500 nm. 2 orders of magnitude increase in resolution at v=1 m/s !!!

37. Identical bosonic atoms interact through collisions.  Good for evaporative cooling.  Bad for phase stability: interaction potential energy depends on density -- AB is unstable. PROBLEM Better Idea: Use a gas of degenerate fermions • Ultra-cold identical fermions don’t interact. AB is independent of density !!! • Small/minor reduction in energy resolution since E ~ EF . EF Bosons and Fermions … again 1st Idea: use a Bose-Einstein condensate • Photons (bosons)  87Rb (bosons) • Laser has all photons in same “spatial mode”/state. • BEC has all atoms in the same trap ground state.

38. Energy x h RF beamsplitter How do you beamsplit ultra-cold atoms ?

39. Energy x h RF beamsplitter How do you beamsplit ultra-cold atoms ?

40. Energy x h RF beamsplitter How do you beamsplit ultra-cold atoms ?

41. Energy Position of well is determined by  hrabi = Atom-RF coupling x h RF beamsplitter How do you beamsplit ultra-cold atoms ?

42. Implementation figure from Schumm et al., Nature Physics1, 57 (2005).

43. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

44. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

45. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

46. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

47. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

48. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

49. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss

50. RF splitting of ultra-cold 87Rb Scan the RF magnetic field from 1.6 MHz to a final value BRF ~ 1 Gauss