Review of Atomic Gas Bose-Einstein Condensation Experiments for "Hawking Radiation in Condensed Matter Systems

1. A review of atomic-gas Bose-Einstein condensation experiments for Workshop: “Hawking Radiation in condensed-matter systems” Eric Cornell JILA Boulder, Colorado

2. The basic loop. Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers.

3. The basic loop.(once every minute) Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers.

5. MOT Laser cooling 2.5 cm

12. The basic loop. Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers. Basic cooling idea leads to Basic cooling limit. Heating happens.

13. V(x) m x Self-interacting condensate expands to fill confining potential to heightm

14. n(x) V(x) m x Self-interacting condensate expands to fill confining potential to heightm

15. n(x) V(x) kT x Cloud of thermal excitations made up of atoms on trajectories that go roughly to where the confining potential reaches kT

16. n(x) V(x) m kT x When kT < m then there are very few thermal excitations extending outside of condensate. Thus evaporation cooling power is small.

17. BEC experiments must be completed within limited time. Bang! Three-body molecular-formation process causes condensate to decay, and heat! Lifetime longer at lower density, but physics goes more slowly at lower density!

18. Dominant source of heat: Bang! Decay products from three-body recombination can collide “as they depart”, leaving behind excess energy in still-trapped atoms.

20. Bose-Einstein Condensation in a Dilute Gas: Measurement of Energy and Ground-State Occupation, J. R. Ensher, D. S. Jin, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 77, 4984 (1996)

21. The basic loop. Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers.

22. F=2 F=1 m=2 m=-2 Energy m=-1 m=0 m=1 Typical single-atom energy level diagram in the presence of a magnetic field. Note Zeeman splitting.

23. m=-1 U(B) m=0 B m=+1 B(x) x

24. m=-1 U(B) m=0 B m=+1 B(x) x U(x) m=-1 m=0 x m=+1

25. Gravity (real gravity!) often is important force in experiments U(z) m=-1 Why do atoms rest at equilibrium here? m=0 z m=+1

26. Gravity (real gravity!) often is important force in experiments U(z) m=-1 Why do atoms rest at equilibrium here? m=0 z m=+1 m=-1 UB(z)+mgz m=0 z m=+1

27. Shape of magnetic potential. U= a x2 + b y2 + g z2 Why? electromagnet coils typically much larger, farther apart, than size of atom cloud R L D D, L >> R so, order x3 terms are small. Magnetic confining potential typically quadratic only, except…

28. Cross-section of tiny wire patterned on chip Atom chip substrate If electromagnets are based on “Atom chip” design, one can have sharper, more structured magnetic potentials.

29. If electromagnets are based on “Atom chip” design, one can have sharper, more structured magnetic potentials. But there is a way to escape entirely from the boring rules of magnetostatics….

30. Interaction of light and atoms. Laser beam nlaser Laser too blue +atom diffracts light +light provides conservative, repulsive potential Laser quasi-resonant +atom absorbs light +light can provide dissipative (heating, cooling) forces Laser too red +atom diffracts light +light provides conservative, attractive potential

31. One pair of beams: standing wave in intensity Can provide tight confinement in 1-D with almost free motion in 2-d. (pancakes) This is a one-D array of quasi-2d condensates

32. Two pairs of beams: Can provide tight confinement in 2-D, almost-free motion in 1-d (tubes) Can have a two-D array of quasi-1d condensates

33. Why K-T on a lattice? • Ease of quantitative comparison. • Makes it easier to get a quasi-2d system • This is the Frontier in Lattices Session!!! • (come on!) Our aspect ratio, (2.8:1), is modest, but... addition of 2-d lattice makes phase fluctuations much “cheaper” in 2 of 3 dimensions. z, the “thin dimension” x, y, the two “large dimemsions”.

34. Three pairs of beams: Can provide tight confinement in 3-D, (dots) Can have a three-D array of quasi-0d condensates

35. Single laser beam brought to a focus. Rayleigh range Can provide a single potential (not an array of potentials) with extreme, quasi-1D aspect ratio. Additional, weaker beams can change free-particle dispersion relation.

36. The basic loop. Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers.

37. Observables: It’s all about images. Temperature, pressure, viscosity, all these quantities are inferred from images of the atomic density.

38. Off-resonant imaging: index of refraction mapping. Signal-noise typically less good, but (mostly) nondestructive.. Near-resonant imaging: absorption. signal-noise typically good, but sample is destroyed.

39. Watching a shock coming into existence 110 ms V2003102764, 110 ms expansion

41. Bigger beam now 12.4 pixel, 7.2 mW using a bigger beam

43. Absorption imaging: one usually interprets images as of a continuous density distribution, but density distribution actually os made up discrete quanta of mass known, (in my subdiscipline of physics) as “atoms”.. Hard to see an individual atom, but can see effects of the discrete nature. Absorption depth observed in a given box of area A is OD= (N0 +/- N01/2) s /A The N01/2 term is the”atom shot noise”. and it can dominate technical noise in the image.

44. Absorption depth observed in a given box of area A is OD= (N0 +/- N01/2) s /A The N01/2 term is the”atom shot noise”. and it can dominate technical noise in the image. Atom shot noise will likely be an important background effect which can obscure Hawking radiation unless experiment is designed well.

45. Atom shot noise limited imaging Data from lab of Debbie Jin.

46. N.B: imaging atoms with light is not the only way to detect them: I think we will hear from Chris Westbrook about detecting individual metastable atoms.

47. The basic loop. Cooling. Minimum temperature. Stray heating. Confinement. Magnetic. Optical. Reduced dimensions. Arrays Observables. Images. Shot noise. Atom counting. Interactions. The G-P equation. Speed of sound. Time-varying interactions. feshbach resonance. Reduced dimensions. Thermal fluctuations. A range of numbers.

48. Why are BECs so interesting? QM: Particle described by Schrödinger equation BEC: many weakly interacting particles Gross-Pitaevskii equation The condensate is self-interacting (usually self-repulsive)

49. BEC: many weakly interacting particles Gross-Pitaevskii equation Can be solved in various approximations. The Thomas-Fermi approximation: ignore KE term, look for stationary states

50. BEC: many weakly interacting particles Gross-Pitaevskii equation m Can be solved in various approximations. The Thomas-Fermi approximation: ignore KE term, look for stationary states