1. R.G. Scott1, A.M. Martin2, T.M.Fromhold1, F.W. Sheard1.
Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
R.G. Scott1, A.M. Martin2, T.M.Fromhold1, F.W. Sheard1.
1School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.
2School of Physics, University of Melbourne, Parkville, Vic. 3010, Australia.

2. Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
Motivation:
Analysis of experiments.

3. Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
Motivation:
Analysis of experiments.
Study of BEC excitations.

4. Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
Motivation:
Analysis of experiments.
Study of BEC excitations.
Probe of surfaces.

5. Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
Motivation:
Analysis of experiments.
Study of BEC excitations.
Probe of surfaces.
Possibility of making atom optical devices.

6. Disruption of Bose-Einstein Condensates on Classical and Quantum Reflection
Motivation:
Analysis of experiments.
Study of BEC excitations.
Probe of surfaces.
Possibility of making atom optical devices.
Wider implications for atom lasers, interferometers.

7. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
At high incident velocities, measured reflection probability agrees well with “single-atom” theory.
Below 2 mm/s, measured reflection probability is constant.

8. y x T. Pasquini et al. Quantum reflection from a Si surface
PRL (2004) y
BEC prepared in 3D magnetic trap x
Equipotentials of 3D magnetic trap

9. Dx T. Pasquini et al. Quantum reflection from a Si surface
PRL (2004)
Equilibrium destroyed by shifting origin of the harmonic trap
Silicon wafer Dx
BEC accelerates towards Si surface.

10. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
The interaction of an atom with a Si surface can be described an attractive potential known as the Casimir-Polder potential.
Silicon wafer
~3 m

11. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

12. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

13. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

14. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

15. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

16. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

17. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
In a classical picture, no atoms would be reflected.
~3 m

18. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

19. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

20. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

21. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

22. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

23. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

24. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

25. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

26. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

27. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m

28. Quantum reflection from a Si surface
T. Pasquini et al.
Quantum reflection from a Si surface
PRL (2004)
Silicon wafer
Quantum reflection can occur if:
~3 m
We assume that atoms which are not reflected are either adsorbed by the Si or scatter inelastically.

29. The BEC reflects cleanly: no disruption occurs.
Reflection from a hard wall
Potential profile
High impact velocity: 2.1 mm/s
Large displacement
The BEC reflects cleanly: no disruption occurs.

30. The BEC becomes disrupted and two vortex rings form.
Reflection from a hard wall
Potential profile
Low impact velocity: 1.2 mm/s
Small displacement
The BEC becomes disrupted and two vortex rings form.

31. Reflection from a hard wall
t = 0 ms

32. Reflection from a hard wall
t = 90 ms
t = 0 ms
Due to the inter-atomic interactions, the high density in the standing wave causes atoms to be pushed into “side-lobes”.
At higher incident velocities, the BEC has insufficient time to respond to the high density in the standing wave.

33. For lobes to form: lobe formation time < reflection time
Reflection from a hard wall
t = 90 ms
t = 0 ms
For lobes to form: lobe formation time < reflection time
Radial width
Longitudinal width
Speed of sound
Impact speed
<
At higher incident velocities, the BEC has insufficient time to respond to the high density in the standing wave.

34. For lobes to form: lobe formation time < reflection time
Reflection from a hard wall
t = 90 ms
t = 0 ms
For lobes to form: lobe formation time < reflection time
Radial width
Longitudinal width
Speed of sound
Impact speed
<
Speed of sound n½

35. Reflection from a hard wall
t = 122 ms
t = 90 ms
t = 0 ms
The “side-lobes” are pushed back towards the axis of cylindrical symmetry by the trap, producing a soliton.

36. Reflection from a hard wall
t = 122 ms
t = 90 ms
t = 143 ms
t = 0 ms
The soliton decays into two vortex rings. At the end of the oscillation the atom cloud has a fragmented appearance.

37. Reflection from a hard wall
t = 122 ms
t = 90 ms
t = 143 ms
t = 0 ms
The soliton decays into two vortex rings. At the end of the oscillation the atom cloud has a fragmented appearance.

38. The BEC reflects cleanly: no disruption occurs.
Reflection from an abrupt potential drop
Potential profile
High impact velocity: 2.1 mm/s
Large displacement
The BEC reflects cleanly: no disruption occurs.

39. The BEC becomes disrupted and a vortex ring forms.
Reflection from an abrupt potential drop
Potential profile
Low impact velocity: 1.2 mm/s
Small displacement
The BEC becomes disrupted and a vortex ring forms.

40. The BEC reflects cleanly: no disruption occurs.
Reflection from a Si wall (Casimir-Polder potential)
Potential profile
High impact velocity: 2.1 mm/s
Large displacement
The BEC reflects cleanly: no disruption occurs.

41. The BEC becomes disrupted and a vortex ring forms.
Reflection from a Si wall (Casimir-Polder potential)
Potential profile
Low impact velocity: 1.2 mm/s
Small displacement
The BEC becomes disrupted and a vortex ring forms.

42. Hard Wall Step Silicon HIGH impact velocity (vx = 2.1 mm/s) LOW

43. For lobes to form: lobe formation time < reflection time
The role of the atom cloud aspect ratio
For lobes to form: lobe formation time < reflection time
Radial width
Longitudinal width
Speed of sound
Impact speed
<

44. For lobes to form: lobe formation time < reflection time
The role of the atom cloud aspect ratio
For lobes to form: lobe formation time < reflection time
Radial width
Longitudinal width
Speed of sound
Impact speed
<
× Speed of sound
Impact speed
Radial width
Longitudinal width
<

45. The role of the atom cloud aspect ratio
The simulation was repeated for a cigar-shaped BEC of identical density, for an impact velocity vx = 2.1 mm/s, for which no disruption was seen previously.

46. On quantum reflection side-lobes do indeed form…
The role of the atom cloud aspect ratio
On quantum reflection side-lobes do indeed form…

47. The role of the atom cloud aspect ratio
At the end of the oscillation the atom cloud contains a vortex ring, and has a fragmented appearance.

48. Reflection from a Si wall (Casimir-Polder potential)
With inter-atomic interactions
0.5
0.5
Without inter-atomic interactions

49. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms

50. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms

51. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms

52. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms

53. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms

54. Reflection from a Si wall (Casimir-Polder potential)
0.5
0.5
3×105 atoms
106 atoms

55. Reflection from a Si wall (Casimir-Polder potential)
Slope=½
3×105 atoms
106 atoms

56. Collisions between two BECs
(Analogous to reflection problem)
High impact velocity (large initial separation)
BECs pass through each other without disruption.

57. Collisions between two BECs
(Analogous to reflection problem)
Low impact velocity (small initial separation)
BECs become disrupted and vortex rings are formed.

58. Collisions between two BECs
t = 0 ms
Laser
How then can interference patterns be observed?
e.g. M.R. Andrews et al. Science 275 

59. Collisions between two BECs
t = 0 ms
t = 5 ms
Due to the rapid expansion the inter-atomic interactions are negligible once the interference pattern has formed.

60. Collisions between two BECs
t = 0 ms
t = 5 ms
Due to the rapid expansion the inter-atomic interactions are negligible once the interference pattern has formed.

61. Collisions between two BECs
t = 0 ms
Could the experiment be modified to observe different behaviour?
Let’s try turning the laser off 10 ms before the trap…

62. Collisions between two BECs
t = 0 ms
t = 1 ms
t = 4 ms
t = 10 ms

63. Collisions between two BECs
t = 0 ms
t = 1 ms
t = 4 ms
t = 10 ms

64. Future work Strategies for increasing R
Tailor the BEC’s initial state to suppress fragmentation of the atom cloud, e.g. pancake-shaped BECs
Engineer the surface to optimise the Casimir-Polder potential for quantum reflection, e.g. porous Si, near surface 2DEG.
Etched surfaces for atom optics
Curved surfaces, e.g concave mirror.
Zone plate
Scott et al. PRL (2003), PRA (2004), cond-mat/

65. Future work Strategies for increasing R
Tailor the BEC’s initial state to suppress fragmentation of the atom cloud, e.g. pancake-shaped BECs
Engineer the surface to optimise the Casimir-Polder potential for quantum reflection, e.g. porous Si, near surface 2DEG.
Etched surfaces for atom optics
Curved surfaces, e.g concave mirror.
Zone plate Si
Scott et al. PRL (2003), PRA (2004), cond-mat/

66. Future work Strategies for increasing R
Tailor the BEC’s initial state to suppress fragmentation of the atom cloud, e.g. pancake-shaped BECs
Engineer the surface to optimise the Casimir-Polder potential for quantum reflection, e.g. porous Si, near surface 2DEG.
Etched surfaces for atom optics
Curved surfaces, e.g concave mirror.
Zone plate
Scott et al. PRL (2003), PRA (2004), cond-mat/