Disruption of BoseEinstein Condensates on Classical and Quantum Reflection

1
Disruption of Bose-Einstein Condensates
onClassical 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
onClassical and Quantum Reflection

• R.G. Scott1, A.M. Martin2, S. Bujkiewicz1,
  T.M.Fromhold1, F.W. Sheard1,
• N. Malossi3, O. Morsch3, M. Cristiani3 and E.
  Arimondo3.
• 1School of Physics and Astronomy, University of
  Nottingham,Nottingham NG7 2RD, UK.
• 2School of Physics, University of Melbourne,
  Parkville, Vic. 3010, Australia.
• 3INFM, Dipartimento di Fisicia, Università di
  Pisa, Via Buonarroti 2, I-56127 Pisa, Italy.

3
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Overview

• Bragg reflection in optical lattices.

4
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Overview

• Bragg reflection in optical lattices.
• Classical reflection from a hard wall.

5
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Overview

• Bragg reflection in optical lattices.
• Classical reflection from a hard wall.
• Quantum reflection from an abrupt potential drop.

6
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Overview

• Bragg reflection in optical lattices.
• Classical reflection from a hard wall.
• Quantum reflection from an abrupt potential drop.
• Quantum reflection from a Si surface.

7
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Overview

• Bragg reflection in optical lattices.
• Classical reflection from a hard wall.
• Quantum reflection from an abrupt potential drop.
• Quantum reflection from a Si surface.
• Colliding BECs.

8
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Motivation

• Analysis of experiments.

9
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Motivation

• Analysis of experiments.
• Study of BEC excitations.

10
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Motivation

• Analysis of experiments.
• Study of BEC excitations.
• Probe of surfaces.

11
Disruption of Bose-Einstein Condensates
onClassical and Quantum Reflection
Motivation

• Analysis of experiments.
• Study of BEC excitations.
• Probe of surfaces.
• Possibility of making atom optical devices.

12
Disruption of Bose-Einstein Condensates
onClassical 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.

13
Optical lattice
390 nm
The optical lattice is formed by two
counter-propagating laser beams.
VLAT(x)
36 peV
The atom experiences the optical lattice as a
periodic potential.
x
14
Optical lattice
E
VLAT(x)

kx
The motion of an atom in an OL can be understood
in terms of Band theory.
x
15
Morsch et al. drove the BEC through the band by
accelerating the OL, rather than the BEC itself.

• Morsch observed Bloch oscillations of a 87Rb BEC.
  PRL 87 140402 (2001).

BEC dynamics modelled using time-dependent
Gross-Pitaevskii equation.
16
Morsch et al. drove the BEC through the band by
accelerating the OL, rather than the BEC itself.

• Morsch observed Bloch oscillations of a 87Rb BEC.
  PRL 87 140402 (2001).

Condensate motion
Semiclassical trajectory
17
Morsch et al. drove the BEC through the band by
accelerating the OL, rather than the BEC itself.

• Morsch observed Bloch oscillations of a 87Rb BEC.
  PRL 87 140402 (2001).

• We identify a new regime of condensate behaviour
  by accelerating the optical potential more slowly.

18
Stills from the movie
19
?Solitons form in response to the density nodes
and phase phase shifts imprinted on Bragg
relfection.
?Solitons form most readily if Bloch oscillations
are slow BEC can respond to standing wave.
20
?Solitons form in response to the density nodes
and p phase shifts imprinted on Bragg relfection.
?Solitons form most readily if correlation time
tcltlt Bloch period TB.
21
Collaboration with O. Morsch et al.
Fast OL acceleration tcTB
Slow OL acceleration tcltltTB
22
Collaboration with O. Morsch et al.
Fast Bloch oscillations
Slow Bloch oscillations
23
Collaboration with O. Morsch et al.
Fast Bloch oscillations
Slow Bloch oscillations
24
Experiments of S. Burger et al.
PRL 86 4447 (2001)
As before, BEC prepared in 1D optical lattice and
3D magnetic trap
Equipotentials of 3D magnetic trap
25
Experiments of S. Burger et al.
y
Equilibrium destroyed by shifting origin of the
harmonic trap
26
Experiments of S. Burger et al.
Burger observed highly damped oscillations, and
distortion and broadening of the condensate
profile.
12 ms
27
Experiments of S. Burger et al.
Burger observed highly damped oscillations, and
distortion and broadening of the condensate
profile.
18 ms
28
Experiments of S. Burger et al.
Burger observed highly damped oscillations, and
distortion and broadening of the condensate
profile.
29
Experiments of S. Burger et al.
Burger observed highly damped oscillations, and
distortion and broadening of the condensate
profile.
30
Experiments of S. Burger et al.
Burger observed highly damped oscillations, and
distortion and broadening of the condensate
profile.
31
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)

• At high incident velocities, measured reflection
  probability agrees well with single-atom
  theory.
• Below 2 mm/s, measured reflection probability is
  constant.

32
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
y
BEC prepared in 3D magnetic trap
x
Equipotentials of 3D magnetic trap
33
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Equilibrium destroyed by shifting origin of the
harmonic trap
Silicon wafer
Dx
BEC accelerates towards Si surface.
34
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (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
35
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
36
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
37
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
38
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
39
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
40
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
41
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
In a classical picture, no atoms would be
reflected.
3 ?m
42
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
43
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
44
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
45
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
46
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
47
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
48
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
49
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
50
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
51
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (2004)
Silicon wafer
Quantum reflection can occur if
3 ?m
52
T. Pasquini et al.
Quantum reflection from a Si surface
PRL 93 223201 (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.
53
Reflection from a hard wall
High impact velocity 2.1 mm/s
Potential profile
Large displacement
The BEC reflects cleanly no disruption occurs.
54
Reflection from a hard wall
Low impact velocity 1.2 mm/s
Potential profile
Small displacement
The BEC becomes disrupted and two vortex rings
form.
55
Reflection from a hard wall
t 0 ms
56
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.
57
Reflection from a hard wall
t 90 ms
t 0 ms
For lobes to form lobe formation time lt
reflection time
At higher incident velocities, the BEC has
insufficient time to respond to the high density
in the standing wave.
58
Reflection from a hard wall
t 90 ms
t 0 ms
For lobes to form lobe formation time lt
reflection time
Speed of sound ?n½
59
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.
60
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.
61
Reflection from a hard wall
t 122 ms
t 90 ms
t 143 ms
t 0 ms
High density in the standing wave leads to
formation of side-lobes.
The Side-lobes are pushed back by the trap,
producing a soliton
which decays into vortex rings.
62
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.
63
Reflection from an abrupt potential drop
High impact velocity 2.1 mm/s
Potential profile
Large displacement
The BEC reflects cleanly no disruption occurs.
64
Reflection from an abrupt potential drop
Low impact velocity 1.2 mm/s
Potential profile
Small displacement
The BEC becomes disrupted and a vortex ring
forms.
65
Reflection from a Si wall (Casimir-Polder
potential)
High impact velocity 2.1 mm/s
Potential profile
Large displacement
The BEC reflects cleanly no disruption occurs.
66
Reflection from a Si wall (Casimir-Polder
potential)
Low impact velocity 1.2 mm/s
Potential profile
Small displacement
The BEC becomes disrupted and a vortex ring
forms.
67
HIGH impact velocity (vx 2.1 mm/s)
Hard Wall
LOW impact velocity (vx 1.2 mm/s)
68
HIGH impact velocity (vx 2.1 mm/s)
Disruption at low
velocities is a
generic feature
of reflection from
regions of rapid
LOW impact velocity (vx 1.2 mm/s)
potential variation.
69
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.
70
The role of the atom cloud aspect ratio
71
The role of the atom cloud aspect ratio
72
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.
73
The role of the atom cloud aspect ratio
On quantum reflection side-lobes do indeed form
74
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.
75
Reflection from a Si wall (Casimir-Polder
potential)
With inter-atomic interactions
0.5
0.5
Without inter-atomic interactions
76
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
77
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
78
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
79
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
80
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
81
Reflection from a Si wall (Casimir-Polder
potential)
0.5
0.5
3105 atoms
106 atoms
82
Reflection from a Si wall (Casimir-Polder
potential)
Slope½
3105 atoms
106 atoms
83
Reflection from a Si wall (Casimir-Polder
potential)
a 2.9 nm
0.5
a 0
3105 atoms
106 atoms
84
(Analogous to reflection problem)
Collisions between two BECs
High impact velocity (large initial separation)
BECs pass through each other without disruption.
85
(Analogous to reflection problem)
Collisions between two BECs
Low impact velocity (small initial separation)
BECs become disrupted and vortex rings are formed.
86
Collisions between two BECs
t 0 ms
Laser
How then can interference patterns be observed?
e.g. M.R. Andrews et al. Science 275 637-641.
87
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.
88
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.
89
Collisions between two BECs
Could the experiment be modified to observe
different behaviour?
Lets try turning the laser off 10 ms before the
trap
90
Collisions between two BECs
91
Collisions between two BECs
92
Future work

• Strategies for increasing R
• Tailor the BECs 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 90 110404 (2003), PRA 69 033605
(2004), cond-mat/0412380.
93
Future work

• Strategies for increasing R
• Tailor the BECs 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 90 110404 (2003), PRA 69 033605
(2004), cond-mat/0412380.
94
Future work

• Strategies for increasing R
• Tailor the BECs 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 90 110404 (2003), PRA 69 033605
(2004), cond-mat/0412380.
95
Summary

• We have simulated Bloch oscillations of dilute
  gas 87Rb Bose-Einstein condensates in optical
  lattices.
• Bragg reflection can lead to the formation of
  solitons.
• The solitons decay into vortex rings.
• The formation of solitons and vortex rings cause
  disruption the condensate, and damping of the
  Bloch oscillations.
• Under certain conditions, the formation of
  solitons and vortex rings triggers explosive
  expansion of the condensate.

Scott et al. PRL 90 110404 (2003), PRA 69 033605
(2004).