Atom transport in optical light beams and photonic crystal fibres

1
Atom transport in optical light beams and
photonic crystal fibres
Kishan Dholakia University of St Andrews ,
Scotland
2
http//antwrp.gsfc.nasa.gov/apod/ap980717.html
3
FORCES OF LIGHT...
Light radiation pressure sailing out of the
solar system.?
http//www.spacetoday.org/Rockets/NASASpaceSails/S
ailingToStars.html
4
Forces on an atom?
5
Interactions with light
Atom-light interaction defines refractive index
of vapour n nreal i nimaginary
Dipole force real Radiation pressure
imaginary guiding cooling
6
Getting Cool
Unidirectional absorption of photon
7
Radiation pressure - atom cooling
8
Getting Cool
Whole process is cyclic
9
From cooling to trapping
Six lasers (plus re-pump) give us cooling,
but not spatial confinement.
10
Cold atoms trapped close to the surface of a
mirror
11
Dipole force

• Atom guides/optical traps rely on the
  conservative dipole force
• Optical potential can be both positive and
  negative!
• red-detuned attractive guides
• blue-detuned repellent guides

D frequency detuning ( D wL - wA )g
natural line width ISat Saturation intensity
12
Interferometric tweezers trapping hollow
spheres and rod-like samples
n1
Force
Laser Intensity Profiles
Force
n 13
Atomic guides
Magnetic guides accurate lithography - high
guiding potential split and curve
guides Hollow fibres Robust - can take out of
vacuum guide round bends Optical
guides Simple imaging - easy to put into vacuum
trap quick to reconfigure
14
Why guide atoms at all?

• High precision atom interferometric measurements
  allow
• confirmation of fundamental constants,
• probing of atomic properties, inertial forces
  and rotations.

• 1997 Nobel prize awarded for,
• methods of cooling and trapping atoms with
  laser light
• 2001 Nobel prize awarded for,
• the achievement of Bose-Einstein condensation
  in dilute gases of alkali atoms
• separate atomic species, new science (fermi
  gases), devices

15
Other Option for Guidance Magnetic Guiding

• Pros
• Guides can be created using current technology
• Can be switched at electronic rates

• Cons
• Guide channel cannot be exposed to atmosphere
• Problematic thermal dependence along guide
• Difficult to fabricate guiding geometry in 3D
• Issues to currents in small wires (heating)

16
Extracting atoms from the MOT

• Low Velocity Intense Source (LVIS) Z. T. Lu et
  al., Phys Rev Lett 77,3331 (1996)

• MOT with a hollow beam so the trapped atoms
  leak out

Re-circulated atoms
Hollow beam created using a spot on the
retro-reflector

• Intensity imbalance pushes the atoms out of the
  cloud.
• Cloud is refilled by re-circulated atoms

17
Laguerre-Gaussian modes

• Higher order transverse modes exist
• Laguerre-Gaussian modes are circular symmetric
  higher order modes, characterised by
• radial mode index p (determines
  radial structure)
• azimuthal mode index l (determines helicity)

p 0, l 4
p 1, l 1
p 0, l 0
p 0, l 1
18
Generating LG beams

• They can be produced using computer generated
  holograms
• We fabricate special holograms to generate
  various types of beams

l1
l6
l3
l2
19
Bessel light beams
Bessel beams have an intensity cross-section that
does not change as they propagate termed
non-diffracting. THE CENTRE DOES NOT SPREAD.
With and being the radial and
longitudinal components of the wavevector
Radial intensity profile
intensity
Zeroth order Bessel beam
The Bessel beam showing the narrow central maximum
20
Experimental Bessel beam

• Finite experimental aperture limits propagation
  distance of non-diffracting central maximum to
  zmax
• The on-axis intensity is no longer constant
• The axicon offers the most efficient method for
  generating a Bessel beam in the laboratory

21
(No Transcript)
22
Extended horizontal guiding of microspheres (a
precursor to atoms)
Gaussian beam guiding Ashkin, Phys Rev. Lett 24,
156 (1970)
Bessel beam is much better! And acts like a
washboard Phys Rev. Lett. 91, 012345 (2003)
23
Spatial light modulator a dynamic hologram!
24
Optical manipulation with SLMs at St Andrews.
25
Patterns created by the SLM for atom optics D.
McGloin et al, Optics Express 11, 158 (2003)
Mach-Zender pattern atomic interferometer
atomic beamsplitter
Can make blue-detuned patterns too...
26
Generating linear arrays of dipole traps (a)
zeroth order diffracted beam in pattern
centre (b) increase lattice constant then
spatially filter (c) design hologram for zeroth
order beam to be off-axis (upper right)
27
Creation of an optical bottle beam using an
SLM a blue detuned dark seeking trap
Arlt and Padgett, Optics Letters, 25 191
(2000) Freegarde and Dholakia, Phys. Rev. A 66,
013413(2002) Davidson group, Weizmann Institute
PRA (1996)
28
Aim of effort enhance manipulation of cold atoms
using novel light beam geometries

• Overview of cold atom work
• Laguerre-Gaussian/Bessel light beams
• Results for atom guiding
• Simulations for novel dipole traps for
  low-dimensional Bose-Einsteincondensates.

29
What stops atoms accelerating out of control?
Doppler effect works in our favour! It shifts the
absorption frequency of a moving atom such that
it absorbs a counter-propagating laser more
strongly.
Absorption increases as velocity
increases pushing-force is disabled when the
atom is cold
30
Tools for cold atoms
31
What do they look like?
32
(No Transcript)
33
Aim of effort enhance manipulation of cold atoms
using novel light beam geometries

• Overview of cold atom work
• Laguerre-Gaussian/Bessel light beams
• Simulations for novel dipole traps for
  low-dimensional Bose-Einstein condensates.

34
Why Guide Atoms?
Atom lithography Atom interferometers more
accurate measurements of rotating systems and
fundamental constants such as gravity Separating
samples transport to clean cells loading
cold atoms for BEC
35
Optical potentials for BEC

• Optical dipole trap rely on the conservative
  optical gradient force, which can be described
  using an optical potential
• For far off resonant light (DG) the optical
  potential is proportional to the light intensity.
• For red detuned light atoms are attracted to high
  intensity
• Optical potentials
• are state independent
• can be switched fast
• are easy to be loaded/used
• can be tailored easily to almost any desired shape

D Detuning, G natural linewidth, ISat
Saturation intensity
36
Cold atom source
Slow atoms using radiation pressure
Red-detuned lasers are used to add a velocity
dependence to the absorption
6 beams used to slow in 3-D but a magnetic field
is needed to trap the atoms - Magneto-Optical
Trap
37
M.O.T.
Lasers cool the atoms to 100mk 2cm/s
Linear magnetic field gives position
dependence Overcomes Earnshaws theorem
38
High-Order LG Beams
e.g. l4
l1
l4
Simulation of guiding potential along propagation
length up to the focus of an LG beam

• The dipole force accelerates the atoms to the
  centre of the guide

• Higher values for l increase the potential and
  can better guide atoms at the focus

J. Arlt et al.,Appl Phys B 71, 549 (2000)
39
Experiments -On Axis LG guiding

• 250mW, l2 beam focused to 800mm hole diameter
  detuned by 5GHz from resonance

40
Experiments -On Axis guiding

• 250mW, l2 beam focused to 800mm hole diameter
  detuned by 5GHz from resonance

1mm
LVIS
LVIS with guide
41
(No Transcript)
42
Far off resonant guiding
r500mm Gaussian beam 9W _at_ 1064nm
40 increase 4-5mm along LVIS
1mm
O. Houde et al., Phys. Rev. Lett. 85 5543
(2000) K. Szymaniec et al., Europhys. Lett. 45
450 (1999) J.Livesey et al., to be submitted
(2002)
43
Non-adiabatic kick to cold atomic beam (see also
O. Houde et al., Phys. Rev. Lett. 85 5543 (2000)

• Surge in fluoresceence as guide is introduced.
• Decay time of 0.34s in this instancepulsed
  guide gives enhanced flux.

(J. Livesey et al., to be submitted for
publication)
44
Oblique blue-detuned LG guiding

• Guiding using an l3 LG beam at 8o. An
  incoherent atom beamsplitter. Guide focused to
  give a 250mm diameter hollow region

5GHz blue guide, 180mW
LVIS
D.P. Rhodes et al., submitted for publication
(2002)
45
Effect of the guide beam

• The guide acts as a repulsive tube so few atoms
  get coupled into the centre of the guide

Re-circulating atoms are traveling slower and
build up around the guide more
Slower atoms are deflected around the guide
46
Blue detuned gaussian beams
(verification of the re-circulation of the LVIS
atoms)
180mW, 300mm radius, 5GHz detuned
47
Improving coupling into the guide

• Image an obstruction in the beam to create a hole
  in one side of the guide beam

• Diffraction fills in the small obstruction to
  give a solid beam further along the guide

LVIS
Blacked cover-slip used to block guide
The image of the beam has a hole on one side
48
Improved coupling with obstruction
180mW, l 3 guide with 600mm diameter hole, 5GHz
detuned
49
(No Transcript)
50
Propagation of obstructed light beams
Gap fills in after rayleigh range Allows atom
transport into oblique guides all optical atom
interferometry
51
Advanced scheme for Bessel beam guiding
ultra-cold atoms may propagate in modes along
this light beam
52
Dipole potential
wo300mm hollow region15mm D3GHz
prop. distance 5 cm
53
Toroidal trap for BEC

• Laguerre-Gaussian (LG) modes with radial mode
  index p 0 have an annular intensity cross
  section
• The peak radius rl increases with the azimuthal
  index l

P0 Power in LG beam, w waist size l
azimuthal mode index
An LG mode focused into a 2D BEC forms an annular
(toroidal) trap!
54
Loading a toroidal BEC (simulations)

• Efficient transfer (about 90) even into shallow
  traps (P0 0.1 mW, corresponding to a trap
  depth u1 -5.3 nK)
• For lower l considerably larger transients

55
Loading a peaked BEC
w rT
w 1.4 rT

• Even for initially peaked BEC an efficient
  transfer can be achieved (about 90)
• However, the peak radius of the initial BEC has
  to be wider than the ring radius of the trap

56
Bessel beams

• Bessel beams have an intensity cross-section that
  does not change as they propagate
• non-diffracting
• Bright narrow non-diffracting central maximum
• linear quasi-1D trap
• Finite experimental aperture limits the
  propagation distance of Bessel beams

57
Experimental Bessel beam

• Finite experimental aperture limits propagation
  distance of non-diffracting central maximum to
  zmax
• The on-axis intensity is no longer constant
• The axicon offers the most efficient method for
  generating a Bessel beam in the laboratory

58
Linear 1-D trap

• An experimental approximation to a Bessel beam
  has a maximum that propagates without spreading
  for a distance zmax
• Central intensity varies with propagation 3D
  trap
• Propagation distance zmax and radius of central
  maximum r0 can be changed independently
  Aspect ratio is adjustable
• Traps with extreme aspect ratios can be achieved!

zmax 3.4 cm
59
Summary low-dimensional traps

• Special light beams offer a simple way to realise
  low-dimensional trap geometries
• Focused LG beam to realize toroidal optical
  dipole traps
• Efficient loading should be possible straight
  from an centrally peaked 2D BEC
• Several studies are possible including
  persistent currents on a torus and vortices
• Bessel beam to realize linear 1-D trap
• 1D trap We show that the requirements for the
  observations of a Tonks gas can be achieved by
  tuning the scattering length
• E.M. Wright, J. Arlt, K. Dholakia, Phys. Rev A
  63, 013608 (2001)
• J.Arlt, K. Dholakia, J. Soneson and E.M. Wright,
  Phys. Rev. A 63, 063602 (2001)

60
Tonks gas

• New phenomena possible in 1D trap due to
  different statistics (even for classical
  gases)
• Tonks gas of impenetrable Bosons Bosons show
  some Fermionic behaviour!
• The spatial density distributions is proportional
  to that of a Fermi system the probability
  vanishes if the Bosons are in exactly the same
  state (Pauli exclusion principle for Fermions)
• This mix of Bosonic and Fermionic properties
  makes Tonks gas of great theoretical interest

61
Possible experimental realisation

• Stringent requirements on trap dimensions,
  particle number N and temperature T

N
with
From D. S. Petrov et al., PRL 85, 3745 (2000)
a s-wave scattering length W
longitudinal trap frequency wr, wz radial and
longitudinal ground state width wB
radius of central maximum
62
An example

• Trapping of rubidium atoms lA 780 nm using a
  NdYAG laser (lL 1064 nm)
• Bessel beam with wB 1.25 mm
  zmax 10 cm
  P0 5 W
• Radial ground state width wr
  82 nm, low aspect ratio
  (wr/wz)2 3.5 10-4
• For commonly used 87Rb isotope the scattering
  length is only a 5 nm, giving a modest N 420.
  
• However, for the 85Rb isotope the scattering
  length can be tuned using a Feshbach resonance.
• Even a moderate a 50 nm would make it possible
  to create a big Tonks gas with N ? 2000.

63
(No Transcript)
64
What is Fibre Guiding?

• The use of hollow tubes to guide light which, in
  turn, guides atoms.
• Many different types of tubes exist.

65
Why Fibre Guiding?
Fibres allow guiding around bends and through
atmosphere.
66
What do we need for Fibre guiding?
67
Atomic Flumes!
68
Coupling guide-light into the Fibre
Guide light can be coupled into the fibre by a
number of methods
But how do these propagate?
69
Guidance Efficiency
Basic Capillary guide
Guide beams
Limits
In both, the atoms need to overcome Van der
Waals attraction from the capillary walls.
70
Photonic Crystal Fibre PCF
A fibre with holes running parallel to its core.
Holes have a specific periodic
spacing, Periodicity creates a 2D photonic
bandgap A cylindrical Bragg reflector running
the length of fibre.
71
Photonic Band Gap Crystals
Photonic Bandgap (PBG) traps light through
interference (cf. TIR)
72
Index guidance ? Large-core single-optical mode
performance good for data comms.
PBG guidance ? Supports different intensity
profiles (eg. LG) !! confinement of atoms
to even smaller diameters !! Very low
attenuation of light in hollow cores.
73
What does PCF mean for Atom guidance?
74
Better Flumes!
Red -Significant reduction in guide
attenuation. -Can tailor fibre to support
specific guide frequencies.
Blue -Efficient true mode support. -Can now tune
light-pipe diameter.
75
Single Atomic-Mode Propagation
Multi-mode guidance ? Atom hosepipe Single mode
guidance? Highly localised spatialy coherent atoms
Coherent propagation occurs when De Broglie
wavelength approaches diameter of guide fibre
can confine guide diam.
BEC
Guide diameter dependence similar to
optical-single mode operation (ie. V number,
V
MOT
Attenuation distance scales as a3/?2 severely
limiting red guidance.
76
Recap Capillary vs. PCF
77
Whats been done?
Atom guidance performed in Capillary fibres by
Renn et al. (1995)
- Red injection with blue guidance along 3cm
giving multimode hosepipe. Proving it works but
inefficient.
Macroscopic particles guided in PCF by Bath group
(2002)
- Red guiding of ?m sized glass spheres.
LG/Bessel guiding at St Andrews. PCF atom vapour
guiding attempted in St Andrews

• Red guiding of Rb vapour current
  light-transmission efficiency 10 trans. over
  15cm.
• Unable to detect atoms at end facet yet!

78
Aims of project
- Cold Rb guidance from MOT
- Long distance atom transport
(20cm)
- Guiding round bends
15cm