Novel light beams for manipulation of cold atoms, BoseEinstein condensates and microscopic objects

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Novel light beams for manipulation of cold atoms,
Bose-Einstein condensates and microscopic
objects

• Dr Kishan Dholakia
• University of St Andrews

Dr Jochen Arlt Prof Ewan Wright, Tucson,
Arizona John Livesey Prof W Sibbett Daniel
Rhodes Gavin Lancaster (Innsbruck) Dr Michael
MacDonald Lynn Paterson Veneranda
Garces-Chavez
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Outline of talk

• Objectives of our research use of light beams
  to manipulate cold atoms and microscopic
  particles
• Introduction to Laguerre-Gaussian and Bessel
  light beams
• Recent results at St Andrews
• cold atom guiding
• optical traps for BEC
• rotation of trapped particles
• Bessel beam tweezers

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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
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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
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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
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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

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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.

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Why Guide Atoms?
Atom lithography Atom interferometers more
accurate measurements of rotating systems and
fundamental constants such as gravity. NEED
OBLIQUE AND INCLINED GUIDES Separating
samples transport to clean cells loading cold
atoms for BEC
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Atomic guides
Magnetic guides accurate lithography - high
guiding potential split and curve
guides Hollow fibres Robust - can take out of
vacuum bend Optical guides Simple imaging
- easy to put into vacuum trap quick to
reconfigure
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Interactions with light
Atom-light interaction defines refractive index
of vapour n nreal i nimaginary
Dipole force real Radiation pressure
imaginary guiding cooling
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Optical potentials

• Optical dipole trap rely on the conservative
  optical gradient force, which can be described
  using an optical potential
• For far off resonant light (DgtgtG) 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
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Dipole force

• Atom guides 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
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Radiation pressure - atom cooling
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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 -gt Magneto-Optical
Trap
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M.O.T.
Lasers cool the atoms to 100mk 2cm/s
Linear magnetic field gives position
dependence Overcomes Earnshaws theorem
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Cold atoms trapped close to the surface of a
mirror
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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

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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)
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Experiments -On Axis guiding

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

1mm
LVIS
LVIS with guide
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Oblique 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
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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
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Blue detuned gaussian beams
(verification of the re-circulation of the LVIS
atoms)
180mW, 300mm radius, 5GHz detuned
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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
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Improved coupling with obstruction
180mW, l 3 guide with 600mm diameter hole, 5GHz
detuned
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Red-detuned guiding
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Far off resonant guiding
r500mm Gaussian beam 9W _at_ 1064nm
70 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., in preparation
(2001)
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Exponential decay seen due to non-adiabatic kick
of the atoms when guide introduced
Enhanced pulsed fluxes from cold atom ensembles
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Advanced scheme for guidingBessel beam
ultra-cold atoms may propagate in modes along
this light beam
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Dipole potential
wo300mm hollow region15mm D3GHz
prop. distance 5 cm
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Annular 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
trap!
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Numerical simulations
Quasi 2D Gross-Pitaevskii equation
g is the effective short range interaction
length U the dipole potential the 2D
Laplacian
Use Thomas-Fermi solution mean field energy gt
kinetic energy. Ring width lttoroid radius
(Harmonic oscillator)
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Loading a toroidal BEC

• 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

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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

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Bessel beams

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

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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

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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 gt 3D
  trap
• Propagation distance zmax and radius of central
  maximum r0 can be changed independentlygt
  Aspect ratio is adjustable
• Traps with extreme aspect ratios can be achieved!

zmax 3.4 cm
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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

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Possible experimental realisation

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

N lt N and T lt N ? W
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
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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.

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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 et al., Phys. Rev. A 63, 063602 (2001)

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Optical tweezers

• Particle makes rays experience a change in
  momentum, thus the particle experiences an equal
  but opposite change in momentum

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Optical levitation
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Graphical view of how tweezers work
Multitude of biological applications. Pick laser
light frequency so that sample does not absorb -
no optocution
Controlled movement and positioning of biological
samples
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Optical tweezers

• NdYAG laser commonly used (1064nm) - does not
  optocute biological samples

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Optical tweezers
Laser beam - typically near IR
Sample slide

• Excellent tool for biologists

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Interferometric tweezers
Light can exhibit wave like properties and show
interference
Motivation We can utilise this to trap multiple
particles and rod-like samples (chromosomes) in
the fringes!
Instead of a single beam use two beams and
interfere them at the position of the particles.
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Trapping using interference patterns

• Optical tweezers generally make use of a focused
  Gaussian beam
• Interference patterns could give greater control
  of particles in tweezer experiments
• Interference fringes could be used to align rod
  shaped particles
• Low-index particles usually repelled from
  optical tweezers
• Rotational control is needed in some cases but
  cannot be easily achieved (can only move in x y
  and z)

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Trapping using interference fringes

• Changing the path length of one of the beams
  makes the fringes sweep across the beam spot

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The Experiment
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Interferometric tweezers trapping hollow
spheres and rod-like samples
ngt1
Force
Laser Intensity Profiles
Force
nlt1
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Interference fringes result
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Laguerre-Gaussian Light beams

• Helical phase front (compare a plane wave)

Orbital angular momentum

• Poynting vector S follows a helical path

l0
l3
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Rotation
Pasta (l 2 phase fronts)
Rope (l 3 phase fronts)
Plane wave l 3 LG beam

• l 2 and l 3 beams are double or triple start
  helices - the phase follows a corkscrew like path
• Changing path length of one of the beams results
  in a change of phase difference between the two
  beams therefore the intensity pattern changes.
  The spiral appears to rotate around the central
  axis.

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Spiral pattern for rotating trapped particles
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How changing path length in the interferometer
rotates the pattern
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Rotation Results
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The Angular Doppler Effect continuous rotation
of particles
Frequency of light shifts going through a
rotating half-wave plate. The frequency
difference between the two arms results in
pattern rotation.
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Continuous rotation
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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
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Experimental Bessel tweezers
J. Arlt et al., Opt. Commun. 197, 239 (2001)
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Stacking of trapped particles
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Alignment of particles 1
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Alignment of particles 2
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Potential future biological applications of
Bessel tweezers

• All-optical guide - e.g. transport chromatid
  fragment away from parent chromosome (to a PCR
  chamber)

• Tissue engineering deposition of tissue culture
  in specific regions

target
E.g. hepatocytes cultured as a monolayer overlaid
with collagen gel retain liver-specific functions
Bessel beam
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Vertical guiding of particles
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Horizontal guiding of particles
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First order Bessel beam
Radial intensity profile
The first (and higher) order Bessel beams have
on-axis singularities (vortex)
intensity
They have a central non-diffracting dark core of
radius

A first order Bessel beam can be generated by
illuminating and axicon with a beam with a phase
singularity a Laguerre-Gaussian beam. This beam
will have orbital angular momentum (helical
wavefronts).
Novel method of high order Bessel beam formation
(J. Arlt and K. Dholakia, Opt. Commun. 177, 297
(2000)
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Orbital angular momentum of a Bessel Light beam
V. Garces-Chavez et al. submitted for publication
(2001).
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Novel Optical Light Beams
Tweezing of low-index particles/arrays of
high-index particles Rotation of trapped
particles Bessel beam tweezers
Studies of cold atom guiding Advanced
manipulation of BECs Atom Interferomtery
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Chromosomes

• The DNA double helix contains all the genetic
  information of an organism
• At a certain stage in the cell division cycle the
  DNA condenses
• Changes in the sequence of the DNA molecule can
  lead to cancer

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Application of tweezers to chromatid break studies

• One double strand break in the DNA double
  helix, caused by radiation or genotoxins, can
  lead to chromatid breaks visible in metaphase
  chromosomes under microscope
• How does one dsb lead to an apparent loss of up
  to 40 mega bases (One third of a chromatid arm)?
  (It is not caused by two cuts)

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The Signal Model

• Proposes that one dsb causes the chromatid break
• dsb signals to cell to make exchange at neck of
  loop
• results in inter- or intra- chromatid exchanges

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The Signal Model
Possible mechanisms for a colour-switch
rearrangement
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The Signal Model
Non colour-switch rearrangements can be oncogenic
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Plan of Action
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Current set-up for generating chromosome specific
paint probes
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Chromosome results
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Novel Optical Tweezers for Biosciences
Tweezing of low-index particles/arrays of
high-index particles (M.P. MacDonald et al., Opt.
Lett. 26, 863 (2001) Rotation of trapped
particles L. Paterson et al, Science 292, 912
(2001) Bessel beam tweezers J. Arlt et al., Opt.
Commun. 271.179 (2001)
Tweezing/cutting chromosomes study of generating
specific paint probes for study of chromosome
damage