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TitleAn Optical Conveyor for Light-Atom Interaction
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Table of Contents
Magneto-Optical Trap: Theory and Setup
	Theory of magneto-optical trapping
		Doppler cooling
		Magnetic trapping
		Multi-level atoms in a magneto-optical trap
	Experimental setup
		Rubidium source
		Vacuum chambers
		Magnetic fields
		Diode lasers
Optical Dipole Trap: Theory and Setup
	Theory of optical dipole trapping
		Classical Lorentz model
		Multi-level atoms in an optical dipole trap
		Trap parameters of the optical dipole trap
	Experimental setup
		Bottom layer
		Top layer
		Imaging techniques
		CCD camera
		Imaging setup
		Experimental control
Optical Dipole Trap: Results
		Number of atoms in the optical dipole trap
		Number of atoms in the magneto-optical trap
	Atomic lifetime in the optical dipole trap
		Experimental conditions
		Experimental results
Optical Conveyor: Theory and Test Setups
	Theory of atoms in moving optical lattices
		Trap parameters of a 1D optical lattice
		Hopping time between lattice sites
	Frequency sweep
		Heating due to frequency sweep
		Block signal
		Cosine signal
	Experimental setups
		Electronic setup
		Optical conveyor prototype
Optical Conveyor: Test Results
	Electronic setup
	Optical conveyor prototype
Optical Conveyor: Final Design
	Lower arm
		Displacement deviation
	Probe level
	Upper arm
	Side view
Appendix LgRb Lg hyperfine structure
Appendix Optical conveyor design
Document Text Contents
Page 1

University of Utrecht

Debye Institute

Cold Atom Nanophotonics Group

An Optical Conveyor for Light-Atom

S. Greveling B.Sc.

B. O. Mussmann M.Sc.
A. J. van Lange M.Sc.

Dr. D. van Oosten

December 22, 2013

Page 48

Optical Dipole Trap: Results

Power N0/U0 N0/NMOT

10.4 W (2.0± 0.5)× 105 atoms/mK (5.13± 0.26)× 10−4 %
9.3 W (2.0± 0.5)× 105 atoms/mK (4.55± 0.23)× 10−4 %
8.2 W (2.0± 0.4)× 105 atoms/mK (4.08± 0.20)× 10−4 %
7.0 W (1.9± 0.3)× 105 atoms/mK (3.19± 0.16)× 10−4 %
5.9 W (1.7± 0.3)× 105 atoms/mK (2.56± 0.13)× 10−4 %

Table 4.4: Fit results for the initial number of atoms N0 , and the ratio N0/NMOT for different trap

ODT from the MOT N0/NMOT is very low. For all different trap depths this ratio is
in the order of 4× 10−4 %. Note that the ODT is much smaller than the MOT.


Page 49

Optical Conveyor: Theory and Test Setups

5 Optical Conveyor: Theory and Test Setups

With the ODT, the atoms will be positioned above the sample at an estimated height
of 5 mm. For the experiment, the final step remaining is to position the atoms several
100 nm above the sample surface. To this end, the atoms are transferred from the
ODT into a standing-wave trap or optical conveyor. The optical conveyor is formed
by two counterpropagating focused-beam traps.

This section is divided into three parts. In Section 5.1, the trap depth and the
scattering rate are derived for the optical conveyor. Potential hopping or tunneling
of atoms between lattice sites is also discussed. In Section 5.2, possible heating effects
of the atoms in a “moving” standing-wave are investigated. With the heating effects
known, the frequency sweeps are derived which can be used to displace the anti-nodes
of the standing wave. In Section 5.3, the experiments used to test the performance
of the optical conveyor are discussed.

5.1 Theory of atoms in moving optical lattices

By interfering two counterpropagating laser beams, which have the same frequency
and intensity, a periodic intensity pattern is created. This is also referred to as an
one-dimensional optical lattice [18–20]. The periodic intensity pattern is described
by a standing wave. Here, the trap depth is determined by the intensity of the laser
beams. As we have seen in Section 3.1.1, atoms are attracted towards regions of high
intensity for red-detuned lasers. Therefore, the atoms are trapped in a 1D optical
lattice with periodicity λ/2. Note that this is the case when the counterpropagating
laser beams are perfectly collinear. The lattice spacing becomes larger when an angle
between the beams is introduced.

In this subsection, the trap depth and the photon scattering rate are derived from
the intensity distribution of the standing wave. The standing wave can be described
as the sum of the two individual counterpropagating beams

~E(y, t) = ~E+(y, t) + ~E−(y, t), (5.1)

where the + and − indices denote the direction of propagation. The propagation or
axial direction of the conveyor is chosen in the y-direction. For a Gaussian beam the
electric fields are given by

~E±(y, t) = E0e

w(y)2 e{(±kLy−! Lt), (5.2)

where E0 denotes the amplitude of the electric field of one laser beam, e

w(y)2 the
Gaussian distribution of the electric field, e{(±kLy−! Lt) the propagation of the electric
field in space and time, and kL = 2π/λ and ωL the wavenumber and frequency of


Page 95


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