Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
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Theses are accepted into the series by invited nomination only
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accessible to scientists not expert in that particular field.
André Xuereb
Optical Cooling Using the
Dipole Force
Doctoral Thesis accepted by
The University of Southampton, UK
123
Author Supervisor
Dr. André Xuereb Dr. Tim Freegarde
Universityof Southampton Universityof Southampton
UK UK
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-642-29714-4 ISBN 978-3-642-29715-1 (eBook)
DOI 10.1007/978-3-642-29715-1
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012939044
(cid:2)Springer-VerlagBerlinHeidelberg2012
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‘‘It is an important and popular fact that
things are not always what they seem. For
instance, on the planet Earth, man had
always assumed that he was more intelligent
than dolphins because he had achieved so
much—the wheel, New York, wars and so
on—whileallthedolphinshadever donewas
muck about in the water having a good time.
But conversely, the dolphins had always
believed that they were far more intelligent
than man—for precisely the same reasons.’’
Douglas Adams
The Hitchhiker’s Guide to the Galaxy
For Sharon, for my family,
and for a hot cup of tea
(u lil ommi, li g(cid:2)hallmitni ng(cid:2)hodd)
Supervisor’s Foreword
Thevibrantfieldsofatomiclasercoolingandoptomechanics,bothofwhichaimto
slow down the random motion of matter using light, have in the past progressed
alonglargelydisparatepaths:theoccasionallinkwasmadebetweenthetwofields,
butaunifiedtheorythatcandescribebothdomainswaslacking.Perhapsthemajor
achievement in this thesis is a scattering theory, based on a compact method of
solving Maxwell’s equations in one dimension, that transcends the distinction
between ‘atom’ and ‘mirror’ and can move smoothly between these two regimes.
As a direct result, this thesis unifies the dissipative dynamics of an atom, particle
or structure within an optical field that is inuenced by the position of the atom,
particle or structure itself.
The first part of this thesis starts with a pedagogic introduction to atomic
physics and laser cooling, and then establishes links to several ideas that are
subsequently used throughout. The concept of cooling by using an optical mem-
ory, which proves to be extremely powerful and wide-ranging, appears early on
and provides a backbone to the thesis. The bulk of this work is then devoted to
using the scattering theory, together with this idea of an optical memory, to
analyse and propose several models for laser cooling atoms, microspheres or
mirrors,indifferentgeometries.Thefocusinthelatterchaptersthenturnstowards
the experimental side of laser cooling: a description of one of the experiments
beingundertakenattheUniversityofSouthamptonisfollowedbyamoregeneral
‘experimentalist’s guide’ to the different concepts covered, in essence answering
the question of which method is likely to work best in different geometries and
under different conditions.
The work described in this thesis is important not only in its own right,
describing as it does several models as different aspects of a single key concept,
butisalreadyprovidingthefoundationforideasthatcanimproveoptomechanical
cooling beyond the current state-of-the-art by several orders of magnitude.
Southampton, UK, February 2012 Dr. Tim Freegarde
ix
Acknowledgments
Istartedmydoctoralresearchnotknowingquiteabit.Iwillforeverbeindebtedto
allthosewhowere theretopatientlyguide me alongthe way and,perhaps justas
patiently,pointmeintherightdirectioninthe1,001occasionswhereIinterrupted
their thoughts to ask some basic question.
TheQuantumControlgroupattheUniversityofSouthamptonhasalwaysbeen
abitofamysterytome:momentsoftremendousinsightaregenerallypunctuated
byperiodswhereweallseemtobe8yearsold.Iappreciatebeingthrownintothe
deep, dark end of experimental atomic physics during the first few weeks of my
stay at Southampton when James Bateman and Matthew Himsworth asked me to
dosomeworkintheirlaboratory.Mysubsequentpredilectionfortheoreticalwork
should not be interpreted as being due to that experience! James also provided
some much needed physical insight at times. Richard Murray, who I am fond of
disagreeingwith,oftenprovidedanextrapointofviewonwhateveritwasthatwe
wouldbediscussingatthetime.BeinganopinionatedMediterranean,Ifoundthis
rather useful (in retrospect, of course). Hamid Ohadi, the experimentalist par
excellence and former ion trapper, and his laboratory provided a well-needed
distractionwheneverIgotboredwithmysums.IwouldalsoliketothankNathan
Cooper, who is working with Hamid to explore experimentally some of our less
crazy ideas and who took over my duty as offcial tea-maker on Fridays.
I must also mention Peter Domokos, whose insight triggered off a sequence of
eventsthatledtotheresultsinthisthesisthatIam perhaps mostproud of.Sandro
Grech and the various advisers and tutors I had at the University of Malta,
especiallyDavidBuhagiarandCharlesSammut,alwaysencouragedmetopursue
my fascination with mathematics and physics.
Finally, I must thank my family for their support; every one of them1 was an
inspiration, and I would have been a very different person were it not for them.
Sharon, who always stuck by my side, listening to my grumbling, pushing me
1 Andtherearequiteafew:Zak,Luke,Rebekah,Konrad,Charmaine,Maria,andofcoursemy
parents.
xi
xii Acknowledgments
alongandgenerallybeingthereforme,Icannothelpbutthankfromthebottomof
my heart.
‘‘Oh, and just one more thing...’’—words probably cannot express how exas-
perated my supervisors, Tim Freegarde and Peter Horak, must have felt at times
because of my hard-headedness. Without their help this work would have never
gottentothestartingblocksand,attheriskofrepeatingmyselfIfeelIhavetotell
them a deeply heartfelt ‘‘thanks!’’ Working with both of them proved to be a
tremendous learning experience and I have nothing but words of praise for them,
both in their role as advisers and in their role as scientists.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Overview of Past Work . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Outline of Thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Logical Connections Between Chapters. . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Part I Atomic Physics Theory and Cooling Methods
2 Atom–Field Interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Atomic Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Density Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 The Optical Bloch Equations . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Interaction with the Quantised Field . . . . . . . . . . . . . . . 15
2.3.2 Interaction with the Incident Field . . . . . . . . . . . . . . . . 15
2.4 Polarisability of a Two-Level Atom. . . . . . . . . . . . . . . . . . . . . 17
2.5 Energy Balance: Work Done on a Two-Level Atom . . . . . . . . . 21
2.6 Forces on a Two-Level Atom. . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 The Fluctuation–Dissipation Theorem . . . . . . . . . . . . . . . . . . . 24
2.8 Beyond Two-Level Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Trapping and Cooling Atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Dipole Traps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Optical Molasses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Magneto-Optical Traps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Memory-Based Approach to Cooling in Laser Light:
The Dipole Force Retarded. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
xiii
