Collective Atom–Light Interactions in Dense Atomic Vapours

153 Pages·2014·5.578 MB·English

by  James Keaveney (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
James Keaveney

Collective
Atom–Light
Interactions in
Dense Atomic
Vapours
Springer Theses
Recognizing Outstanding Ph.D. Research
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James Keaveney
Collective Atom–Light
Interactions in Dense
Atomic Vapours
Doctoral Thesis accepted by
Durham University, UK
123
Author Supervisor
Dr. JamesKeaveney Prof.Charles Adams
Department of Physics Department of Physics
Durham University Durham University
Durham Durham
UK UK
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-319-07099-5 ISBN 978-3-319-07100-8 (eBook)
DOI 10.1007/978-3-319-07100-8
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Supervisor’s Foreword
Theinteractionoflightandmatterunderliesmanyareasofscience.Eventhoughour
understandinghasadvancedenormouslythereremainsomefundamentalquestions
thatareverydifficulttoanswer.Forexample,ifonetakesthesimplestconceivable
systemoflight-induceddipolesandthenallowsthesedipolestointeract,thetheo-
retical description quickly becomes unmanageable as we have N interacting par-
ticles,whereN maybelarge,inanopenquantumsystem.Theinteractingdipoles
establish correlations that invalidate the mean field description of Maxwell’s
equations in a medium. However, if there is strong dephasing of the interacting
dipolesthecorrelationsaredestroyedandamean-fielddescriptionisre-established.
To understand these ideas requires detailed simple model systems where experi-
mentaldatacanbecomparedtotheoreticalsimulations.
This thesis presents one approach to address such questions. The main results
concern an experimental study of interacting atomic dipoles in a thin almost
two-dimensional gaseous layer with a thickness in the range of 100 nm–1 lm.
Thelayerconsists ofalkaliatoms (withasingleactivevalence electron) confined
betweentwosuperpolishedsapphirewindows.Theatomsareprobedusingaweak
laser beam tuned through the main atomic resonance. The ability to compare the
measuredspectrawithamodelthatprovidesanaccuratedescriptionintheweakly
interacting regime makes it possible to extract the interesting physics of strongly
interacting dipoles. Due to the thermal motion of the atoms there is strong
dephasing of the dipoles but, remarkably, it is still possible to observe coherent
features of the dipole–dipole interaction. For example, as the length of the cell is
varied one sees that the dipole–dipole-induced shift of the atomic resonance line
oscillates with a period equal to one half the wavelength of the incident light.
Historically, this propagation dependence of the mean-field shift is referred to
as the collective or cooperative Lamb shift. This term arose because the
dipole–dipole interactions within an ensemble may be modelled in terms of the
exchange of virtual photons, similar to the self-interaction of an electron with a
field of virtual photons. Despite the fact that these ideas have a long history, this
thesis reports the first experimental measurement of the length dependence of the
collective Lamb shift.
v
vi Supervisor’sForeword
The experiment reported here has stimulated new theoretical work and further
experiments that have enhanced our understanding of light–matter interactions
in simple systems where the full many-body description is still challenging.
Thisknowledgecannowbeexploitedtodesignopticalsystemswiththepotential
for new applications in quantum optics.
Durham, April 2014 Prof. Charles Adams
Abstract
This thesis presents an investigation of the fundamental interaction between light
andmatter,realisedwitharubidiumvapourconfinedinacellwhosethickness(in
the propagation direction) is less than the optical wavelength. This confinement
allows observation of spectroscopic features not found in longer cells, such as
Dicke narrowing. These effects are measured experimentally and a theoretical
model is developed, which allows the characterisation of the medium in terms of
the atomic electric susceptibility. Interactions between the atoms and their
surroundings, whether this be the walls of the cell or other nearby atoms, are
explored. In the frequency domain we observe broadening and shifts of
the spectral features due to these interactions. The atom–surface interaction shifts
the spectral lines, following the expected 1/r3 van-der-Waals behaviour. The
interatomic dipole–dipole interactions are more complex, and we find collective
effects play an important role. We present an experimental verification of the full
spatial dependence of the cooperative Lamb shift, which follows the theoretical
predictionmade40yearsago,animportantdemonstrationofcoherentinteractions
in a thermal ensemble.
The interactions also play a role in determining the refractive index of the
medium,limitingthemaximumnear-resonantindexton=1.31.Usingheterodyne
interferometry, we experimentally measure an index of n = 1.26 ± 0.02. This
index enhancement leads to large bandwidth regions where a significant slow- or
fast-light effect is present. We verify the fast-light effect in the time domain by
observing the superluminal propagation of a sub-nanosecond optical pulse, and
measurethegroupindexofthemediumtoben = -1.0 ± 0.1 9 105,thelargest
g
negative group index measured to date.
Weinvestigatetheradiativedecayrateusingtime-domainfluorescence,andwe
observe radiation trapping effects in a millimetre-thickness vapour. Finally, we
present results on sub-nanosecond coherent dynamics in the system which are
achieved by pumping the medium with a strong optical pulse.
vii
Acknowledgments
This thesis would not have been possible without the help and support of many
people. First and foremost I would like to thank my supervisor, Charles Adams,
without whom this thesis would not have been possible. His passion and enthu-
siasm for science is second to none, and his guidance and insight have been
invaluable over the past few years. My thanks also go to Ifan Hughes for his
valuable contributions to the project, innumerable enlightening conversations
about physics and proof-reading of this thesis, as well as many ‘fruitful discus-
sions’ about all things football.Aspecial mention must goto ourcollaborators in
Armenia, Armen and David, who make the finest, thinnest vapour cells in the
world. Certainly without these cells this thesis would not be what it is today.
Thanks go to my office mates Lee (cheers, mush), Dan and Tim. Their
friendship and banter has made the days spent in the office more enjoyable, par-
ticularlyinthelastfewmonthswhilstwritingup.ItisagreatrelieftoknowthatI
will never again be forced to listen to Radio 1 Xtra, courtesy of Chris.
Questionable taste in music aside, it has been a pleasure to share a lab with him
andIamfortunatetohavebenefittedfromhisexpertise(andoftenhisequipment)
overtheyears.IamalsogratefultoUlrichforteachingmetheexperimentalskills
andsettingmeoffontherighttrackinthelabatthebeginningofmyPh.D.andto
Christophe and Rob for many discussions about dipole–dipole interactions. Kate
joinedtheprojectinOctober2012,andItakethisopportunitytowishherluckfor
the future, as well as thank her for proof-reading a large part of this thesis.
I would like to extend my thanks to the rest of AtMol. I am sure that the
friendly atmosphere and real camaraderie that exists in the group has a direct
influence on its success, whether that be through stimulating discussions in the
tea room or the willingness of every member to share their time and expertise to
help someone else out.
My acknowledgments would not be complete without thanking the most
important people in my life. To mam, dad, Veronica and Joseph—thank you for
helping me achieve as much as I have done, for your constant encouragement in
everythingthatIdo.Andfinally,toZara—thelastthreeandahalfyearshavehad
their ups and downs, and you’ve been there with me through all of it. Thank you
for all of your love and support, I couldn’t have done it without you.
ix
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Strong Interactions and Collective Effects. . . . . . . . . . . . . . . . 1
1.2 Thermal Vapours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Nano-Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Structure of this Thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Atom–Light Interactions for Independent Atoms. . . . . . . . . . . . . 9
2.1 The Two-Level Atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Hamiltonian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Electric Susceptibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Motion and the Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Lineshapes: Lorentzians, Gaussians and the Voigt Profile. . . . . 16
2.5 Atomic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Thin Cell Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Dicke Narrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Modelling Dicke Narrowing . . . . . . . . . . . . . . . . . . . . 24
3.2 Mixing of Reflection and Transmission. . . . . . . . . . . . . . . . . . 26
3.2.1 Thin Film Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 The Weak-Probe Limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Atom–Surface Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 The van der Waals Atom–Surface Interaction . . . . . . . . . . . . . 35
4.1.1 Atom–Surface Potential in the Nano-Cell . . . . . . . . . . . 36
4.2 Monte-Carlo Simulation of Interaction Time Distribution . . . . . 37
4.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
xi