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High-resolution ultra-short optical pulse shaping and coherent control over the photoasociation of ultra-cold atoms [Elektronische Ressource] / vorgelegt von Terence Gerald Mullins

144 pages
High-Resolution Ultra-short Optical PulseShaping and Coherent Control over thePhotoassociation of Ultra-Cold AtomsTerence Gerald MullinsFakult¨at fu¨r Mathematik und PhysikAlbert-Ludwigs-Universita¨t FreiburgHigh-Resolution Ultra-short OpticalPulse Shaping and CoherentControl over the Photoassociationof Ultra-Cold AtomsInaugural-DissertationzurErlangung des Doktorgradesder Fakulta¨t fu¨r Mathematik und Physikder Albert-Ludwigs-Universit¨atFreiburg im Breisgauvorgelegt vonTerence Gerald Mullins BSc., P.G.Dip.Sci., MSc. (hons.)aus Wanganuiim Oktober 2010Dekan: Prof. Kay Ko¨nigsmannLeiter der Arbeit: Prof. Dr. Matthias Weidemu¨llerReferent: Prof. Dr. Matthias Weidemu¨llerKoreferent:Pru¨fer: Prof. Dr. Frank StienkemeierProf. Dr. Andreas BuchleitnerTag der mu¨ndlichen Pru¨fung 12. November 2010AcknowledgementsIwould like to thankthefollowing people for their help, support,encourage-ment, money, time, company, suggestions, discussions, beer, humour (goodand bad), and general presence during the time I worked on this PhD:First I would like to thank the person who influenced me most duringmytimeinFreiburg: mysupervisor,MatthiasWeidemulle¨ r,whosenever-endingquestfor“ein einfachesBild”forcesyou toactually thinkaboutwhatyou are doing. Luckily my artistic ability only extends as far as stick figuresanyway.A big thank-you to Roland Wester for all his tips and great adviceover the last few years.
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High-Resolution Ultra-short Optical Pulse
Shaping and Coherent Control over the
Photoassociation of Ultra-Cold Atoms
Terence Gerald Mullins
Fakult¨at fu¨r Mathematik und Physik
Albert-Ludwigs-Universita¨t FreiburgHigh-Resolution Ultra-short Optical
Pulse Shaping and Coherent
Control over the Photoassociation
of Ultra-Cold Atoms
Inaugural-Dissertation
zur
Erlangung des Doktorgrades
der Fakulta¨t fu¨r Mathematik und Physik
der Albert-Ludwigs-Universit¨at
Freiburg im Breisgau
vorgelegt von
Terence Gerald Mullins BSc., P.G.Dip.Sci., MSc. (hons.)
aus Wanganui
im Oktober 2010Dekan: Prof. Kay Ko¨nigsmann
Leiter der Arbeit: Prof. Dr. Matthias Weidemu¨ller
Referent: Prof. Dr. Matthias Weidemu¨ller
Koreferent:
Pru¨fer: Prof. Dr. Frank Stienkemeier
Prof. Dr. Andreas Buchleitner
Tag der mu¨ndlichen Pru¨fung 12. November 2010Acknowledgements
Iwould like to thankthefollowing people for their help, support,encourage-
ment, money, time, company, suggestions, discussions, beer, humour (good
and bad), and general presence during the time I worked on this PhD:
First I would like to thank the person who influenced me most during
mytimeinFreiburg: mysupervisor,MatthiasWeidemulle¨ r,whosenever-
endingquestfor“ein einfachesBild”forcesyou toactually thinkaboutwhat
you are doing. Luckily my artistic ability only extends as far as stick figures
anyway.
A big thank-you to Roland Wester for all his tips and great advice
over the last few years. A genuine physics enthusiast coupled with a hard-
ened Mensa veteran, Roland somehow manages to contribute to, if not lead,
in-depth lunchtime discussions whilst somehow managing to find so-called
“Schnitzel mit Pommes” actually palatable. I wish you all the very best in
Innsbru¨ck.
When I arrived in Freiburg my life was initially organized by Wenzel
Salzmann, both at work and privately. An enormous thank-you to him for
that as well as his general competence and positive, relaxed attitude in the
lab, not to mention the after-work drinking sessions at KGB and various
other seedy establishments. Oh my ^¨ head! I would also like to thank the
other lucky people with whom I worked on this project: Simon Bernon,
MagnusAlbert(phew,Iwasfaster),JudithEng,SimoneG¨otz(mahna
mahna),InaBlank,KatjaReiser,ChrisLimbach,andBrettDePaola
(who seemed to especially enjoy the wine festivals and beer gardens). It was
a lot of fun, let’s do it again sometime.
Thanks to the many other people who have been part of the group at
various times, namely: Peter Staanum,Anna Grochola, Stefan Kraft,
J¨org Lange, Johannes Deigelmayr (for proof-reading this thesis, and
especially for the loan of his girlfriend whilst he was in Paris),Marc Repp,
Benjamin Mulle¨ r, Leif Vogel, Christian Giese, Christian Gluc¨ k,
Karin M¨ortlbauer, Markus Reetz-Lamour, Thomas Amthor, Han-
nah Schemp, Christoph Hoffman, Sebastian Westermann, Janne
Denskat,WendelinSprenger,PetrHlavenka,ThorstenBest,Jochen
Mikosch,SebastianTrippel(“It’sreallygood,youjusthavetotryharder!”),
iRico Otto (who’s ability for interesting time-wastage is comparable to my
own), Christph Eichhorn, Ruth Billen, Sebastian Kaiser, Christian
Greve, Markus Debatine, Marten Stai, Alex von Zastrow, Steffi
Eistenbach, Jonathan Brox, Sebastien Jezouine, Anna Go¨ritz, Jo-
hannes von Vangerow, and Helga Mulle¨ r. Thanks for the good com-
pany, interesting discussions, and general attempts at making life more fun.
To the rest of the Heidelberg contingent, thanks for the desk space, free
coffee, and lunchtime pizzas when I came to visit.
The whole group ofLudger W¨oste deserves a big thank-you for all the
help and support during my time in Berlin.
Ich mo¨chteallen Mitarbeitern der Mechanikwerkstatt danken, die
immer bereit waren, mir zu helfen. Einen ganz herzlichen Dank vor allem
an Tobi Schellhammer fu¨r seine Zeit und Hilfe mit dem Shaperaufbau,
den -verbesserungen, -verbesserungen Mk. II, dem -umbau, und fu¨r seine
allgemein gute Laune (“machen ma alles”).
I would also like to thank my family: My parents, Terry and Lesley,
my siblings, Theresa, Cathy andPatrick, and all the other aunts, uncles
and cousins for whom, thanks to the family’s high-productivity, there is
unfortunately not enough space to name. Thank-you most of all for all
the fun, but also for your love, help and support over the last 30 years,
without which I wouldn’t be where I am today. To my soon-to-be family:
Joachim, Wiltrud, Rebekka, Andreas, andRaphael, thank-you all for
the ridiculous volumes of coffee and cake we managed to consume together,
but most of all thanks for making me feel so welcome.
And last, but especially not least,Dejana, thanks for not saying no. :-P
stTerry Mullins, 1 October, 2010
iiList of publications covered in this thesis:
W. Salzmann, T. Mullins, J. Eng, M. Albert, R. Wester, M. Wei-
demu¨ller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise,
L. W¨oste, and A. Lindinger. Coherent transients in the femtosec-
ond photoassociation of ultracold molecules. Physical Review Letters,
100:233003, 2008.
Magnus Albert, Terence Mullins, Simone Go¨tz, Wenzel Salzmann,
Roland Wester, and Matthias Weidemu¨ller. The interaction of a spec-
trallycutlaser-pulsewithatwo-level atom. Journal of Modern Optics,
55:3359-3368, 2008.
TerryMullins,WenzelSalzmann,SimoneG¨otz, MagnusAlbert,Judith
Eng, Roland Wester, Matthias Weidemu¨ller, Fabian Weise, Andrea
Merli, Stefan M. Weber, Franziska Sauer, Ludger W¨oste, and Albrecht
Lindinger. Photoassociationandcoherenttransientdynamicsinthein-
teraction ofultracoldrubidiumatomswithshapedfemtosecond pulses.
I. experiment. Physical Review A, 80:063416, 2009.
Andrea Merli, Frauke Eimer, Fabian Weise, Albrecht Lindinger, Wen-
zel Salzmann, Terry Mullins, Simone Go¨tz, Roland Wester, Matthias
Weidemu¨ller, Ruzin Aganoglo, and Christiane P. Koch. Photoassoci-
ation and coherent transient dynamics in the interaction of ultracold
rubidium atoms with shaped femtosecond pulses. II. theory. Physical
Review A, 80:063417, 2009.
Terry Mullins, Magnus Albert, Wenzel Salzmann, Roland Wester, and
Matthias Weidemu¨ller. Dual high resolution amplitude and phase
femtosecond-picosecond pulse shaper. Submitted to Optics Letters.
Terry Mullins, Magnus Albert, Wenzel Salzmann, Roland Wester, and
Matthias Weidemu¨ller. High resolution femtosecond/picosecond pulse
shaper. In preparation.
In addition, the author has contributed to the following publica-
tions:
FabianWeise,SaschaBirkner,AndreaMerli,StefanM.Weber,Franziska
Sauer, Ludger W¨oste, Albrecht Lindinger, Wenzel Salzmann, Terence
G. Mullins, JudithEng, Magnus Albert, Roland Wester, and Matthias
Weidemu¨ller. OptimalcontrolofmultiphotonionizationofRb2molecules
in a magneto-optical trap. Physical Review A, 76:063404, 2007.
Eimer F., Weise F., Merli A ., Birkner., Sauer F., W¨oste L., Lindinger
A., Aganoglu R., Koch C. P., Salzmann W., Mullins T., Go¨tz S.,
iiiWester R., and Weidemu¨ller M. Spectrally resolved coherent transient
signal for ultracold rubidiummolecules. European Physical Journal D,
54:711-714, 2009.
WeiseF.,MerliA., EimerF.,BirknerS.,SauerF., W¨osteL.,Lindinger
A.,SalzmannW.,MullinsT.G.,WesterR.,Weidemu¨llerM.,Aganoglu
R.,andKochC.P.Characteristicoscillationsinthecoherenttransients
of ultracold rubidium molecules using red and blue detuned pulses
for photoassociation. Journal of Physics B: Atomic, Molecular and
Optical Physics, 42:215307, 2009.
Additional publications related to the Master thesis:
Sadgrove M., Hilliard A., Mullins T., Parkins S., and Leonhardt R.
Observation of robust quantum resonance peaks in an atom optics
kickedrotorwithamplitudenoise. Physical Review E,70:036217, 2004.
Sadgrove M., Mullins T., Parkins S., Leonhardt R. Deviations from
early-time quasilinear behavior for the atom-optics kicked rotor near
the classical limit. Physical Review E, 71:027201, 2005.
Sadgrove M., MullinsT., ParkinsS., LeonhardtR.Theeffect ofampli-
tude noise on the quantumand diffusion resonances of the atom optics
kicked rotor. Physica E: Low-dimensional systems and nanostructures,
29:367-374, 2005.
ivContents
Contents
1 Introduction 3
2 Pulsed Photoassociation 7
2.1 Light-Matter Interaction . . . . . . . . . . . . . . . . . . . . . 7
2.2 Simulation of the Light-Molecule Interaction . . . . . . . . . . 11
2.3 General Considerations. . . . . . . . . . . . . . . . . . . . . . 11
2.4 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . 14
2.5 Pump-Probe Scans . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.1 Dynamics of the Pump-Probe Ionization . . . . . . . . 23
2.6.2 Competing Processes . . . . . . . . . . . . . . . . . . . 26
2.6.3 Ground State Molecules . . . . . . . . . . . . . . . . . 32
2.7 Coherent Control . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Shaping of femtosecond laser pulses 37
3.1 General Considerations for Shaping of Femtosecond Pulses . . 37
3.1.1 Mathematical Description of Laser Pulses . . . . . . . 38
3.1.2 General Shaping of Laser Pulses . . . . . . . . . . . . 46
3.1.3 Spatial Light Modulation . . . . . . . . . . . . . . . . 47
3.1.4 Transfer Function for a 4-f Setup with an LC-SLM . . 53
3.2 Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Setup and Diagnostics . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1 The Femtosecond Setup . . . . . . . . . . . . . . . . . 60
3.3.2 Second Harmonic Generation . . . . . . . . . . . . . . 66
3.3.3 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . 67
3.3.4 Cross-correlation . . . . . . . . . . . . . . . . . . . . . 69
3.4 Characterization of the System . . . . . . . . . . . . . . . . . 70
3.4.1 Pulses Without Spatial Light Modulation . . . . . . . 70
3.4.2 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.3 Linear Phase . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.4 Quadratic Phase . . . . . . . . . . . . . . . . . . . . . 80
3.4.5 Sinusoidal Phase . . . . . . . . . . . . . . . . . . . . . 82
3.4.6 Square Pulses . . . . . . . . . . . . . . . . . . . . . . . 86
vContents
4 Shaping of picosecond laser pulses 89
4.1 General Considerations for Shaping of Picosecond Pulses . . . 89
4.1.1 Spatial Light Modulation for Picosecond Pulses . . . . 89
4.2 Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Design Criteria for Combined Femtosecond/ Picosecond Setup 93
4.4 SetupandDiagnosticsfortheCombinedFemtosecond/Picosecond
Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.4.1 Frequency-resolved optical gating . . . . . . . . . . . . 100
4.5 Characterization of the System . . . . . . . . . . . . . . . . . 100
4.5.1 Pulses Without Spatial Light Modulation . . . . . . . 101
4.5.2 Linear Phase . . . . . . . . . . . . . . . . . . . . . . . 102
4.5.3 Quadratic Phase . . . . . . . . . . . . . . . . . . . . . 105
4.5.4 Sinusoidal Phase . . . . . . . . . . . . . . . . . . . . . 108
4.5.5 Square Pulses . . . . . . . . . . . . . . . . . . . . . . . 111
5 Conclusion and Outlook 115
vi

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