La lecture en ligne est gratuite
Le téléchargement nécessite un accès à la bibliothèque YouScribe
Tout savoir sur nos offres

Partagez cette publication

Interactions in an ultracold gas
Rydberg atoms
Erlangung des Doktorgrades
der Fakult¨at fu¨r Mathematik und Physik
der Albert-Ludwigs-Universitat¨
Freiburg im Breisgau, Germany
vorgelegt von
Dipl.-Phys. Kilian Talo Theodor Singer
¨aus Uberlingen am Bodensee
im Oktober 2004Dekan: Professor Dr. Josef Honerkamp
Leiter der Arbeit: Professor Dr. Matthias Weidemu¨ller
Referent: Professor Dr. Matthias Weidemuller¨
Korreferent: Professor Dr. Hanspeter Helm
Tag der Verkundigung¨
des Pru¨fungsergebnisses: 26.11.2004
Part of the work presented in this thesis is based on the following publications:
• M. Weidemu¨ller, K. Singer, M. Reetz-Lamour, T. Amthor and L. G. Marcasse
Ultralong-Range Interactions and Blockade of Excitation in a Cold
Rydberg Gas
to appear in Atomic Physics XIX (Proceedings of ICAP 2004) and in Braz. J.
Phys. (2004)
• K. Singer, J. Stanojevic, M. Weidemu¨ller, and R. Cotˆ ´e
Long range interaction potentials for the ns-ns, np-np and nd-nd
asymptotes for rubidium Rydberg atom pairs
J. Phys. B in press (2004)
• K. Singer, M. Reetz-Lamour, T. Amthor, S. F¨olling, M. Tscherneck, and M.
Spectroscopy of an ultracold Rydberg gas and signatures of Rydberg-
Rydberg interactions
J. Phys. B in press (2004)
• K. Singer, M. Reetz-Lamour, T. Amthor, L. G. Marcassa, and M. Weidemu¨ller
Spectral Broadening and Suppression of Excitation Induced by
Ultralong-Range Interactions in a Cold Gas of Rydberg Atoms
Phys. Rev. Lett. 93, 163001 (2004)
also selected for the October 25 issue of
Virtual Journal of Nanoscale Science & Technology (2004)
• K. Singer, M. Tscherneck, M. Eichhorn, M. Reetz-Lamour, and M. Weidemuller¨
Method and apparatus for the coherent addition of laser beams from
distinct laser sources
German Patent DE 102 43 367 (2004)
• K. Singer, M. Tscherneck, M. Eichhorn, M. Reetz-Lamour, S. Fol¨ ling, and M.
Phase-coherent addition of laser beams with identical spectral prop-
Optics Communications 218, 371 (2003)
3• K. Singer, M. Reetz-Lamour, M. Tscherneck, S. F¨olling, and M. Weidemu¨ller
Towards an ultracold dense gas of Rydberg atoms
in: Interaction in Ultracold Gases: From Atoms to Molecules (Wiley, New York
• K. Singer, S. Jochim, M. Mudrich, A. Mosk, and M. Weidemu¨ller
Low-cost mechanical shutter for light beams
Rev. Sci. Instrum. 73, 4402 (2002)
In addition the author contributed to the following publications:
• M. Mudrich, S. Kraft, K. Singer, A. Mosk, and M. Weidemuller¨
Thermodynamics in an ultracold mixture of optically trapped atomic
in: Interaction in Ultracold Gases: From Atoms to Molecules (Wiley, New York
• G. Fahsold, K. Singer, and A. Pucci
In-situ IR-transmission study of vibrational and electronic properties
during the formation of thin-film β-FeSi2
Journal of Applied Physics 91, 145 (2002)
• M. Mudrich, S. Kraft, K. Singer, R. Grimm, A. Mosk, and M.
Sympathetic Cooling with Two Atomic Species in an Optical Trap
Phys. Rev. Lett. 88, 253001-1 (2002)
• S. Kraft, M. Mudrich, K. Singer, R. Grimm, A. Mosk, and M. Weidemuller¨
Sympathetic cooling of lithium by laser-cooled cesium
in: Laser Spectroscopy XV, Proceedings of the International Conference on
Laser Spectroscopy (ICOLS01), 341-344 (2002)
• A. Mosk, M. Mudrich, S. Kraft, K. Singer, W. Wohlleben, R. Grimm, and M.
Mixture of ultracold lithium and cesium atoms in an optical dipole
Appl. Phys. B 79, 791 (2001)
4Abstract: This thesis presents observations of ultralong range interac-
tions in a frozen Rydberg gas. The observed signatures are interaction-
induced line broadenings and a suppression of resonant Rydberg excita-
tion. The latter effect can be interpreted as the onset of a local dipole
ing with mesoscopic ensembles. The dominating interaction between a
pair of Rydberg atoms separated as far as 100 000 Bohr radii is the
van der Waals interaction. The strength of this interaction is calculated
quantitatively in a perturbative approach. We describe in detail our
experimental apparatus which employs narrow-bandwidth continuous-
87afrozenRydberggasfrommagneto-opticallytrapped Rbatoms. Asa
generate Raman sideband cooling resulting in atom cloud temperatures
in the sub-μK range. Systematic studies of the Rydberg spectra as
a function of excitation-laser intensity, density of excitable atoms and
excitation time are presented.
Zusammenfassung: In dieser Doktorarbeit werden die langreichweiti-
tersucht. DiebeobachtetenSignaturensindwechselwirkungsverursachte
Linienverbreiterungen und eine Anregungsunterdru¨ckung bei resonan-
ter Rydberganregung. Der letztere Effekt kann als Beginn einer lokalen
Dipolblockade interpretiert werden, welche zur Realisierung von Quan-
teninformationsverarbeitung mit mesoskopischen Gesamtheiten aus-
genutzt werden kann. Die dominierende Wechselwirkung zwischen zwei
Rydbergatomen in einem Abstand von 100 000 Bohrradien ist die
van-der-Waals-Wechselwirkung. Die Starke der Wechselwirkung wurde¨
quantitativ in einem sto¨rungstheoretischen Ansatz berechnet. Der ex-
perimentelle Aufbau wird detailliert beschrieben. Wir setzen schmal-
bandige kontinuierliche Laseranregung in einem Zweiphotonenprozess
87zur Rydberganregung aus magneto-optisch gefangenen Rb Atomen
ein. InunseremAufbaukommteinneuartigesVerfahrenzurkoha¨renten
Addition von Laserintensitaten zum Einsatz. Des Weiteren wurde 3D¨
entartete Ramanseitenbandku¨hlung implementiert und Atomwolken-
temperaturen im unteren μK Bereich erreicht. Systematische Studien
der Rydbergspektren als Funktion der Anregungslaserintensitaten, der¨
Dichte der anregbaren Atomen und der Anregungszeit wurden durchge-
1 Introduction 9
2 Creation of an ultracold gas of atoms 13
2.1 Laser cooling and trapping . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 3D degenerate Raman sideband cooling . . . . . . . . . . . . . . . 27
3 Rydberg atoms 33
3.1 Background on Rydberg atoms . . . . . . . . . . . . . . . . . . . 33
3.2 Excitation and detection of Rydberg atoms . . . . . . . . . . . . . 42
3.3 Spectra of Rydberg atoms . . . . . . . . . . . . . . . . . . . . . . 48
4 Interactions in a frozen gas of Rydberg atoms 55
4.1 Qualitative theoretical description . . . . . . . . . . . . . . . . . . 56
4.2 Quantitative perturbative approach . . . . . . . . . . . . . . . . . 60
4.3 Interaction-induced line broadening of Rydberg resonances . . . . 72
5 Blockade of Rydberg excitation on resonance 85
5.1 Quantum information processing with Rydberg atoms . . . . . . . 85
5.2 Interaction-induced inhibition of excitation . . . . . . . . . . . . . 90
5.3 Excitation of dipole-forbidden states . . . . . . . . . . . . . . . . 97
6 Conclusion and perspectives 101
A Experimental control system 105
B Detailed expressions for the interaction potentials 115
Bibliography 123
Acknowledgements 131
8Chapter 1
Rydberg atoms are atoms in highly excited electronic states at energies close to
the ionization limit. The orbital radius of the electron extends over more than
thousandsofbohrradii. Theseexaggeratedpropertiesleadtoverystrongpolariz-
abilitiesofRydbergatoms. Theyareveryfragileandcaneasilybeperturbed e.g.
by electric fields. Rydberg atoms at room temperatures have been extensively
studied over many decades since the end of the 19th century [Gallagher, 1994].
With the advances in laser cooling and trapping, the creation of an ultracold gas
of Rydberg atoms became realizable and totally new perspectives for the inves-
tigation of Rydberg states have opened since then. With modern laser cooling
techniques, Rydberg atoms can now be excited out of a gas of trapped alkali
10 −3atoms at densities exceeding 10 cm , and at temperatures in the micro-Kelvin
range. An important feature of Rydberg atoms excited out of laser-cooled atoms
is that they do not move significantly during their radiative lifetime (“frozen
Rydberg gas”). The situation can be compared to an amorphous solid. In the
frozen Rydberg gas, resonant excitation exchange (Fo¨rster process) was reported
, leading to unexpected effects such as the many-body diffusion of excitation
[Mourachko et al., 1998, Anderson et al., 1998]. Other interesting effects are the
population of long-living high angular-momentum states through free charges
[Dutta et al., 2001] and the spontaneous formation and recombination of ultra-
cold plasmas [Robinson et al., 2000, Gallagher et al., 2003].
The interaction strength between Rydberg atoms can easily be tuned over
several orders of magnitude e.g. by changing the density or by exciting them
to different principal quantum numbers n. Adjacent Rydberg atoms interact
mainly by the long-range van der Waals interaction whose strength scales with
11 −6n . The interaction declines with internuclear distance (R) as R but is still
strong enough that Rydberg atoms more than a thousand Bohr radii apart are
predicted to form a bound molecular state at temperatures reachable by modern
lasercoolingtechniques[Boisseau et al., 2002]. Furthermoremoleculesconsisting
of a ground state atom and a Rydberg atom with very high dipole moments are
predicted to form[Greene et al., 2000]. In this molecules the ground state atom
Figure 1.1: Schematic explanation of the dipole blockade. (a) Energy lev-
els for a pair of atoms. |gi and |ri denote the ground and Rydberg state
respectively. The ultralong range dipole interaction splits the Rydberg pair
state and thus suppresses excitation of a Rydberg pair by a resonant laser
field, as indicated by the vertical arrows for small internuclear distances. (b)
An excitation laser beam is overlapped with a cloud of cold atoms. Rydberg
excitation out of the gas is suppressed in the vicinity of a Rydberg atom by
the interaction, resulting in many domains within which only one Rydberg
atom is excited.
is trapped in one of the nodes of the Rydberg electron wave function.
Observed signatures of the interaction between Rydberg atoms are density-
dependent line broadening of resonances [Raimond et al., 1981], modification of
collisionalprocesses[de Oliveira et al., 2003], andmolecularcrossoverresonances
due to avoided crossings [Farooqi et al., 2003]. Apart from tunable interaction,
Rydberg atoms offer the unique possibility of tuning the energy level of the Ryd-
berg state with small electric fields by exploiting the dc-Stark effect. This can
be done by applying only small fields of several V/cm as Rydberg states are very
field sensitive. If Rydberg levels are tuned exactly between two other levels to
which dipole transitions are allowed, then the interaction between the Rydberg
atoms is strongly increased due to resonant dipole-dipole interaction scaling as
−3R .
This strong dipole-dipole interaction between Rydberg atoms has been pro-
posed to be used in the implementation of a fast phase gate for quantum in-
formation processing [Jaksch et al., 2000]. In contrast to already implemented
systems with ions [Schmidt-Kaler et al., 2003] where the Coulomb interaction is
the basic coupling mechanism used for entanglement, [Jaksch et al., 2000] pro-
posed to use long-lived metastable ground states of neutral atoms as storage
states and entangle states by exciting for a short period of time into Rydberg
states which strongly interact. This approach would have the great advantage
that the atoms are decoupled from the environment during storage time, which
avoids decoherence effects. The proposal of [Jaksch et al., 2000] was extended
to a version using mesoscopic clouds of atoms avoiding the need for single atom

Un pour Un
Permettre à tous d'accéder à la lecture
Pour chaque accès à la bibliothèque, YouScribe donne un accès à une personne dans le besoin