Probing strongly correlated states of ultracold atoms in optical lattices [Elektronische Ressource] / Simon Fölling

Simon Fölling

Sujets

• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2008
• Nombre de lectures: 18
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Probing Strongly Correlated States of Ultracold
Atoms in Optical Lattices
Dissertation
zur Erlangung des Grades
"Doktor
der Naturwissenschaften"
am Fachbereich Physik
der Johannes Gutenberg-Universität
in Mainz
Simon Fölling
geboren in Münster
Mainz, den 16.10.2008D77
ArchiMeD Mainz (online) Version
Datum der mündlichen Prüfung: 16. Oktober 2008
iiAbstract
This thesis describes experiments which investigate ultracold atom ensembles in an
optical lattice. Such quantum gases are powerful models for solid state physics. Sev-
eral novel methods are demonstrated that probe the special properties of strongly
correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals
spatial correlations in such states, which are hidden when using the usual methods of
probing atomic gases. Another spectroscopic technique makes it possible to demon-
strate the existence of a shell structure of regions with constant densities. Such co-
existing phases separated by sharp boundaries had been theoretically predicted for
the Mott insulating state. The tunneling processes in the optical lattice in the strongly
correlated regime are probed by preparing the ensemble in an optical superlattice
potential. This allows the time-resolved observation of the tunneling dynamics, and
makes it possible to directly identify correlated tunneling processes.
Zusammenfassung
In dieser Arbeit werden Experimente vorgestellt, in denen die Eigenschaften eines
ultrakalten atomaren Gases in einem optischen Gitterpotential untersucht werden.
Solche Quantengase sind sehr vielseitige Modellsysteme für Phänomene der Festkör-
perphysik. Um die besonderen Eigenschaften stark korrelierter Zustände in optischen
Gittern zu untersuchen, werden neuartige Methoden realisiert, die in dieser Form
erstmalig zum Einsatz kommen. So erlaubt es die Spektroskopie des Quantenrau-
schens in atomaren Ensembles erstmals, die Korrelationen in der räumlichen Dichte
eines solchen Zustands sichtbar zu machen. Mittels einer anderen spektroskopischen
Technik gelingt es ausserdem, die Existenz getrennter Phasen konstanter Dichte, die
sogenannte Schalenstruktur des Mott Isolators, direkt nachzuweisen. Die komple-
xe Dynamik von Tunnelprozessen im optischen Gitter im stark korrelierten Regime
wird durch Einsatz eines optischen Übergitters untersucht. Dadurch ist es möglich,
die Tunneldynamik zeitaufgelöst zu erfassen und korrelierte Tunnelprozesse direkt
zu beobachten.
iiiivContents
1 Introduction 1
2 Ultracold atoms in optical lattice potentials 9
2.1 Bose-Einstein condensates with repulsive interactions . . . . . . . . . . 11
2.2 Optical lattice potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Standing wave optical lattice . . . . . . . . . . . . . . . . . . . . 16
2.3 Quantum mechanics of particles in periodic potentials . . . . . . . . . . 17
2.3.1 Band structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Bose-Hubbard description for deep potentials . . . . . . . . . . 20
2.3.3 Superfluid to Mott insulator transition . . . . . . . . . . . . . . . 22
2.3.4 The influence of the confining potential . . . . . . . . . . . . . . 25
2.3.5 Mott insulator in potential: the shell structure . . . . 26
2.4 Shell structure at non-zero temperatures . . . . . . . . . . . . . . . . . . 27
3 Experimental setup and techniques 35
3.1 Implementation of the experiment . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 BEC preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Optical lattice setup . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Absorption imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Time of flight imaging of atoms from deep lattices . . . . . . . . 42
3.2.2 Brillouin zone mapping . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Controlled spin-changing collisions . . . . . . . . . . . . . . . . . . . . 47
3.3.1 The spin exchange process . . . . . . . . . . . . . . . . . . . . . 48
3.3.2 Microwave control of spin-changing collisions . . . . . . . . . . 52
4 Number squeezing and the Mott shell structure 57
4.1 Detection of number squeezing . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.1 Experiment sequence . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.2 Pair fraction results . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2 Probing the density distribution in the trap . . . . . . . . . . . . . . . . 62
4.3 Experimental sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.1 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.2 Counting limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
vContents
4.5.1 Density profile of a Mott insulator . . . . . . . . . . . . . . . . . 66
4.5.2 Spatially selective manipulation of atoms . . . . . . . . . . . . . 67
4.5.3 The influence of the external confinement on the Mott insulator 69
4.6 Site occupation number-dependent probing . . . . . . . . . . . . . . . . 72
4.6.1 Reconstruction and resolution of number-state distributions . . 73
4.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Characterizing quantum states using quantum noise correlation analysis 83
5.1 Spatial correlations in two-particle measurements . . . . . . . . . . . . 84
5.1.1 Correlated detection of bosons released from an optical lattice . 86
5.1.2 Prediction of the detected signal . . . . . . . . . . . . . . . . . . 93
5.1.3 Extracting the noise correlations from CCD images . . . . . . . 95
5.1.4 Image artifacts and filtering . . . . . . . . . . . . . . . . . . . . . 98
5.1.5 Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Experimental results and comparison with theory . . . . . . . . . . . . 103
5.3 Detection of density wave structures in the lattice . . . . . . . . . . . . 105
6 Observation of tunneling processes in two-well potentials 109
6.1 The double well system . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1.1 The double well potential as a miniaturized Josephson junction 110
6.1.2 The well as a minimized optical lattice . . . . . 111
6.1.3 Double well potentials for atoms . . . . . . . . . . . . . . . . . . 112
6.2 Realization of the double well lattice . . . . . . . . . . . . . . . . . . . . 114
6.3 Superlattice band structure . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4 BEC in the superlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.5 Bose-Hubbard model for the double well . . . . . . . . . . . . . . . . . 124
6.5.1 Single particle hamiltonian . . . . . . . . . . . . . . . . . . . . . 125
6.5.2 Two . . . . . . . . . . . . . . . . . . . . . . 126
6.6 Experimental sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.6.1 Lattice loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.6.2 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.6.3 Initial state preparation: patterned loading . . . . . . . . . . . . 130
6.6.4 Final state readout . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.6.5 Time evolution in weakly interacting regime . . . . . . . . . . . 134
6.6.6 Time in the strongly interacting regime . . . . . . . . 134
6.7 Modeling of overall system . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.8 Fitting the model to the data . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.9 Deviations from the standard Bose-Hubbard model . . . . . . . . . . . 143
6.10 Conditional tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7 Outlook 149
7.1 Probing the density distribution and number statistics of Mott shells . 149
viContents
7.2 Noise correlation interferometry . . . . . . . . . . . . . . . . . . . . . . 150
7.3 Optical superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Bibliography 157
viiContents
viii1 Introduction
Ultracold quantum gases – already enjoying much attention due to the spectacular
experimental progress made in recent years – are now increasingly becoming a pop-
ular topic of condensed matter physics. One important contribution to this surge
in interest was the proposal [1] and subsequent realization [2] of the idea that such
gases can be used to almost perfectly implement the Hubbard model. This funda-
mental model was developed in condensed matter physics to describe the behavior
of interacting electrons [3] or bosonic particles (Bose-Hubbard model, [4]) in a crystal
lattice. In the cold atom implementation of the model, this is realized by subjecting
the ultracold atoms to a crystal potential created by laser light.
The strong interest in such systems does not just originate from the geometrical
resemblance of the configuration with real crystal lattices. More importantly, they
provide a an almost idealized realization of a system in a regime that is not