Engineering the Landau-Zener tunneling of ultracold atoms in tilted potentials [Elektronische Ressource] / by Ghazal Tayebirad

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Engineering the Landau–Zener Tunnelingof Ultracold Atoms in Tilted PotentialsInaugural dissertationbyGhazal TayebiradDissertationsubmitted to theCombined Faculties of the Natural Sciences andMathematicsof theRuperto-Carola-University of Heidelberg, Germanyfor the degree ofDoctor of Natural SciencesPut forward byGhazal Tayebirad, M.Sc.born in Ahvaz, IranOral examination: 24 January 2011Engineering the Landau–Zener Tunnelingof Ultracold Atoms in Tilted PotentialsReferees: Dr. Sandro WimbergerProf. Dr. Ulrich SchwarzOut of the cradleonto dry land...here it is standing...atoms with consciousness...matter with curiosity.Stands at the sea...wonders at wondering... I...a universe of atoms...an atom in the universeRichard FeynmannvAbstractA comprehensive study of the time-resolved Landau–Zener tunneling of a Bose–Einstein condensate in a tilted periodic potential is presented in this thesis. Sev-eral ways are discussed how to control the tunneling. In the first collection ofour results, the tunneling from the ground band to the continuum is shown todepend crucially on the initial condition and system parameters, and also on thestrength of atom-atom interactions. The use of different protocols enables usto access the tunneling probability in two different bases, namely, the adiabaticbasis (eigenstates of the Hamiltonian with the potential) and the diabatic basis(free-particle momentum eigenstates).

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Published 01 January 2011
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Engineering the Landau–Zener Tunneling
of Ultracold Atoms in Tilted Potentials
Inaugural dissertation
by
Ghazal TayebiradDissertation
submitted to the
Combined Faculties of the Natural Sciences and
Mathematics
of the
Ruperto-Carola-University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
Put forward by
Ghazal Tayebirad, M.Sc.
born in Ahvaz, Iran
Oral examination: 24 January 2011Engineering the Landau–Zener Tunneling
of Ultracold Atoms in Tilted Potentials
Referees: Dr. Sandro Wimberger
Prof. Dr. Ulrich SchwarzOut of the cradle
onto dry land...
here it is standing...
atoms with consciousness
...matter with curiosity.
Stands at the sea...
wonders at wondering... I...
a universe of atoms...
an atom in the universe
Richard Feynmannv
Abstract
A comprehensive study of the time-resolved Landau–Zener tunneling of a Bose–
Einstein condensate in a tilted periodic potential is presented in this thesis. Sev-
eral ways are discussed how to control the tunneling. In the first collection of
our results, the tunneling from the ground band to the continuum is shown to
depend crucially on the initial condition and system parameters, and also on the
strength of atom-atom interactions. The use of different protocols enables us
to access the tunneling probability in two different bases, namely, the adiabatic
basis (eigenstates of the Hamiltonian with the potential) and the diabatic basis
(free-particle momentum eigenstates). The structure of the survival probability
and the measure of the tunneling time depend on the chosen basis. All these
possibilities have been checked and proved in experiments. We go also beyond
and propose a possibility to manipulate the tunneling probability of ultracold
atoms in the tilted time-dependent stochastic potentials. Our theoretical and
numerical results show that the tunneling in such a potential can be controlled
by adding different types of colored noise. A scaling law is introduced for these
results, which effectively reduces the parameter-dependence of the tunneling and
leads to a better understanding of dynamics in the proposed noisy system.
Kurzzusammenfassung
In dieser Arbeit wird das zeitaufgel¨oste Landau-Zener-Tunneln eines Bose-
Einstein-Kondensates in einem gekippten periodischen Potential umfassend
studiert. Verschiedene M¨oglichkeiten das Tunneln zu kontrollieren werden disku-
tiert. Im ersten Teil unserer Ergebnisse zeigt sich, dass das Tunneln vom Grund-
band ins Kontinuum entscheidend von den Anfangsbedingungen, den Systempa-
rametern und auch von der St¨arke der Atom-Atom-Wechselwirkungen abh¨angt.
Das Verwenden verschiedener Protokolle erlaubt uns auf die Tunnelwahrschein-
lichkeit in zwei verschiedenen Basen zuzugreifen: zum einen in der adiabatis-
chen Basis (Eigenzust¨ande des Hamiltonoperators mit Potential) und zum an-
dern in der diabatischen Basis (Impulseigenzust¨ande der freien Teilchen). Die
¨Struktur der Uberlebenswahrscheinlichkeit und das Maß der Tunnelzeit h¨angen
von der gew¨ahlten Basis ab. All diese M¨oglichkeiten sind in Experimenten
¨uberpr¨uft und nachgewiesen worden. Dar¨uber hinausgehend schlagen wir eine
M¨oglichkeit vor, die Tunnelwahrscheinlichkeit ultrakalter Atome in gekippten
zeitabh¨angig stochastischen Potentialen zu manipulieren. Unsere theoretischen
und numerischen Ergebnisse zeigen, dass das Tunneln in solchen Potentialen
durch das Hinzuf¨ugen verschiedener Arten farbigen Rauschens kontrolliert wer-
den kann. F¨urdiese Ergebnisse wird ein Skalierungsgesetz eingef¨uhrt, das die Pa-
rameterabh¨angigkeit des Tunnelns reduziert und zu einem besseren Verst¨andnis
der Dynamik in dem vorgeschlagenen rauschenden System f¨uhrt.