Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

This thesis reports on coupling optical microresonators to micro- and nanomechanical oscillators. The mutual optomechanical coupling based on radiation pressure between the microcavity and a mechanical degree of freedom modulating its spatial structure thereby allows both transduction and actuation of the motion of the mechanical degree of freedom by the light field launched into the microcavity.

The first part of the thesis reports on a novel experimental approach based on cavity enhanced evanescent near-fields of toroid microresonators. It enables the extension of dispersive cavity optomechanical coupling to sub-wavelength scale nanomechanical oscillators which are at the heart of a variety of precision measurements. The optomechanical coupling present in the developed system is carefully analyzed experimentally and good agreement with theoretical expectations is found. The demonstrated platform allows transduction of nanomechanical motion with an exceptionally high sensitivity, outperforming the previous state-of-the-art transducers. Thereby, for the first time a measurement imprecision lower than the level of the standard quantum limit is achieved. In the present measurements, quantum backaction should already be the dominating contribution to the measurement sensitivity which is however masked by thermal noise.

This may pave the way to the first experimental demonstration of radiation pressure quantum backaction on a solid-state mechanical oscillator.

Moreover, the radiation pressure interaction between evanescent cavity field and nanomechanical oscillator is shown to enable actuating and controlling the motional state of the oscillator. Both amplification, leading to self-sustained mechanical oscillations, and cooling by radiation pressure dynamical backaction is reported. In addition, the capability of the near-field platform to implement resonant interaction of a mechanical mode with two optical modes is shown as well as the feasibility of quadratic coupling to the nanomechanical oscillators.

In the second part of the thesis monolithic on-chip resonators that combine ultra-low optical and mechanical dissipation are designed. To this end, the intrinsic mechanical modes of toroid microresonators are analyzed in detail. High-sensitivity measurements enable the observation of a plethora of mechanical modes and good agreement with finite element modelling is found. In particular the dissipation mechanisms limiting their mechanical quality are studied. Clamping losses are identified as the dominant loss mechanism at room temperature. Using a novel geometric design, these are systematically minimized which leads to spoke-supported microresonators with intrinsic material-loss limited mechanical quality factors rivalling the best published values at similar frequencies.

Im Rahmen dieser Arbeit wurde ein Frequenzkamm entwickelt, um astronomische Spektrographen besser kalibrieren zu können.

Im Jahr 1999 hat die Entwicklung des Frequenzkamms den Bereich der Präzisionsspektroskopie revolutioniert. Mit seiner Hilfe wurde die Messung von Übergängen in atomaren Systemen mit zuvor unerreichter Genauigkeit möglich, was 2005 mit dem Nobelpreis für Theodor W. Hänsch und John Hall gewürdigt wurde.

In dieser Zeit wurde am 3.6m Teleskop in La Silla, Chile der HARPS Spektrograph in Betrieb genommen. Er besitzt bis heute die höchste Sensitivität um die Beschleunigung kosmischer Objekte zu detektieren. Diese wird aus einer Änderung der Rotverschiebung des Lichts geschlossen. Die Präzision, mit der Frequenzänderungen gemessen werden können, ist momentan begrenzt durch die Kalibrationsquellen. Für die Entdeckung erdähnlicher Planeten über ihren Rückstoss oder gar die direkte Beobachtung der beschleunigten Ausdehnung unseres Universums ist diese Genauigkeit jedoch unzureichend. Nur durch den Einsatz neuartiger Kalibrationsquellen kann eine ausreichende Sensitivität auf Änderungen der Rotverschiebung erreicht werden.

Daher wurde in 2005 eine Zusammenarbeit zwischen der Europäischen Südsternwarte (ESO) und dem Max-Planck-Institut für Quantenoptik (MPQ) initiiert um einen Frequenzkamm zu entwickeln, der für die nächste Generation von Spektrographen als Kalibrationsquelle dienen kann. In dieser Arbeit wurde ein Yb-Faserlaser entworfen und erstmals

zu einem Frequenzkamm inklusive Detektion und Stabilisierung der Offset-Frequenz weiterentwickelt.

Um die einzelnen Kalibrationslinien des Kamms mit einem astronomischen Spektrographen auflösen zu können, musste der Modenabstand erhöht werden. Dazu wurden

Fabry-Pérot Resonatoren als schmalbandige Filter entwickelt. Schliesslich musste der spektrale Bereich des Spektrographen von 400-700nm abgedeckt werden, was durch spektrale Verbreiterung in speziell entwickelten, mikrostrukturierten Fasern erreicht wurde.

Mehrere Entwicklungsstufen dieses Systems wurden an einem Spektrographen auf Teneria und an HARPS getestet. Dabei konnte jeweils gezeigt werden, dass der Frequenzkamm

die erwarteten Spezifikationen erfüllt und traditionelle Kalibrationsquellen in ihrer Sensitivität auf Frequenzabweichungen übertrifft. Frequenzänderungen von 200 kHz konnten detektiert werden, was einer Sensitivität auf Geschwindigkeitsänderungen von kosmischen Objekten von 10 cm/s entspricht. Ca. 30% des spektralen Bereiches des HARPS

Spektrometers konnten abgedeckt werden und mit verbesserter spektraler Verbreiterung ist das Erreichen des gesamten Bereichs mit der nächsten Entwicklungsstufe realistisch.

Durch den Einsatz eines solchen, verbreiterten Frequenzkamms an Spektrographen der nächsten Generation werden Geschwindigkeitsänderungen eines kosmischen Objekts von nur 1 cm/s detektierbar. Dies wird die Durchführung der ambitionierten Beobachtugen ermöglichen, die in der Astronomie innerhalb der nächsten Jahrzehnte geplant sind.

A few minutes after the Big Bang that created our Universe, nucleosynthesis reactions forged some lighter isotopes, including 7Li. Ever since then, such reactions have taken place in the hot stellar interiors, providing the stars with the energy to shine and forming all chemical elements necessary for life as we know it. In this thesis I describe how we have inferred the chemical composition of stars in a globular cluster, hosting one of the oldest stellar populations in our Galaxy, in order to address two fundamental astrophysical problems.

The first problem is related to lithium, and the prediction of its primordial abundance from present cosmological theories of how the Universe was born. The Li abundances that we measure in the envelopes of globular cluster stars are lower than this estimate and we investigate the possibility that Li has been drained from the stellar surfaces. This thesis presents observational evidence that low-mass stars experience a small increase in their surface Li abundances during the course of their late phases of evolution, supporting this hypothesis.

The second question is related to the formation and evolution of globular clusters. It appears that these dense stellar environments early underwent a unique form of self- enrichment, by retaining the gas outflow from slow stellar winds. The material was then incorporated into a second stellar generation with identical chemical signatures to the first, except for a handful of lighter elements, including sodium. I here discuss several aspects of this stellar pollution process.

Only with a correct physical description of the radiative and convective energy transport through the stellar atmosphere, and the equilibrium state of the atoms, ions and molecules that form the tenuous gas, can we make solid predictions of the emergent spectrum and derive accurate abundances. In particular, I discuss how the simplifying assumption of local thermal equilibrium give rise to systematic errors in the analysis of Li and Na spectral lines, commonly mis-estimating the elemental abundances in stars by 10–50%, and in certain cases considerably more. Moreover, we have for the first time investigated the combined influence from departures from local thermal equilibrium and hydro-static equilibrium in the determination of the solar Na abundance.

The main topic of this thesis is the study of many-body effects in strongly correlated one- or quasi one-dimensional condensed matter systems. These systems are characterized by strong quantum and thermal fluctuations, which make mean-field methods fail and demand for a fully numerical approach. Fortunately, a numerical method exist, which allows to treat unusually large one -dimensional system at very high precision. This method is the density-matrix renormalization group method (DMRG), introduced by Steve White in 1992. Originally limited to the study of static problems, time-dependent DMRG has been developed allowing one to investigate non-equilibrium phenomena in quantum mechanics.

In this thesis I present the solution of three conceptionally different problems, which have been addressed using mostly the Krylov-subspace version of the time-dependent DMRG. My findings are directly relevant to recent experiments with ultracold atoms, also carried out at LMU in the group of Prof. Bloch.

The first project aims the ultimate goal of atoms in optical lattices, namely, the possibility to act as a quantum simulator of more complicated condensed matter system. The underline idea is to simulate a magnetic model using ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system, which is captured by a two-species Bose-Hubbard model, realizes in a certain parameter range the physics of a spin-1/2 Heisenberg chain, where the spin exchange constant is given by second order processes. Tuning of the superlattice parameters allows one to controlling the effect of fast first order processes versus the slower second order ones. The analysis is motivated by recent experiments,

%\cite{Folling2007,Trotzky2008}

where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were detected. My project investigates the coherent many-particle dynamics, which takes place after coupling the double well. I provide the theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for non-integrable and Bethe ansatz integrable models. It turns out that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models

In the second project I study a many-body generalization of the original Landau-Zener formula. This formula gives the transition probability between the two states of a quantum mechanical two-level system, where the offset between the two levels is varying linearly in time. In a recent experiment this framework has been extended to a many-body system consisting of pairwise tunnel-coupled one-dimensional Bose liquids. It was found that the tunnel coupling between the tubes and the intertube interactions strongly modify the original Landau-Zener picture. After a introduction to the two-level and the three-level Landau-Zener problem I present my own results for the quantum dynamics of the microscopic model and the comparison to the experimental results. I have calculated both Landau-Zener sweeps as well as the time-evolution after sudden quenches of the energy offset. A major finding is that for sufficiently large initial density quenches can be efficiently used to create quasi-thermal states of arbitrary temperatures.

The third project is more mathematical and connects the fields of quantum computation and of quantum information. Here, the main purpose is to analyse systematically the effects of decoherence on maximally entangled multi-partite states, which arise typically during quantum computation processes. The bigger the number of entangled qubits the more fragile is its entanglement under the influence decoh