Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 04/05 Archiv

In this thesis, I report on the cooling of a macroscopic harmonic mechanical oscillator of mass on the order of 10ng close to its quantum ground state. To perform the refrigeration, we exploit the optomechanical interaction that couples the mechanical degree of freedom to an optical cavity mode via the light's radiation pressure. The delayed response of the intracavity field upon mechanical vibration leads to a viscous intracavity radiation pressure force responsible for the dynamical backaction cooling, as is theoretically introduced in chapter 1. In chapter 2, we review the experimental system accommodating this process: the silica microtoroidal cavity. It advantageously hosts a significant optomechanical coupling between the supported high-finesse (close to 10^6) optical whispering-gallery modes and the mechanical radial breathing mode oscillating at radio frequencies (tens of MHz). In chapter 3, we detail the experimental efforts performed to improve the effect of the cooling on the system and thus to reach a lower average number of mechanical energy quanta, or phonons. The various sources of mechanical dissipations are studied. Their magnitude is diminished by optimizing the mechanical structure, therefore reducing the coupling of the mechanical mode to its warm thermal environment. In the newly developed spoke-anchored toroidal microcavities, engineering the intermode coupling minimizes the system’s damping down to the limit imposed by the properties of the vitreous silica material. To reduce the temperature of the environment itself, the experiment is pre-cooled first in a prototype helium-4 cryostat. This enables the observation of novel dispersive optical properties of fused silica and the study of the sample's thermalization at cryogenic temperatures. To further increase the pre-cooling, the setup is finally implemented in a colder helium-3 cryostat operated at 850mK. Using the balanced homodyne interferometer constructed to detect the mechanical vibration with quantum-limited sensitivity, we report on the cooling performed in the resolved-sideband configuration that is fundamentally required to reach the ground state. A mean phonon occupancy of 9 +/-1 is achieved. The fact that only simple technical problems limit further cooling proves that the developed experimental system is finally optimized for revealing quantum signatures of a macroscopic mechanical oscillator cooled by dynamical backaction. Finally, the effect of the optomechanical interaction on the optical properties of the cavity is measured and analyzed, leading to the first observation of optomechanically induced transparency. This constitutes an experimental manifestation of the mutual character of interaction between light and mechanical motion.

This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) [1] and the numerical renormalization group (NRG) [2], respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) [3] which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system’s correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model [4], while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption involving a Kondo exciton [5, 6, 7] and population switching in quantum dots [8, 9, 10, 11, 12, 13, 14, 15]. It turns out that both phenomena rely on the various manifestations of Anderson orthogonality (AO) [16], which describes the fact that the response of the Fermi sea to a quantum quench (i.e. an abrupt change of some property of the impurity or quantum dot) is a change of the scattering phase shifts of all the single-particle wave functions, therefore drastically changing the system. In this context, we demonstrate that NRG, a highly accurate method for quantum impurity models, allows for the calculation of all static and dynamic quantities related to AO and present an extensive NRG study for population switching in quantum dots.

In this dissertation we study the properties of high-mass X-ray binaries (HMXBs) and hot inter-stellar medium in star-forming galaxies and their relation with the star formation rate (SFR), based on the data from Chandra, Spitzer, GALEX and 2MASS public archives. We constructed a large sample of galaxies for which we collected homogeneous sets of multiwavelength measurements in X-ray, ultraviolet (UV), far-infrared (FIR) and near-infrared (NIR) bands. The sample includes 45 star-forming galaxies in total, divided in two sub-samples: the primary sample, consisting of 29 nearby galaxies, having distance < 40 Mpc, so that Chandra can resolve their X-ray point-like source population; the high-SFR sample, including 16 more distant galaxies that allowed us to extend the dynamical range of SFRs by approximately two orders of magnitude. In this sample we detected 1057 compact X-ray sources, of which ~300 are expected to be background active galactic nuclei (AGN). The majority of remaining ~700 sources are young systems associated with star-formation in the host galaxy. Based on their high X-ray luminosities and analogy with the X-ray populations in the Milky Way and few other very nearby galaxies, we conclude that they are high-mass X-ray binaries, powered by accretion of matter from a massive donor star onto a compact object - a black hole or a neutron star. Such a large number of sources allowed us to perform the most detailed study of the population of HMXBs and its dependence on various properties of the host galaxy, as well as to obtain a very accurate calibration of the X-ray luminosity-SFR relation. The study of the population of HMXBs is based on their X-ray luminosity functions (XLF). To this end, we took a special care to minimize the contamination by LMXBs, background AGN and to control the incompleteness of the Chandra source lists. The shape of the HMXB luminosity function is similar in different galaxies with the power law indexes having rms=0.25 with respect to the average value of ~1.6. The XLF normalizations, on the contrary, show significantly larger dispersion with the rms=0.34 dex around the A-SFR law. Combining the data of all galaxies, which include ~700 X-ray sources, we produced the average XLF of high-mass X-ray binaries in nearby star-forming galaxies. Its statistical accuracy exceeds by far that achieved in any of the previous studies of the HMXB luminosity function. The HMXB XLF has a single power law shape in a broad luminosity range of logLx~35-40 and shows a moderately significant evidence for the high luminosity break or cut-off at logLx~40. We did not find any statistically significant features at the Eddington luminosity limits of neutron stars or a 10 Msun black hole. With the knowledge of the relation between the number of high-mass X-ray binaries and star formation rate of the host galaxy, we estimated that the fraction of compact objects that went through an X-ray active phase at least once in their lifetime, powered by accretion of matter from a massive donor star in a binary system is fx~0.2. This constrains the mass distribution of the secondary in massive binaries. For an independent mass distribution of the secondary, the power law index must be flatter than 0.3. In particular, an independent mass distribution of a Kroupa or Salpeter type is strongly excluded. Assuming that the masses of components in a binary are not independent, our results are consistent with the flat mass ratio distribution. For comparison, we obtained a similar estimate for the fraction of compact objects that become X-ray sources powered by accretion from a low-mass donor star in an LMXB. Based on the scaling-laws by Gilfanov (2004), the fraction of compact objects, X-ray active in LMXBs, is small, fx~1e-6, demonstrating that LMXBs are extremely rare objects. This result is in line with the conclusions of the binary population studies. The collective luminosity of high-mass X-ray binaries is a good tracer of the recent star formation activity in the host galaxy: L_XRB(0.5-8 keV)(erg/s) = 2.5 10^{39} SFR (Msun/yr) The rms of points around this relation is 0.4 dex. The observed dispersion is unlikely to be caused by any of the obvious contaminating factors such as CXB or LMXB sources and is likely to have a physical origin. In addition to the emission from XRB population, the X-ray emission from star-forming galaxies includes a hot diffuse gas component with a mean characteristic temperature of 2-3 10^{6} K. We show that its X-ray luminosity correlates with the star formation rate of the host galaxy. Finally we demonstrate that the total X-ray luminosity of a galaxy scales with the star formation rate: L_tot(0.5-8 keV)(erg/s) = 4.5 10^{39} SFR(Msun/yr) with a dispersion sigma = 0.32 dex. We obtained consistent scale factors for nearby galaxies from the resolved sample and galaxies from the high-SFR sample. Among the latter (eight out of 16) are Chandra Deep Field North galaxies, located at the red-shifts of z~0.2-1.3. This proves that the total X-ray luminosity of a galaxy is a powerful tool to measure the star formation rate in distant galaxies.

Komplexe Plasmen bestehen aus geladenen Mikropartikeln, die in ein teil- weise ionisiertes Gas, ein Plasma, eingebettet sind. Die Mikropartikel treten in Wechselwirkung, ihre Dynamik wird vom Gas nur schwach gedämpft. Auf- grund ihrer Größe können die Partikel mikroskopisch beobachtet werden und ihre Positionen bestimmt, sowie ihre Dynamik untersucht werden. Komple- xe Plasmen sind daher ein ideales Modellsystem, um Vorgänge in Fluiden, Festkörpern und bei Phasenübergängen zu studieren. In dieser Arbeit werden insbesondere die Vorgänge während der Kristal- lisation betrachtet. Ein 3-dimensionaler Plasmakristall wird aufgeschmolzen, um ihn anschließend wieder kristallisieren zu lassen. Dabei wird wiederholt die Position der Teilchen innerhalb der Wolke gemessen und ihre Struktur mit der von idealen Kristallen verglichen. So kann man Teilchen individu- ell einer bestimmten Struktur zuweisen. Auf diese Weise ist es möglich, nicht nur die Anteile einer bestimmten Kristallordnung, sondern auch deren exakte räumliche Verteilung zu bestimmen. Das Ergebnis dieser Analyse wird verwendet, um kristalline und flüssige Regionen zu identifizieren, sowie die Grenzflächen dazwischen zu bestimmen. Die zeitliche Entwicklung der Struktur von flüssig über hexagonal-dichteste Kugelpackung hin zu kubisch-flächenzentrierter Ordnung wird mit einem Mo- dell erklärt. Der Kristallisationsprozess wird mit einer molekulardynamischen Simu- lation nachvollzogen. Es wird die gleiche zeitliche Entwicklung der Kristall- strukturen beobachtet. Da die Experimente unter Einfluss der Schwerkraft durchgeführt werden, ergibt sich ein höhenabhängiger Druck innerhalb der Teilchenwolke. Mit Hilfe der Teilchendichte wird dieser Druck bestimmt. Im Vergleich der Kristallisa- tion verschiedener Teilchengrößen wird der Einfluss dieses Druckes sowie der unterschiedlichen Ladung und Dämpfung der Teilchen gezeigt.