Degenerate mixtures of rubidium and ytterbium for engineering open quantum systems

In the last two decades, experimental progress in controlling cold atoms and ions now allows us to manipulate fragile quantum systems with an unprecedented degree of precision. This has been made possible by the ability to isolate small ensembles of atoms and ions from noisy environments, creating truly closed quantum systems which decouple from dissipative channels. However in recent years, several proposals have considered the possibility of harnessing dissipation in open systems, not only to cool degenerate gases to currently unattainable temperatures, but also to engineer a variety of interesting many-body states. This thesis will describe progress made towards building a degenerate gas apparatus that will soon be capable of realizing these proposals. An ultracold gas of ytterbium atoms, trapped by a species-selective lattice will be immersed into a Bose-Einstein condensate (BEC) of rubidium atoms which will act as a bath. Here we describe the challenges encountered in making a degenerate mixture of rubidium and ytterbium atoms and present two experiments performed on the path to creating a controllable open quantum system. The first experiment will describe the measurement of a tune-out wavelength where the light shift of $\Rb{87}$ vanishes. This wavelength was used to create a species-selective trap for ytterbium atoms. Furthermore, the measurement of this wavelength allowed us to extract the dipole matrix element of the $5s \rightarrow 6p$ transition in $\Rb{87}$ with an extraordinary degree of precision. Our method to extract matrix elements has found use in atomic clocks where precise knowledge of transition strengths is necessary to account for minute blackbody radiation shifts. The second experiment will present the first realization of a degenerate Bose-Fermi mixture of rubidium and ytterbium atoms. Using a three-color optical dipole trap (ODT), we were able to create a highly-tunable, species-selective potential for rubidium and ytterbium atoms which allowed us to use $\Rb{87}$ to sympathetically cool $\Yb{171}$ to degeneracy with minimal loss. This mixture is the first milestone creating the lattice-bath system and will soon be used to implement novel cooling schemes and explore the rich physics of dissipation.

A Calogero formulation for four-dimensional black-hole microstates

We extract the leading-order entropy of a four-dimensional extremal black hole in N=2N=2 ungauged supergravity by formulating the CFT1 that is holographically dual to its near-horizon AdS2 geometry, in terms of a rational Calogero model with a known counting formula for the degeneracy of states in its Hilbert space.

Study of tRNA modifying enzymes and codon usage bias in cancer

Recent evidences indicate that tRNA modifications and tRNA modifying enzymes may play important roles in complex human diseases such as cancer, neurological disorders and mitochondrial-linked diseases. We postulate that expression deregulation of tRNA modifying enzymes affects the level of tRNA modifications and, consequently, their function and the translation efficiency of their tRNA corresponding codons. Due to the degeneracy of the genetic code, most amino acids are encoded by two to six synonymous codons. This degeneracy and the biased usage of synonymous codons cause alterations that can span from protein folding to enhanced translation efficiency of a select gene group. In this work, we focused on cancer and performed a meta-analysis study to compare microarray gene expression profiles, reported by previous studies and evaluate the codon usage of different types of cancer where tRNA modifying enzymes were found de-regulated. A total of 36 different tRNA modifying enzymes were found de-regulated in most cancer datasets analyzed. The codon usage analysis revealed a preference for codons ending in AU for the up-regulated genes, while the down-regulated genes show a preference for GC ending codons. Furthermore, a PCA biplot analysis showed this same tendency. We also analyzed the codon usage of the datasets where the CTU2 tRNA modifying enzyme was found deregulated as this enzyme affects the wobble position (position 34) of specific tRNAs. Our data points to a distinct codon usage pattern between up and downregulated genes in cancer, which might be caused by the deregulation of specific tRNA modifying enzymes. This codon usage bias may augment the transcription and translation efficiency of some genes that otherwise, in a normal situation, would be translated less efficiently.

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.