Kasztelan, Christian (2010): Strongly Interacting Quantum Systems out of Equilibrium: Ultracold Quantum Gases and Magnetic Systems. Dissertation, LMU München: Faculty of Physics 

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Abstract
The main topic of this thesis is the study of manybody effects in strongly correlated one or quasi onedimensional condensed matter systems. These systems are characterized by strong quantum and thermal fluctuations, which make meanfield 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 densitymatrix renormalization group method (DMRG), introduced by Steve White in 1992. Originally limited to the study of static problems, timedependent DMRG has been developed allowing one to investigate nonequilibrium phenomena in quantum mechanics. In this thesis I present the solution of three conceptionally different problems, which have been addressed using mostly the Krylovsubspace version of the timedependent 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 twospecies BoseHubbard model, realizes in a certain parameter range the physics of a spin1/2 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 twoparticle dynamics with ultracold bosonic atoms in isolated double wells were detected. My project investigates the coherent manyparticle dynamics, which takes place after coupling the double well. I provide the theoretical background for the next step, the observation of coherent manyparticle dynamics after coupling the double wells. The tunability between the BoseHubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable 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 manybody generalization of the original LandauZener formula. This formula gives the transition probability between the two states of a quantum mechanical twolevel system, where the offset between the two levels is varying linearly in time. In a recent experiment this framework has been extended to a manybody system consisting of pairwise tunnelcoupled onedimensional Bose liquids. It was found that the tunnel coupling between the tubes and the intertube interactions strongly modify the original LandauZener picture. After a introduction to the twolevel and the threelevel LandauZener 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 LandauZener sweeps as well as the timeevolution after sudden quenches of the energy offset. A major finding is that for sufficiently large initial density quenches can be efficiently used to create quasithermal 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 multipartite states, which arise typically during quantum computation processes. The bigger the number of entangled qubits the more fragile is its entanglement under the influence decoherence. As starting point I consider first two entangled qubits, whereby one qubit interacts with an arbitrary environment. For this particular case I have derived a factorization law for the disentanglement. Next, I calculate the decrease of entanglement of two , three and four entangled qubits, general $W$ and general $GHZ$state, coupled to a global spin$1/2$ bath or several independent spin$1/2$ baths , one for each qubit. Although there is no appropriate entanglement measure for three and more qubits, it turns out that this decrease is directly related to the increase of entanglement between the central system and the bath. This implies the formation of a much bigger multipartite entangled network. Thus, using the von Neumann entropy and the Wootters concurrence, I derive a simple upper bound for the bathinduced entanglement breaking power of the initially maximally entangled multipartite states.
Item Type:  Thesis (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  8. December 2010 
1. Referee:  Schollwöck, Ulrich 
MD5 Checksum of the PDFfile:  fd71ee78fc4b80285d1607a277401cf9 
Signature of the printed copy:  0001/UMC 19154 
ID Code:  12482 
Deposited On:  12. Jan 2011 10:32 
Last Modified:  20. Jul 2016 10:26 