Spatial noise correlations of a chain of ultracold fermions - A numerical study

We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the shot noise contains full information on the correlations present in the system. We point out the importance of the sum rules fulfilled by the noise correlations and show that they yield nonsingular structures beyond the predictions of bosonization approaches. Noise correlations can thus serve as a universal probe of order and can be used to characterize the many-body states of cold atoms in optical lattices.Comment: 12 pages, 7 figure

Decay Rates and Survival Probabilities in Open Quantum Systems

We provide the first statistical analysis of the decay rates of strongly driven 3D atomic Rydberg states. The distribution of the rates exhibits universal features due to Anderson localization, while universality of the time dependent decay requires particular initial conditions.Comment: 4 pages, 3 figures, ref. on subjec

Global analysis of parallel analog networks with retarded feedback

We analyze the retrieval dynamics of analog ‘‘neural’’ networks with clocked sigmoid elements and multiple signal delays. Proving a conjecture by Marcus and Westervelt, we show that for delay-independent symmetric coupling strengths, the only attractors are fixed points and periodic limit cycles. The same result applies to a larger class of asymmetric networks that may be utilized to store temporal associations with a cyclic structure. We discuss implications for various learning schemes in the space-time domain

Matrix product state approach for a two-lead, multi-level Anderson impurity model

We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own Wilson chain, instead of using a single Wilson chain for all species together, we achieve a very significant reduction in the numerical resources required to obtain reliable results. We illustrate the power of this approach by calculating ground state properties of a four-level quantum dot coupled to two leads. The success of this proof-of-principle calculation suggests that the star geometry constitutes a promising strategy for future calculations the ground state properties of multi-band, multi-level quantum impurity models. Moreover, we show that it is possible to find an "optimal" chain basis, obtained via a unitary transformation (acting only on the index distinguishing different Wilson chains), in which degrees of freedom on different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chain-to-chain scattering matrix. We demonstrate this for a spinless two-lead model, presenting DMRG-results for the mutual information between two sites located far apart on different Wilson chains, and NRG results with respect to the scattering matrix.Comment: extended version, 11 pages, 12 figure