Measuring entanglement entropy through the interference of quantum many-body twins

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-correlated many-body systems.Comment: 14 pages, 12 figures (6 in the main text, 6 in supplementary material

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We investigate the Bose-Hubbard model on a microscopic level using single atom-single lattice site imaging; our technique enables space- and time-resolved characterization of the number statistics across the superfluid-Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition timescales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low entropy phases in a lattice

Cold Matter Assembled Atom-by-Atom

The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of over 50 atoms in less than 400 ms. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach enables controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.Comment: 12 pages, 9 figures, 3 movies as ancillary file

Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas

We study the impact of coherently generated lattice photons on an atomic Mott insulator subjected to a uniform force. Analogous to an array of tunnel-coupled and biased quantum dots, we observe sharp, interaction-shifted photon-assisted tunneling resonances corresponding to tunneling one and two lattice sites either with or against the force and resolve multiorbital shifts of these resonances. By driving a Landau-Zener sweep across such a resonance, we realize a quantum phase transition between a paramagnet and an antiferromagnet and observe quench dynamics when the system is tuned to the critical point. Direct extensions will produce gauge fields and site-resolved spin flips, for topological physics and quantum computing.Physic

Modern Feynman Diagrammatic One-Loop Calculations

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\to b\bar{b}b\bar{b}+X$.Comment: 10 pages, 2 figures; contribution to the proceedings of the CPP2010 Workshop, 23-25 Sep. 2010, KEK, Tsukuba, Japa

Increases in norepinephrine release and ovarian cyst formation during ageing in the rat

<p>Abstract</p> <p>Background</p> <p>Depletion of ovarian follicles is associated with the end of reproductive function in ageing females. Recently, it has been described that this process parallels increases in the concentration of norepinephrine (NE) in the rat ovary. In sexually mature rats, experimentally-induced increases in the sympathetic tone of the ovary is causally related to ovarian cyst formation and deranged follicular development. Thus, there is a possibility that increased ovarian NE concentrations represent changes in the activity of sympathetic nerves, which consequently participate in the process of ovarian cyst formation observed during ageing in the human and experimental animal models.</p> <p>Methods</p> <p>Sprague-Dawley rats between 6 and 14 months old were used to analyse the capacity of the ovary to release ³H-NE recently incorporated under transmural depolarisation in relation to changes in the ovarian follicular population. Morphometric analysis of ovarian follicles and real time PCR for Bcl2 and Bax mRNA were used to assess follicular atresia.</p> <p>Results</p> <p>From 8 months old, the induced release of recently incorporated ³H-norepinephrine (³H-NE) from the ovary and ovarian NE concentrations increased, reaching their peak values at 12 months old and remained elevated up to 14 months old. Increases in sympathetic nerve activity paralleled changes in the follicular population, as well as disappearance of the corpus luteum. In contrast, luteinised follicles, precystic follicles, and cystic follicles increased. During this period, the relationship between Bax and Bcl2 mRNAs (the proapoptotic/antiapoptotic signals) increased, suggesting atresia as the principal mechanism contributing to the decreased follicular population. When NE tone was increased, the mRNA ratio favoured Bcl2 to Bax and antiapoptotic signals dominated this period of development. Thus, these changing ratios could be responsible for the increase in luteinised follicles, as well as precystic and cystic follicles.</p> <p>Conclusion</p> <p>These data suggest that the ageing process in the ovary of the Sprague-Dawley rat is accompanied by an increased sympathetic tone of the ovary. Consequently, this sympathetic change could be related to a neuroendocrine-driven formation of a polycystic condition similar to that observed in the sympathetic-activated adult ovary.</p