Quantum field tomography

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.Comment: 31 pages, 5 figures, minor change

Renormalization algorithm with graph enhancement

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.Comment: 4 pages, 1 figur

Pinwheel stabilization by ocular dominance segregation

We present an analytical approach for studying the coupled development of ocular dominance and orientation preference columns. Using this approach we demonstrate that ocular dominance segregation can induce the stabilization and even the production of pinwheels by their crystallization in two types of periodic lattices. Pinwheel crystallization depends on the overall dominance of one eye over the other, a condition that is fulfilled during early cortical development. Increasing the strength of inter-map coupling induces a transition from pinwheel-free stripe solutions to intermediate and high pinwheel density states.Comment: 10 pages, 4 figure

Quantum paraelectric phase of SrTiO₃ from first principles

We demonstrate how the quantum paraelectric ground state of SrTiO3 can be accessed via a microscopic ab initio approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectric phase even though a classical description would predict a ferroelectric phase. We find that accounting for quantum fluctuations of the lattice and for the strong coupling between the ferroelectric soft mode and lattice elongation is necessary to achieve quantitative agreement with experimental frequency of the ferroelectric soft mode. The temperature dependent properties in SrTiO3 are also well captured by the present microscopic framework

ANNINE-6plus, a voltage-sensitive dye with good solubility, strong membrane binding and high sensitivity

We present a novel voltage-sensitive hemicyanine dye ANNINE-6plus and describe its synthesis, its properties and its voltage-sensitivity in neurons. The dye ANNINE-6plus is a salt with a double positively charged chromophore and two bromide counterions. It is derived from the zwitterionic dye ANNINE-6. While ANNINE-6 is insoluble in water, ANNINE-6plus exhibits a high solubility of around 1 mM. Nonetheless, it displays a strong binding to lipid membranes. In contrast to ANNINE-6, the novel dye can be used to stain cells from aqueous solution without surfactants or organic solvents. In neuronal membranes, ANNINE-6plus exhibits the same molecular Stark effect as ANNINE-6. As a consequence, a high voltage-sensitivity is achieved with illumination and detection in the red end of the excitation and emission spectra, respectively. ANNINE-6plus will be particularly useful for sensitive optical recording of neuronal excitation when organic solvents and surfactants must be avoided as with intracellular or extracellular staining of brain tissue

Optical Phonon Lasing in Semiconductor Double Quantum Dots

We propose optical phonon lasing for a double quantum dot (DQD) fabricated in a semiconductor substrate. We show that the DQD is weakly coupled to only two LO phonon modes that act as a natural cavity. The lasing occurs for pumping the DQD via electronic tunneling at rates much higher than the phonon decay rate, whereas an antibunching of phonon emission is observed in the opposite regime of slow tunneling. Both effects disappear with an effective thermalization induced by the Franck-Condon effect in a DQD fabricated in a carbon nanotube with a strong electron-phonon coupling.Comment: 8 pages, 4 figure

Entanglement entropy of two disjoint intervals in c=1 theories

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second order Renyi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor network techniques that allowed to obtain the reduced density matrices of disjoint blocks of the spin-chain and to check the correctness of the predictions for Renyi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure