Observation of the ground-state-geometric phase in a Heisenberg XY model

Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.Comment: manuscript (4 pages, 3 figures) + supporting online material (6 pages + 7 figures), to be published in Phys. Rev. Lett. (2010

Inverse Quantum Chemistry: Concepts and Strategies for Rational Compound Design

The rational design of molecules and materials is becoming more and more important. With the advent of powerful computer systems and sophisticated algorithms, quantum chemistry plays an important role in rational design. While traditional quantum chemical approaches predict the properties of a predefined molecular structure, the goal of inverse quantum chemistry is to find a structure featuring one or more desired properties. Herein, we review inverse quantum chemical approaches proposed so far and discuss their advantages as well as their weaknesses.Comment: 43 pages, 5 figure

Computational Study of Lawesson’s Reagent Mediated Fluorenone Dimerization Forming 9,9’-Bifluorenylidene

The ambition of this work is to start a path to the a priori rational design of high yield production for electron acceptors with finely tuned band gaps, from the comfort of an armchair. To this end, organic photovoltaics offer a cheap and sustainable means of manufacture using readily available materials and avoids the toxicity of some of the heavy metals used in first and second-generation solar cells such as cadmium. The microwave assisted Lawesson’s reagent mediated one-pot one-step solventless synthesis takes less than 3 minutes and results in an 84% yield of 9,9’-bifluorenylidene from two equivalents of fluorenone. While fullerenes have traditionally been the most widely used electron acceptors in organic photovoltaics, bifluorenylidenes have been gaining attention due to their superior absorption in the visible spectrum, highly tunable band gap and cheap/efficient synthesis. Using an analog system to study the reaction divided into two parts; intermediate formation and sulfur extrusion, a molecular pathway has been devised that fits the reaction conditions and explains differences in % yields of substituted 9,9’-bifluorenylidenes reported in a manner readily conducive to making predictions based on the substituents chosen in the 9-fluorenylidene scaffold

Adiabatic ground state preparation of fermionic many-body systems from a two-body perspective

A well-known method to prepare ground states of fermionic many-body hamiltonians is adiabatic state preparation, in which an easy to prepare state is time-evolved towards an approximate ground state under a specific time-dependent hamiltonian. However, which path to take in the evolution is often unclear, and a direct linear interpolation, which is the most common method, may not be optimal. In this work, we explore new types of adiabatic paths based on an eigendecomposition of the coefficient tensor in the second quantised representation of the difference between the final and initial hamiltonian (the residual hamiltonian). Since there is an equivalence between this tensor and a projection of the residual hamiltonian onto the subspace of two particles, this approach is essentially a two-body spectral decomposition. We show how for general hamiltonians, the adiabatic time complexity may be upper bounded in terms of the number of one-body modes $L$ and a minimal gap $\Delta$ along the path. Our finding is that the complexity is determined primarily by the degree of pairing in the two-body states. As a result, systems whose two-body eigenstates are uniform superpositions of distinct fermion pairs tend to exhibit maximal complexity, which scales as $O(L^4/\Delta^3)$ in direct interpolation and $O(L^6/\Delta^3)$ in an evolution that follows a path along the corners of a hypercube in parameter space. The usefulness of our method is demonstrated through a few examples involving Fermi-Hubbard models where, due to symmetries, level crossings occur in direct interpolation. We show that our method of decomposing the residual hamiltonian and thereby deviating from a direct path appropriately breaks the relevant symmetries, thus avoiding level crossings and enabling an adiabatic passage.Comment: 14 pages, 5 figure

Molecular Structure and Modeling of Water-Air and Ice-Air Interfaces Monitored by Sum-Frequency Generation.

From a glass of water to glaciers in Antarctica, water-air and ice-air interfaces are abundant on Earth. Molecular-level structure and dynamics at these interfaces are key for understanding many chemical/physical/atmospheric processes including the slipperiness of ice surfaces, the surface tension of water, and evaporation/sublimation of water. Sum-frequency generation (SFG) spectroscopy is a powerful tool to probe the molecular-level structure of these interfaces because SFG can specifically probe the topmost interfacial water molecules separately from the bulk and is sensitive to molecular conformation. Nevertheless, experimental SFG has several limitations. For example, SFG cannot provide information on the depth of the interface and how the orientation of the molecules varies with distance from the surface. By combining the SFG spectroscopy with simulation techniques, one can directly compare the experimental data with the simulated SFG spectra, allowing us to unveil the molecular-level structure of water-air and ice-air interfaces. Here, we present an overview of the different simulation protocols available for SFG spectra calculations. We systematically compare the SFG spectra computed with different approaches, revealing the advantages and disadvantages of the different methods. Furthermore, we account for the findings through combined SFG experiments and simulations and provide future challenges for SFG experiments and simulations at different aqueous interfaces