Number-Phase Wigner Representation for Efficient Stochastic Simulations

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.Comment: 7 pages, 1 figur

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the purely classical simulation, suggesting that observing such exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.Comment: Close to the published versio

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with a tendency towards double welled potentials using model coupled harmonic diabatic potential-energy surfaces. The von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions in such a bipartite system. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local minima). However, in this region two distinct types of entanglement are found: (1) entanglement that arises purely from the degeneracy of energy levels in the two potential wells and which is destroyed by slight asymmetry, and (2) entanglement that involves strongly interacting states in each well that is relatively insensitive to asymmetry. These two distinct regions are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, semibullvalene, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated

Spin correlations as a probe of quantum synchronization in trapped ion phonon-lasers

We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser whilst also being driven by a blue-detuned laser which results in self-oscillation. Working in a non-classical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom within each ion and find that when two ions synchronize their spin degrees of freedom in turn become correlated. This allows one to indirectly infer the presence of synchronization by measuring the ions' internal state

Non-destructive shadowgraph imaging of ultracold atoms

An imaging system is presented that is capable of far-detuned non-destructive imaging of a Bose-Einstein condensate with the signal proportional to the second spatial derivative of the density. Whilst demonstrated with application to $^{85}\text{Rb}$, the technique generalizes to other atomic species and is shown to be capable of a signal to noise of ${\sim}25$ at $1$GHz detuning with $100$ in-trap images showing no observable heating or atom loss. The technique is also applied to the observation of individual trajectories of stochastic dynamics inaccessible to single shot imaging. Coupled with a fast optical phase lock loop, the system is capable of dynamically switching to resonant absorption imaging during the experiment.Comment: 4 pages, 5 figure

Lattice Relaxation and Charge-Transfer Optical Transitions Due to Self-Trapped Holes in Non-Stoichiometric LaMnO3_3 Crystal

We use the Mott-Littleton approach to evaluate polarisation energies in LaMnO$_3$ lattice associated with holes localized on both Mn$^{3+}$ cation and O$^{2-}$ anion. The full (electronic and ionic) lattice relaxation energy for a hole localized at the O-site is estimated as 2.4 eV which is appreciably greater than that of 0.8 eV for a hole localized at the Mn-site, indicating on the strong electron-phonon interaction in the former case. Using a Born-Haber cycle we examine thermal and optical energies of the hole formation associated with electron ionization from Mn$^{3+}$, O$^{2-}$ and La$^{3+}$ ions in LaMnO$_3$ lattice. For these calculations we derive a phenomenological value for the second electron affinity of oxygen in LaMnO$_3$ lattice by matching the optical energies of La$^{4+}$ and O$^-$ hole formation with maxima of binding energies in the experimental photoemission spectra. The calculated thermal energies predict that the electronic hole is marginally more stable in the Mn$^{4+}$ state in LaMnO$_3$ host lattice, but the energy of a hole in the O$^-$ state is only higher by a small amount, 0.75 eV, rather suggesting that both possibilities should be treated seriously. We examine the energies of a number of fundamental optical transitions, as well as those involving self-trapped holes of Mn$^{4+}$ and O$^-$ in LaMnO$_3$ lattice. The reasonable agreement with experiment of our predicted energies, linewidths and oscillator strengths leads us to plausible assignments of the optical bands observed. We deduce that the optical band near 5 eV is associated with O(2p) - Mn(3d) transition of charge-transfer character, whereas the band near 2.3 eV is rather associated with the presence of Mn$^{4+}$ and/or O$^-$ self-trapped holes in non-stoichiometric LaMnO$_3$ compound.Comment: 18 pages, 6 figures, it was presented partially at SCES-2001 conference in Ann Arbor, Michiga

Functional significance may underlie the taxonomic utility of single amino acid substitutions in conserved proteins

We hypothesized that some amino acid substitutions in conserved proteins that are strongly fixed by critical functional roles would show lineage-specific distributions. As an example of an archetypal conserved eukaryotic protein we considered the active site of ß-tubulin. Our analysis identified one amino acid substitution—ß-tubulin F224—which was highly lineage specific. Investigation of ß-tubulin for other phylogenetically restricted amino acids identified several with apparent specificity for well-defined phylogenetic groups. Intriguingly, none showed specificity for “supergroups” other than the unikonts. To understand why, we analysed the ß-tubulin Neighbor-Net and demonstrated a fundamental division between core ß-tubulins (plant-like) and divergent ß-tubulins (animal and fungal). F224 was almost completely restricted to the core ß-tubulins, while divergent ß-tubulins possessed Y224. Thus, our specific example offers insight into the restrictions associated with the co-evolution of ß-tubulin during the radiation of eukaryotes, underlining a fundamental dichotomy between F-type, core ß-tubulins and Y-type, divergent ß-tubulins. More broadly our study provides proof of principle for the taxonomic utility of critical amino acids in the active sites of conserved proteins

From chaos to order: Chain-length dependence of the free energy of formation of meso-tetraalkylporphyrin self-assembled monolayer polymorphs

© 2016 American Chemical Society. We demonstrate that systematic errors can be reduced and physical insight gained through investigation of the dependence of free energies for meso-tetraalkylporphyrin self-assembled monolayers (SAMs) polymorphism on the alkyl chain length m. These SAMs form on highly ordered pyrolytic graphite (HOPG) from organic solution, displaying manifold densities and atomic structures. SAMs with m = 11-19 are investigated experimentally while those with m = 6-28 are simulated using density-functional theory (DFT). It is shown that, for m = 15 or more, the alkyl chains crystallize to dominate SAM structure. Meso-tetraalkylporphyrin SAMs of length less than 11 have never been observed, a presumed effect of inadequate surface attraction. Instead, we show that free energies of SAM formation actually enhance as the chain length decreases. The inability to image regular SAMs stems from the appearance of many polymorphic forms of similar free energy, preventing SAM ordering. We also demonstrate a significant odd/even effect in SAM structure arising from packing anomalies. Comparison of the chain-length dependence of formation free energies allows the critical dispersion interactions between molecules, solvent, and substrate to be directly examined. Interpretation of the STM data combined with measured enthalpies indicates that Grimme's D3 explicit-dispersion correction and the implicit solvent correction of Floris, Tomasi and Pascual Ahuir are both quantitatively accurate and very well balanced to each other

Constructive function approximation: theory and practice

In this paper we study the theoretical limits of finite constructive convex approximations of a given function in a Hilbert space using elements taken from a reduced subset. We also investigate the trade-off between the global error and the partial error during the iterations of the solution. These results are then specialized to constructive function approximation using sigmoidal neural networks. The emphasis then shifts to the implementation issues associated with the problem of achieving given approximation errors when using a finite number of nodes and a finite data set for training