Scholarly Works - Physics - Theory of Condensed Matter
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Item Open Access Accepted version Peer-reviewed Entanglement negativity and sudden death in the toric code at finite temperature(APS, 2018-04-16) Hart, Oliver; Castelnovo, Claudio; Castelnovo, Claudio [0000-0003-1752-6343]We study the fate of quantum correlations at finite temperature in the two dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. The toric code has two types of elementary excitations (defects) costing different energies. We show that an $\mathcal{O}(1)$ density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an $\mathcal{O}(1)$ density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low energy states. We demonstrate this behaviour both for small subsystems, where we can prove that the negativity is a necessary and sufficient condition for separability, as well as for extended subsystems, where it is only a sufficient condition. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.Item Open Access Accepted version Peer-reviewed Dynamic scaling of topological ordering in classical systems(American Physical Society, 2018-01-29) Xu, N; Castelnovo, C; Melko, RG; Chamon, C; Sandvik, AW; Castelnovo, Claudio [0000-0003-1752-6343]We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a nonlocal order parameter (defined using Wilson loops) and a dynamic exponent z=2.70±0.03, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature - the Ising chain, the two-dimensional Z2 gauge model, and a three-dimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is nonsmooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.Item Open Access Accepted version Peer-reviewed Semiclassical dynamics, Berry curvature, and spiral holonomy in optical quasicrystals(American Physical Society (APS), 2018) Spurrier, S; Cooper, NR; Spurrier, Stephen [0000-0002-1030-2796]; Cooper, Nigel [0000-0002-4662-1254]We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive conditions on the external force that allow for a "semiadiabatic" regime in which semiclassical equations of motion can apply, leading to Bloch oscillations between the edges of a pseudo-Brillouin-zone. We verify this semiclassical theory by comparing to the results of an exact numerical solution. Interesting features appear in the semiclassical dynamics for the quasicrystal for a particle driven in a cyclic trajectory around the corner of the pseudo-Brillouin-zone: The particle fails to return to its initial state, providing a realization of a "spiral holonomy" in the dynamics. We show that there can appear anomalous velocity contibutions, associated with nonzero Berry curvature. We relate these to the Berry phase associated with the spiral holonomy, and show how the Berry curvature can be accessed from the semiclassical dynamics. Finally, by identifying the pseudo-Brillouin-zone as a higher genus surface, we show that the Chern number classification for periodic systems can be extended to a quasicrystal, thereby determining a topological index for the system.Item Open Access Accepted version Peer-reviewed Materials data validation and imputation with an artificial neural network(Elsevier BV, 2018) Verpoort, PC; MacDonald, P; Conduit, GJ; Verpoort, Philipp [0000-0003-1319-5006]; Conduit, Gareth [0000-0003-3807-6361]We apply an artificial neural network to model and verify material properties. The neural network algorithm has a unique capability to handle incomplete data sets in both training and predicting, so it can regard properties as inputs allowing it to exploit both composition-property and property-property correlations to enhance the quality of predictions, and can also handle a graphical data as a single entity. The framework is tested with different validation schemes, and then applied to materials case studies of alloys and polymers. The algorithm found twenty errors in a commercial materials database that were confirmed against primary data sources.Item Open Access Accepted version Peer-reviewed Ferromagnetic-nematic order and strongly correlated phases of fermions in optical flux lattices(American Physical Society (APS), 2015) Davenport, Simon C; Cooper, Nigel R; Cooper, Nigel [0000-0002-4662-1254]We study a model of a 2D ultracold atomic gas subject to an "optical flux lattice": a laser configuration where Raman-dressed atoms experience a strong artificial magnetic field. This leads to a bandstructure of narrow energy bands with non-zero Chern numbers. We consider the case of two-level (spin-$1/2$) fermionic atoms in this lattice, interacting via a repulsive $s$-wave contact interaction. Atoms restricted to the lowest band are described by an effective model of spinless fermions with interactions that couple states in a momentum-dependent manner across the Brillouin zone; a consequence of the Raman dressing of the two spin states. We present the results of detailed exact diagonalization studies of the many-body states for a range of filling factors, $\nu$. First, we present evidence for the existence of a phase with coupled ferromagnetic--nematic ordering, which was previously suggested by a mean-field analysis. Second, we present evidence indicating the presence of a Laughlin-like fractional quantum Hall state occurring at filling factor $\nu = 1/3$. Finally, we observe a charge density wave state at $\nu=1/2$, which we are able to cleanly distinguish from the Laughlin-like state by its translational symmetry breaking and relatively small participation ratio.Item Open Access Accepted version Peer-reviewed Bosonic integer quantum Hall effect in optical flux lattices.(American Physical Society (APS), 2015-09-11) Sterdyniak, A; Cooper, Nigel R; Regnault, N; Cooper, Nigel [0000-0002-4662-1254]In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters.Item Open Access Accepted version Peer-reviewed Synthetic Spin-Orbit Coupling in an Optical Lattice Clock.(American Physical Society (APS), 2016-01-22) Wall, Michael L; Koller, Andrew P; Li, Shuming; Zhang, Xibo; Cooper, Nigel R; Ye, Jun; Rey, Ana Maria; Cooper, Nigel [0000-0002-4662-1254]We propose the use of optical lattice clocks operated with fermionic alkaline-earth atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation, when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers can perform momentum-resolved band tomography and determine SOC-induced s-wave collisions in nuclear-spin-polarized fermions. With the use of a second counterpropagating clock beam, we propose a method for engineering controlled atomic transport and study how it is modified by p- and s-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.Item Open Access Accepted version Peer-reviewed Dynamic Optical Lattices of Subwavelength Spacing for Ultracold Atoms.(American Physical Society (APS), 2015-10-02) Nascimbene, Sylvain; Goldman, Nathan; Cooper, Nigel R; Dalibard, Jean; Cooper, Nigel [0000-0002-4662-1254]We propose a scheme for realizing lattice potentials of subwavelength spacing for ultracold atoms. It is based on spin-dependent optical lattices with a time-periodic modulation. We show that the atomic motion is well described by the combined action of an effective, time-independent lattice of small spacing, together with a micromotion associated with the time modulation. A numerical simulation shows that an atomic gas can be adiabatically loaded into the effective lattice ground state, for time scales comparable to the ones required for adiabatic loading of standard optical lattices. We generalize our scheme to a two-dimensional geometry, leading to Bloch bands with nonzero Chern numbers. The realization of lattices of subwavelength spacing allows for the enhancement of energy scales, which could facilitate the achievement of strongly correlated (topological) states.Item Open Access Accepted version Peer-reviewed Anomalous diffusion in a dynamical optical lattice(American Physical Society (APS), 2018) Zheng, W; Cooper, NR; Cooper, Nigel [0000-0002-4662-1254]Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-Andr\'e model which can cause localization of single-particle wavefunctions. We show that atomic wavepackets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between super-diffusive and sub-diffusive regimes. This anomalous diffusion arises from an interplay between quantum localization and quantum fluctuations of the cavity field.Item Open Access Accepted version Peer-reviewed Universality of clone dynamics during tissue development.(Springer Science and Business Media LLC, 2018-05) Rulands, Steffen; Lescroart, Fabienne; Chabab, Samira; Hindley, Christopher J; Prior, Nicole; Sznurkowska, Magdalena K; Huch, Meritxell; Philpott, Anna; Blanpain, Cedric; Simons, Benjamin D; Rulands, Steffen [0000-0001-6398-1553]; Hindley, Christopher [0000-0002-5294-1270]; Prior, Nicole [0000-0003-2856-7052]; Huch Ortega, Meritxell [0000-0002-1545-5265]; Philpott, Anna [0000-0003-3789-2463]; Simons, Benjamin [0000-0002-3875-7071]The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease (1, 2). But what can be learned from clonal dynamics in development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as a laboratory to study non-equilibrium statistical physics.Item Open Access Published version Peer-reviewed Frame, metric and geodesic evolution in shape-changing nematic shells.(Royal Society of Chemistry (RSC), 2017-11-29) Mostajeran, Cyrus; Warner, Mark; Modes, Carl D; Mostajeran, Cyrus [0000-0001-8910-9755]; Warner, Mark [0000-0003-3172-0265]; Modes, Carl D [0000-0001-9940-0730]Non-uniform director fields in flat, responsive, glassy nematic sheets lead to the induction of shells with non-trivial topography on the application of light or heat. Contraction along the director causes metric change, with, in general, the induction of Gaussian curvature, that drives the topography change. We describe the metric change, the evolution of the director field, and the transformation of reference state material curves, e.g. spirals into radii, as curvature develops. The non-isometric deformations associated with heat or light change the geodesics of the surface, intriguingly even in regions where no Gaussian curvature results.Item Open Access Pathological Disbelief(2004-06-30) Josephson, Brian DThis talk mirrors "Pathological Science", a lecture given by Chemistry Laureate Irving Langmuir. Langmuir discussed cases where scientists, on the basis of invalid processes, claimed the validity of phenomena that were unreal. My interest is in the counter- pathology involving cases where phenomena that are almost certainly real are rejected by the scientific community, for reasons that are just as invalid as those of the cases described by Langmuir. For complete abstract follow the abstract link.Item Open Access Towards time-dependent current-density-functional theory in the non-linear regime.(AIP Publishing, 2015-02-28) Escartín, JM; Vincendon, M; Romaniello, P; Dinh, PM; Reinhard, P-G; Suraud, ETime-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.Item Open Access Network analysis and data mining in food science: the emergence of computational gastronomy(Springer Science and Business Media LLC, 2013-12) Ahnert, Sebastian EAbstract The rapidly growing body of publicly available data on food chemistry and food usage can be analysed using data mining and network analysis methods. Here we discuss how these approaches can yield new insights both into the sensory perception of food and the anthropology of culinary practice. We also show that this development is part of a larger trend. Over the past two decades large-scale data analysis has revolutionized the biological sciences, which have experienced an explosion of experimental data as a result of the advent of high-throughput technology. Large datasets are also changing research methodologies in the social sciences due to the data generated by mobile communication technology and online social networks. Even the arts and humanities are seeing the establishment of ‘digital humanities’ research centres in order to cope with the increasing digitization of literary and historical sources. We argue that food science is likely to be one of the next beneficiaries of large-scale data analysis, perhaps resulting in fields such as ‘computational gastronomy’.Item Open Access The Relativistic Shift in the Mössbauer Effect AND Coupled Superconductors(Trinity College, University of Cambridge, 2012-10-26) Josephson, BrianPart I of this dissertation predicts a temperature dependence, with relativistic causes, of the frequency of Mössbauer effect gamma rays. Part II contains the original analysis of the behaviour of two superconductors linked in a way that permits electron exchange.Item Open Access Presentations of bdj50 conference lectures(2012-06-23) SpeakersItem Open Access The Evolution of Telepathy(2011-02-09) Sheldrake, RupertThese are the slides that accompanied the lecture by Rupert Sheldrake, which can heard at http://sms.cam.ac.uk/media/1097239. They are available in both Powerpoint and PDF format. A number of the slides, including the first one, are intentionally blank.Item Open Access A Critical Point for Science?(2008-03-05) Josephson, B DSlides accompanying the lecture 'A Critical Point for Science?' at http://sms.cam.ac.uk/media/749894 (which should be opened in a separate window). A web search should be able to identify the references listed in the last slide.