A Multi-path Interferometer with Ultracold Atoms Trapped in an Optical Lattice

We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-square fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials and can be further improved by preparing a properly correlated initial state in the lattice.Comment: 11 pages, 3 fugire

Discrete Breathers in a Realistic Coarse-Grained Model of Proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin (discrete breathers) emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. In the case of the small $\beta$-barrel structure that we consider, localization occurs on the turns connecting the strands. At high energies, discrete breathers stabilize the structure by concentrating energy on few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of this two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.Comment: Submitted to Physical Biolog

Energy transfer in nonlinear network models of proteins

We investigate how nonlinearity and topological disorder affect the energy relaxation of local kicks in coarse-grained network models of proteins. We find that nonlinearity promotes long-range, coherent transfer of substantial energy to specific, functional sites, while depressing transfer to generic locations. Remarkably, transfer can be mediated by the self-localization of discrete breathers at distant locations from the kick, acting as efficient energy-accumulating centers.Comment: 4 pages, 3 figure

The IR-Completion of Gravity: What happens at Hubble Scales?

We have recently proposed an "Ultra-Strong" version of the Equivalence Principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: quartically divergent with the cut-off and with no spacetime dependent (subleading) ter ms. The presence of such terms seems in fact related to some known difficulties, such as the black hole information loss and the cosmological constant problem. Since the terms that we want to get rid of are subleading in the high-momentum expansion, we attempt to explore the conjectured theory by "IR-completing" GR. We consider a scalar field in a flat FRW Universe and isolate the first IR-correction to its Fourier modes operators that kills the quadratic (next to leading) time dependent divergence of the stress energy tensor VEV. Analogously to other modifications of field operators that have been proposed in the literature (typically in the UV), the present approach seems to suggest a breakdown (here, in the IR, at large distances) of the metric manifold description. We show that corrections to GR are in fact very tiny, become effective at distances comparable to the inverse curvature and do not contain any adjustable parameter. Finally, we derive some cosmological implications. By studying the consistency of the canonical commutation relations, we infer a correction to the distance between two comoving observers, which grows as the scale factor only when small compared to the Hubble length, but gets relevant corrections otherwise. The corrections to cosmological distance measures are also calculable and, for a spatially flat matter dominated Universe, go in the direction of an effective positive acceleration.Comment: 27 pages, 2 figures. Final version, references adde

New insight into cataract formation -- enhanced stability through mutual attraction

Small-angle neutron scattering experiments and molecular dynamics simulations combined with an application of concepts from soft matter physics to complex protein mixtures provide new insight into the stability of eye lens protein mixtures. Exploring this colloid-protein analogy we demonstrate that weak attractions between unlike proteins help to maintain lens transparency in an extremely sensitive and non-monotonic manner. These results not only represent an important step towards a better understanding of protein condensation diseases such as cataract formation, but provide general guidelines for tuning the stability of colloid mixtures, a topic relevant for soft matter physics and industrial applications.Comment: 4 pages, 4 figures. Accepted for publication on Phys. Rev. Let

Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.Comment: 8 pages, 7 figures; v3: Journal reference added, minor changes to tex

Exploring gravitational theories beyond Horndeski

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G$^3$ into Horndeski theories.Comment: 33 pages, added comments and corrected typos as in JCAP versio

Phase Estimation from Atom Position Measurements

We study the measurement of the position of atoms as a means to estimate the relative phase between two Bose-Einstein condensates. First, we consider $N$ atoms released from a double-well trap, forming an interference pattern, and show that a simple least-squares fit to the density gives a shot-noise limited sensitivity. The shot-noise limit can instead be overcome by using correlation functions of order $\sqrt{N}$ or larger. The measurement of the $N\mathrm{th}$-order correlation function allows to estimate the relative phase at the Heisenberg limit. Phase estimation through the measurement of the center-of-mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of the overlap between the two clouds on the phase estimation, when Mach-Zehnder interferometry is performed in a double-well.Comment: 20 pages, 6 figure

Collisional strong-field QED kinetic equations from first principles

Starting from nonequilibrium quantum field theory on a closed time path, we derive kinetic equations for the strong-field regime of quantum electrodynamics (QED) using a systematic expansion in the gauge coupling $e$. The strong field regime is characterized by a large photon field of order $\mathcal{O}(1/e)$, which is relevant for the description of, e.g., intense laser fields, the initial stages of off-central heavy ion collisions, and condensed matter systems with net fermion number. The strong field enters the dynamical equations via both quantum Vlasov and collision terms, which we derive to order $\mathcal{O}(e^2)$. The kinetic equations feature generalized scattering amplitudes that have their own equation of motion in terms of the fermion spectral function. The description includes single photon emission, electron-positron pair photoproduction, vacuum (Schwinger) pair production, their inverse processes, medium effects and contributions from the field, which are not restricted to the so-called locally-constant crossed field approximation. This extends known kinetic equations commonly used in strong-field QED of intense laser fields. In particular, we derive an expression for the asymptotic fermion pair number that includes leading-order collisions and remains valid for strongly inhomogeneous fields. For the purpose of analytically highlighting limiting cases, we also consider plane-wave fields for which it is shown how to recover Furry-picture scattering amplitudes by further assuming negligible occupations. Known on-shell descriptions are recovered in the case of simply peaked ultrarelativistic fermion occupations. Collisional strong-field equations are necessary to describe the dynamics to thermal equilibrium starting from strong-field initial conditions