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preprint2016arXiv

Performing Hong-Ou-Mandel-type Numerical Experiments with Repulsive Condensates: The case of Dark and Dark-bright Solitons

The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously reaching a 50:50 beam splitter to emerge on the same port through two-photon interference. Motivated by this phenomenon, we consider numerical experiments of the same flavor for classical, {\it wave} objects in the setting of repulsive condensates. We examine dark solitons interacting with a repulsive barrier, a case in which we find no significant asymmetries in the emerging waves after the collision, presumably due to their topological nature. We also consider case examples of two-component systems, where the dark solitons trap a bright structure in the second-component (dark-bright solitary waves). For these, pronounced asymmetries upon collision {\it are} possible for the non-topological bright component. We also show an example of a similar phenomenology for ring dark-bright structures in two dimensions.

preprint2016arXiv

The chiral anomaly in real space

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. We here describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edge of a quantum spin Hall insulator on the basis of three magnetic impurities. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strength. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring where the relative angle between the magnetization directions of the impurities takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space.

preprint2016arXiv

Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for defining quantum pumps, demonstrating that, as opposed to the conventional two-dimensional case, pumped quantities depend not only on the initial and final points of Hamiltonian evolution but also on the class of the chosen path and preserved symmetries. As such, we distinguish the scenarios of closed/open paths of Hamiltonian evolution, finding that different closed cycles can lead to the pumping of different quantum numbers, and that different open paths may point to distinct scenarios for surface physics. As explicit examples, we consider models similar to simple models used to describe topolo

preprint2015arXiv

Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions

The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency $ω$, are predicted in one dimension, in contrast to the breathing modes with frequency $2ω$ in two dimensions.

preprint2016arXiv

Raman evidence for nonadiabatic effects in optical phonon self-energies of transition metals

We report a Raman study of the effect of temperature on the self-energies of optical phonons in a number of transition metals with hexagonal-close-packed structure. Anisotropic softening of phonon energies and narrowing of phonon linewidths with increasing temperature are observed. These effects are reproduced in the calculations of phonon spectral functions based on \textit{ab initio} electronic structures and with carrier scattering by phonons taken into account. The combined observations and results of simulations indicate a relation between observed anomalies and the renormalization of the electron spectrum due to electron-phonon interaction. It is emphasized that the temperature dependence of the phonon energies resembles anharmonic behavior but is actually an electron-induced effect.

preprint2016arXiv

Breaking the superfluid speed limit

Coherent condensates appear as emergent phenomena in many systems, sharing the characteristic feature of an energy gap separating the lowest excitations from the condensate ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation spectrum in the scatter frame to become gapless, can create excitations at no energy cost, initiating the breakdown of the condensate. This limit is the well-known Landau velocity. While, for the neutral Fermionic superfluid 3He-B in the T=0 limit, flow around an oscillating body displays a very clear critical velocity for the onset of dissipation, here we show that for uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and exceeded. Since the Landau velocity is such a pillar of our understanding of superfluidity, this is a considerable surprise, with implications for the understanding of the dissipative effects of moving objects in all coherent condensate systems.

preprint2016arXiv

Decoupling between first sound and second sound in $^3$He - superfluid $^4$He mixtures

Bulk superfluid helium supports two sound modes: first sound is an ordinary pressure wave, while second sound is a temperature wave, unique to inviscid superfluid systems. These sound modes do not usually exist independently, but rather variations in pressure are accompanied by variations in temperature, and vice versa. We studied the coupling between first and second sound in dilute $^3$He - superfluid $^4$He mixtures, between 1.6 K and 2.2 K, at $^3$He concentrations ranging from 0 to 11 %, under saturated vapor pressure, using a quartz tuning fork oscillator. Second sound coupled to first sound can create anomalies in the resonance response of the fork, which disappear only at very specific temperatures and concentrations, where two terms governing the coupling cancel each other, and second sound and first sound become decoupled.

preprint2016arXiv

Quantifying the degree of average contraction of Collatz orbits

We here elaborate on a quantitative argument to support the validity of the Collatz conjecture, also known as the (3x + 1) or Syracuse conjecture. The analysis is structured as follows. First, three distinct fixed points are found for the third iterate of the Collatz map, which hence organise in a period 3 orbit of the original map. These are 1, 2 and 4, the elements which define the unique attracting cycle, as hypothesised by Collatz. To carry out the calculation we write the positive integers in modulo 8 (mod8 ), obtain a closed analytical form for the associated map and determine the transitions that yield contracting or expanding iterates in the original, infinite-dimensional, space of positive integers. Then, we consider a Markov chain which runs on the reduced space of mod8 congruence classes of integers. The transition probabilities of the Markov chain are computed from the deterministic map, by employing a measure that is invariant for the map itself. Working in this setting, we demonstrate that the stationary distribution sampled by the stochastic system induces a contracting behaviour for the orbits of the deterministic map on the original space of the positive integers.

preprint2016arXiv

First Sound in Holographic Superfluids at Zero Temperature

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed the case. Working at zero temperature, we explicitly find the quadratic action for the superfluid phonon at the boundary in an arbitrary number of dimensions and for an arbitrary scalar field potential, recovering the known dispersion relation for conformal first sound.

preprint2016arXiv

"Pseudoisomorphs" in liquids with intramolecular degrees of freedom

Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be identified by requiring scale invariance of the inherent-structure reduced-unit low-frequency vibrational spectrum evaluated for a single equilibrium configuration. This rationalizes why excess-entropy scaling, density scaling, and isochronal superposition apply for many liquids with internal degrees of freedom.

preprint2016arXiv

Practical quantum realization of the ampere from the electron charge

One major change of the future revision of the International System of Units (SI) is a new definition of the ampere based on the elementary charge \emph{e}. Replacing the former definition based on Ampère's force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from \emph{e}, accurate to within $10^{-8}$ in relative value and fulfilling traceability needs, is still missing despite many efforts have been spent for the development of single-electron tunneling devices. Starting again with Ohm's law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are quantized in terms of $ef_\mathrm{J}$ ($f_\mathrm{J}$ is the Josephson frequency) with a measurement uncertainty of $10^{-8}$. This new quantum current source, able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibr

preprint2015arXiv

Multiple Mode Torsional Oscillator Studies and Evidence for Supersolidity in Bulk 4He

The discovery by Kim and Chan (KC) of an anomalous decrease in the period of torsional oscillators (TO) containing samples of solid $^4$He at temperatures below 0.2 K was initially interpreted as a superfluid-like decoupling of a fraction of the solid moment of inertia from the TO. These experiments appeared to confirm the thirty-year-old theoretical prediction by Chester, Andreev, and Leggett of the existence of a low-temperature Bose-condensed supersolid phase in solid $^4$He. The initial results of KC lead to a flurry of experimental and theoretical activity and their results for bulk $^4$He samples were soon confirmed in a number of laboratories. The early excitement in this field, however, has been tempered by the realization that an anomaly in the shear modulus of solid helium $^4$He may explain most if not all of the period shifts observed in the early TO experiments. In principle, it is possible to distinguish experimentally between shear modulus induced period shifts and period shifts resulting from other physical mechanisms through the use of multiple frequency torsional oscillators. In this paper we shall discuss our recent results on bulk solid $^4$He with double and tr

preprint2016arXiv

Observation of half-quantum vortices in topological superfluid 3He

One of the most sought-after objects in topological quantum matter systems is a vortex carrying half a quantum of circulation. They were originally predicted to exist in superfluid 3He-A, but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid 3He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery provides a pathway for studies of unpaired Majorana modes bound to the HQV cores in the polar-distorted A phase.

preprint2016arXiv

Energy spectra of a spin-$\tfrac12$ XY spin molecule interacting with a single mode field cavity: Numerical study

In a previous paper [J. Phys.: Conf. Ser. 682 (2016) 012032}, arXiv:1605.05593] we studied analytically the energy spectra of a finite-size spin $\tfrac12$ XY chain (molecule) coupled at an arbitrary spin site to a single mode of an electromagnetic field via the Jaynes-Cummings model. We considered spin rings and open spin molecules with up to 4 spins and an interaction restricted to nearest-neighbours. Here we extend our investigation, addressing numerically the energy spectra of molecules of up to 10 spins with nearest-neighbour or long-range interaction. Furthermore we analyze the behaviour of an invariant operator, constructed by combining the magnetization of the spin-chain and the total number of photons in the system. We found a strong dependence on the number (even or odd) of sites in the molecules. This study is aimed at finding the appropriate combination of the physical parameters that could make the system suitable for use in quantum computations.

preprint2013arXiv

Nonlinear Effects in Multi-Photon Polaritonics

We consider theoretically nonlinear effects in a semiconductor quantum well embedded inside a photonic microcavity. Two-photon absorption by a 2p exciton state is considered and investigated; the matrix element of two-photon absorption is calculated. We compute the emission spectrum of the sample and demonstrate that under coherent pumping the nonlinearity of the two photon absorption process gives rise to bistability.

preprint2016arXiv

Coupled dynamics for superfluid $^4$He in the channel

We study the coupled dynamics of normal and superfluid components of the superfluid $^4$He in the channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case when the dynamic of the normal component is "frozen". We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore coupling, becomes stronger. The commonly measured flow properties also change when the coupling between two components is taken into account.

preprint2009arXiv

Variational Formulation for the KPZ and Related Kinetic Equations

We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension.

preprint2016arXiv

Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study

In nuclear physics, Density Functional Theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and Renormalization Group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of $N$ identical fermions interacting

preprint2016arXiv

Temperature coefficients of crystalline-quartz elastic constants over the cryogenic range [4 K, 15 K]

This paper brings out results of a measurement campaign aiming to determine the temperature coefficients of synthetic quartz elastic constants at liquid helium temperature. The method is based on the relationship between the resonance frequencies of a quartz acoustic cavity and the elastic constants of the material. The temperature coefficients of the elastic constants are extracted from experimental frequency-temperature data collected from a set of resonators of various cut angles, because of the anisotropy of quartz, measured on the very useful cryogenic range [4 K - 15 K]. The knowledge of these temperature coefficients would allow to further design either quartz temperature sensors or conversely frequency-temperature compensated quartz cuts. With extremely low losses, lower than $10^{-9}$ for the best ones, key applications of such devices are ultra-low loss mechanical systems used in many research areas including frequency control and fundamental measurements. The Eulerian formalism is used in this study to identify the temperature coefficients.

preprint2016arXiv

Chemical ordering beyond the superstructure in long-range ordered systems

To describe chemical ordering in solid solutions systems Warren-Cowley short-range parameters are ordinarily used. However, they are not directly suited for application to long-range ordered systems, as they do not converge to zero for large separations. It is the aim of this paper to generalize the theory to long-range ordered systems and quantitatively discuss chemical short-range order beyond the superstructure arrangements. This is demonstrated on the example of a non-stoichiometric B2-ordered intermetallic alloy. Parameters of interatomic potentials are taken from an embedded atom method (EAM) calculations and the degree of order is simulated by the Monte Carlo method. Both on-lattice and off-lattice methods, where the latter allows individual atoms to deviate from their regular lattice sites, were used, and the resulting effects are discussed.

preprint2016arXiv

Spooky correlations and unusual van der Waals forces between gapless and near-gapless molecules

We consider the zero-temperature van der Waals interaction between two molecules, each of which has a zero or near-zero electronic gap between a groundstate and the first excited state, using a toy model molecule ( equilateral H3) as an example. We show that the van der Waals energy between two groundstate molecules falls off as D^(-3) instead of the usual D^(-6) dependence, when the molecules are separated by distance D: We show that this is caused by perfect "spooky" correlation between the two fluctuating electric dipoles. The phenomenon is related to, but not the same as, the "resonant" interaction between an electronically excited and a groundstate molecule introduced by Eisenschitz and London in 1930. It is also an example of "type C van der Waals non- additivity" recently introduced by one of us ( Int. J. Quantum Chem. 114, 1157 (2014)). Our toy molecule H3 is not stable, but symmetry considerations suggest that a similar vdW phenomenon may be observable, despite Jahn-Teller effects, in molecules with discrete rotational symmetry and broken inversion symmetry, such as certain metal atom clusters. The motion of the nuclei will need to be included for a

preprint2016arXiv

Superfluid behavior of quasi-1D p-H$_2$ inside carbon nanotube

We perform ab-initio Quantum Monte Carlo simulations of para-hydrogen (pH$_2$) at $T=0$ K confined in carbon nanotubes (CNT) of different radii. The radial density profiles show a strong layering of the pH$_2$ molecules which grow, with increasing number of molecules, in solid concentric cylindrical shells and eventually a central column. The central column can be considered an effective one-dimensional (1D) fluid whose properties are well captured by the Tomonaga-Luttinger liquid theory. The Luttinger parameter is explicitly computed and interestingly it shows a non-monotonic behavior with the linear density similar to what found for pure 1D $^3$He. Remarkably, for the central column in a (10,10) CNT, we found an ample linear density range in which the Luttinger liquid is (i) superfluid and (ii) stable against a weak disordered external potential, as the one expected inside realistic pores. This superfluid behavior could be experimentally revealed in bundles of carbon nanotubes, where deviations from classical inertial values associated with superfluid density could be measured via torsional oscillator techniques. In summary, our results suggest that pH$_2$ within carbon nanopores

preprint2015arXiv

Acoustic topological insulator and robust one-way sound transport

Discovery of novel topological orders of condensed matters is of a significant interest in both fundamental and applied physics due to the associated quantum conductance behaviors and unique symmetry-protected backscattering-immune propagation against defects, which inspired similar fantastic effects in classical waves system, leading to the revolution of the manipulation of wave propagation. To date, however, only few theoretical models were proposed to realize acoustic topological states. Here, we theoretically and experimentally demonstrate a two dimensional acoustic topological insulators with acoustic analogue of quantum spin Hall Effect. Due to the band inversion mechanism near the double Dirac cones, acoustic one-way pseudospin dependent propagating edge states, corresponding to spin-plus and spin-minus, can be observed at the interface between two graphene-like acoustic crystals. We have also experimentally verified the associated topological immunity of such one-way edge states against the different lattice defects and disorders, which can always lead to inherent propagation loss and noise. We show that this unique acoustic topological phenomenon can offer a new promising

preprint2016arXiv

2d Fu-Kane-Mele invariant as Wess-Zumino action of the sewing matrix

We show that the Fu-Kane-Mele invariant of the 2d time-reversal-invariant crystalline insulators is equal to the properly normalized Wess-Zumino action of the so-called sewing matrix field defined on the Brillouin torus. Applied to 3d, the result permits a direct proof of the known relation between the strong Fu-Kane-Mele invariant and the Chern-Simons action of the non-Abelian Berry connection on the bundle of valence states.

1027 works