Showing papers on "Quantization (physics) published in 2015"

Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field.

Abstract: Surface plasmon polaritons can confine electromagnetic fields in subwavelength spaces and are of interest for photonics, optical data storage devices and biosensing applications. In analogy to photons, they exhibit wave-particle duality, whose different aspects have recently been observed in separate tailored experiments. Here we demonstrate the ability of ultrafast transmission electron microscopy to simultaneously image both the spatial interference and the quantization of such confined plasmonic fields. Our experiments are accomplished by spatiotemporally overlapping electron and light pulses on a single nanowire suspended on a graphene film. The resulting energy exchange between single electrons and the quanta of the photoinduced near-field is imaged synchronously with its spatial interference pattern. This methodology enables the control and visualization of plasmonic fields at the nanoscale, providing a promising tool for understanding the fundamental properties of confined electromagnetic fields and the development of advanced photonic circuits.

Precise Quantization of the Anomalous Hall Effect near Zero Magnetic Field.

Abstract: Thin films of magnetic topological insulators can exhibit a nearly ideal quantum Hall effect without requiring an applied magnetic field.

Pilot-Wave Hydrodynamics

Abstract: Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantumlike behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie’s original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

Abstract: This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator

Abstract: When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Crx(Bi,Sb)(2-x)Te3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer-Buttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization.

Landau level quantization and almost flat modes in three-dimensional semimetals with nodal ring spectra

Abstract: We investigate Landau level structures of semimetals with nodal ring dispersions. When the magnetic field is applied parallel to the plane in which the ring lies, there exist almost nondispersive Landau levels at the Fermi level (${E}_{F}=0$) as a function of the momentum along the field direction inside the ring. We show that the Landau levels at each momentum along the field direction can be described by the Hamiltonian for the graphene bilayer with fictitious interlayer couplings under a tilted magnetic field. Near the center of the ring where the in-terlayer coupling is negligible, we have Dirac Landau levels which explain the appearance of the zero modes. Although the interlayer hopping amplitudes become finite at higher momenta, the splitting of zero modes is exponentially small and they remain almost flat due to the finite artificial in-plane component of the magnetic field. The emergence of the density of states peak at the Fermi level would be a hallmark of the ring dispersion.

New Exact Quantization Condition for Toric Calabi-Yau Geometries

Abstract: We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau threefolds. Our proposal includes all contributions to the energy spectrum which are nonperturbative in the Planck constant, and is much simpler than the available quantization condition in the literature. We check that our proposal is consistent with previous works and implies nontrivial relations among the topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries. Together with the recent developments, our proposal opens a new avenue in the long investigations at the interface of geometry, topology and quantum mechanics.

Superradiant Quantum Heat Engine

Abstract: Quantum physics revolutionized classical disciplines of mechanics, statistical physics, and electrodynamics. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to quantum regimes. Development of quantum heat engines (QHEs) requires emerging field of quantum thermodynamics. Studies of QHEs debate whether quantum coherence can be used as a resource. We explore an alternative where it can function as an effective catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work output becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up QHE, our result is a fundamental difference of a quantum fuel from its classical counterpart.

Quantization of Hall Conductance for Interacting Electrons on a Torus

Abstract: We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e^2/h, up to exponentially small corrections in the linear size L. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.

Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics

Abstract: We measure the quantum speed of the state evolution of the field in a weakly driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment-assisted speed-up is realized: the quantum speed of the state repopulation in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the number of atoms).

Advances in algebraic quantum field theory

Abstract: Structural aspects of quantum field theory.- Introduction to Algebraic Quantum Field Theory.- Algebraic Quantum Field Theory on curved backgrounds.- QED and infrared sectors.- Applicative aspects of algebraic quantum field theory.- Hadamard States and Microlocal Analysis.- Applications of algebraic quantum field theory to cosmology.- Conformal Field Theory and its applications.- Supersymmetric algebraic quantum field theory.- Interacting field theories.- Perturbative Algebraic Quantum Field Theory.- Integrable models and construction of interacting quantum field theories.- Kitaev's Toric Code model.- Algebraic quantum field theory on non commutative spacetimes.

Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state

Abstract: Topological insulators doped with transition metals have recently been found to host a strong ferromagnetic state with perpendicular to plane anisotropy as well as support a quantum Hall state with edge channel transport, even in the absence of an external magnetic field. It remains unclear, however, why a robust magnetic state should emerge in materials of relatively low crystalline quality and dilute magnetic doping. Indeed, recent experiments suggest that the ferromagnetism exhibits at least some superparamagnetic character. We report on transport measurements in a sample that shows perfect quantum anomalous Hall quantization, while at the same time exhibits traits in its transport data which suggest inhomogeneities. We speculate that this may be evidence that the percolation path interpretation used to explain the transport during the magnetic reversal may actually have relevance over the entire field range.

One world, one beable

Abstract: Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits

Covariance in models of loop quantum gravity: Spherical symmetry

Abstract: Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

A new vacuum for loop quantum gravity

Abstract: We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy–flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013 arXiv:1311.7565). This supports the proposal for a construction of the physical vacuum made in Dittrich and Steinhaus (2013 arXiv:1311.7565) and Dittrich (2012 New J. Phys. 14 123004), and for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity.

Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in the p state: A tool for exploring chirality-sensitive processes

Abstract: $S$-matrix theory of high-order harmonic generation (HHG) is generalized to multielectron atoms. In the multielectron case the harmonic power is expressed via a coherent sum of the time-dependent dipoles, while for the one-electron models a corresponding incoherent sum appears. This difference is important for the inert atomic gases having a $p$ ground state as used in a recent HHG experiment with a bicircular field [Nat. Photonics 9, 99 (2015)]. We investigate HHG by such a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$. Selection rules for HHG by a bicircular field are analyzed from the aspects of dynamical symmetry of the system, conservation of the projection of the angular momentum on a fixed quantization axis, and the quantum number of the initial and final atomic ground states. A distinction is made between the selection rules for atoms with closed [J. Phys. B 48, 171001 (2015)] and nonclosed shells. An asymmetry in emission of the left- and right-circularly polarized harmonics is found and explained by using a semiclassical model and the electron probability currents which are related to a nonzero magnetic quantum number. This asymmetry can be important for the application of such harmonics to the exploration of chirality-sensitive processes and for generation of elliptic or even circular attosecond pulse trains. Such attosecond pulse trains are analyzed for longer wavelengths than in Opt. Lett. 40, 2381 (2015), and for various field-component intensities.

Observation of isolated monopoles in a quantum field

Abstract: Topological defects play important roles throughout nature, appearing in contexts as diverse as cosmology, particle physics, superfluidity, liquid crystals, and metallurgy Point defects can arise naturally as magnetic monopoles resulting from symmetry breaking in grand unified theories We devised an experiment to create and detect quantum mechanical analogs of such monopoles in a spin-1 Bose-Einstein condensate The defects, which were stable on the time scale of our experiments, were identified from spin-resolved images of the condensate density profile that exhibit a characteristic dependence on the choice of quantization axis Our observations lay the foundation for experimental studies of the dynamics and stability of topological point defects in quantum systems

Quanta of geometry: noncommutative aspects.

Abstract: In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

Validation of a quantized-current source with 0.2 ppm uncertainty

Abstract: We report on high-accuracy measurements of quantized current, sourced by a tunable-barrier single-electron pump at frequencies f up to 1 GHz. The measurements were performed with an ultrastable picoammeter instrument, traceable to the Josephson and quantum Hall effects. Current quantization according to I = ef with e being the elementary charge was confirmed at f = 545 MHz with a total relative uncertainty of 0.2 ppm, improving the state of the art by about a factor of 5. The accuracy of a possible future quantum current standard based on single-electron transport was experimentally validated to be better than the best (indirect) realization of the ampere within the present SI.

Observation of unconventional splitting of Landau levels in strained graphene

Abstract: In strained graphene, lattice deformation can create pseudomagnetic fields affecting the behavior of massless Dirac fermions and result in zero-field Landau level-like quantization. In the presence of an external magnetic field, valley-polarized Landau levels are predicted to be observed because the strain-induced pseudomagnetic fields are of opposite directions in the $K$ and ${K}^{\ensuremath{'}}$ valleys of graphene. However, an experimental verification of such a unique valley-polarized Landau quantization has not been reported so far. Here, we present experimental spectroscopic measurements in strained graphene on Rh foil by scanning tunneling microscopy. We directly observed the splitting of the Landau level in the quantum Hall regime and we interpreted the experimental result as the valley-polarized Landau level induced by the coexistence of the pseudomagnetic fields and external magnetic fields. The observed result paves the way to exploit novel electronic properties in graphene through the combination of the spatially varying strain (or the pseudomagnetic fields) and the external magnetic fields.

Quantum Memristors

Abstract: Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems

Validation of a quantized-current source with 0.2 ppm uncertainty

Abstract: We report on high-accuracy measurements of quantized current, sourced by a tunable-barrier single-electron pump at frequencies $f$ up to $1$ GHz. The measurements were performed with a new picoammeter instrument, traceable to the Josephson and quantum Hall effects. Current quantization according to $I=ef$ with $e$ the elementary charge was confirmed at $f=545$ MHz with a total relative uncertainty of 0.2 ppm, improving the state of the art by about a factor of 5. For the first time, the accuracy of a possible future quantum current standard based on single-electron transport was experimentally validated to be better than the best realization of the ampere within the present SI.

Operators from mirror curves and the quantum dilogarithm

Abstract: Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local P2, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.

Basis Light-Front Quantization Approach to Positronium

Abstract: We present the first application of the recently developed basis light-front quantization (BLFQ) method to self-bound systems in quantum field theory, using the positronium system as a test case. Within the BLFQ framework, we develop a two-body effective interaction, operating only in the lowest Fock sector, that implements photon exchange, neglecting fermion self-energy effects. We then solve for the mass spectrum of this interaction at the unphysical coupling $\ensuremath{\alpha}=0.3$. The resulting spectrum is in good agreement with the expected Bohr spectrum of nonrelativistic quantum mechanics. We examine in detail the dependence of the results on the regulators of the theory.

Quantum mechanics of a spin-orbit coupled electron constrained to a space curve

Abstract: We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow quantum degrees of freedom This procedure is capable of yielding a correct Hermitian one-dimensional Schrodinger-Pauli operator We find that the torsion of the space curve generates an additional quantum geometric potential, adding to the well-known curvature-induced one Finally, we derive an analytic form of the one-dimensional Hamiltonian for spin-orbit coupled electrons in a nanoscale helical wire

How unimodular gravity theories differ from general relativity at quantum level

Abstract: We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the metric, while still being equivalent to other unimodular gravity theories at the classical level. The path integral has the same form as in general relativity (GR), except that the cosmological constant is an unspecified value of a variable, and it thus is unrelated to any coupling constant. When the state of the universe is a superposition of vacuum states, the path integral is extended to include an integral over the cosmological constant. Second, we analyze the standard unimodular theory of gravity, where the metric determinant is fixed by a constraint. Its path integral differs from the one of GR in two ways: the metric of spacetime satisfies the unimodular condition only in average over space, and both the Hamiltonian constraint and the associated gauge condition have zero average over space. Finally, the canonical relation between the given unimodular theories of gravity is established.

The Quantum Vacuum

Abstract: The vacuum is the lowest energy state of a field in a certain region of space. This definition implies that no particles can be present in the vacuum state. In classical physics, the only features of vacuum are those of its geometry. For example, in the general theory of relativity the geometry is a dynamical structure that guides the motion of matter, and, in turn, it is bent and curved by the presence of matter. Other than this, the classical vacuum is a structure void of any physical properties, since classically properties are strictly associated with physical objects such as particles and finite-amplitude fields. The situation is very different in quantum physics. As I will show in this paper, the difference stems from the fact that in quantum physics the properties are not strictly tied to objects. We know for example that physical properties come into existence - as values of observables - only when the object is measured. Thus, quantum physics allows us to detach properties from objects. This has consequences: one does not need pre-existing real objects to create actual properties, and indeed under certain perturbations the quantum vacuum produces observable effects such as energy shifts and creation of particles. An open question is if by necessity the vacuum comes with an embedded geometry, and if it is possible to construct viable physical theories in which geometry is detached from the vacuum.

Spherically symmetric canonical quantum gravity

Abstract: Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor-ordering choices ensuring in an anomaly free quantum constraint algebra. Comparison with previous work [Nucl. Phys. B399, 211 (1993)] reveals that the resulting physical Hilbert space has the same form, although the basic canonical variables are different in the two approaches. As an extension, holonomy modifications from loop quantum gravity are shown to deform the Dirac space-time algebra, while going beyond ``effective'' calculations.