Momentum Quantum Research Articles

Landau Levels in Strained Optical Lattices.

We propose a hexagonal optical lattice system with spatial variations in the hopping matrix elements. Just like in the valley Hall effect in strained graphene, for atoms near the Dirac points the variations in the hopping matrix elements can be described by a pseudomagnetic field and result in the formation of Landau levels. We show that the pseudomagnetic field leads to measurable experimental signatures in momentum resolved Bragg spectroscopy, Bloch oscillations, cyclotron motion, and quantization of insitu densities. Our proposal can be realized by a slight modification of existing experiments. In contrast to previous methods, pseudomagnetic fields are realized in a completely static system avoiding common heating effects and therefore opening the door to studying interaction effects in Landau levels with cold atoms.

Chiral properties of topological-state loops

The angular momentum quantization of chiral gapless modes confined to a circularly shaped interface between two different topological phases is investigated. By examining several different setups, we show analytically that the angular momentum of the topological modes exhibits a highly chiral behavior, and can be coupled to spin and/or valley degrees of freedom, reflecting the nature of the interface states. A simple general one-dimensional model, valid for arbitrarily shaped loops, is shown to predict the corresponding energies and the magnetic moments. These loops can be viewed as building blocks for artificial magnets with tunable and highly diverse properties.

Bekenstein–Hawking Entropy by energy quantization from Schwarzschild-de Sitter black hole

The energy of a test particle orbiting a Schwarzschild-de Sitter (SdS) black hole is quantized with the help of the quantization of angular momentum. We have investigated the change of entropy between two nearby states using energy quantization. We have shown that the change of entropy as well as purely thermal emission rate is dependent of quantum number and approach to zero for large quantum number.

Average Transverse Momentum Quantities Approaching the Lightfront

In this contribution to Light Cone 2014, three average transverse momentum quantities are discussed: the Sivers shift, the dijet imbalance, and the $p_T$ broadening. The definitions of these quantities involve integrals over all transverse momenta that are overly sensitive to the region of large transverse momenta, which conveys little information about the transverse momentum distributions of quarks and gluons inside hadrons. TMD factorization naturally suggests alternative definitions of such integrated quantities, using Bessel-weighting and rapidity cut-offs, with the conventional definitions as limiting cases. The regularized quantities are given in terms of integrals over the TMDs of interest that are well-defined and moreover have the advantage of being amenable to lattice evaluations.

Investigating students’ mental models about the quantization of light, energy, and angular momentum

This paper is the first part of a multiphase study examining students’ mental models about the quantization of physical observables—light, energy, and angular momentum. Thirty-one second-year physics and physics education college students who were taking a modern physics course participated in the study. The qualitative analysis of data revealed six variations in students’ mental models about the quantization of physical observables: scientific model, primitive scientific model, shredding model, alternating model, integrative model, and evolution model. These models were determined to be context dependent. In addition, some students are in a mixed-model state where they use multiple mental models in explaining a phenomenon and use these models inconsistently.3 MoreReceived 8 January 2014DOI:https://doi.org/10.1103/PhysRevSTPER.10.020127This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

Chaos driven by interfering memory.

The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots the dynamics of a particle. Such a system can be implemented by a bouncing drop generating surface waves sustained by a parametric forcing. The motion of the resulting "walker" when confined in a harmonic potential well is generally disordered. Here we show that these trajectories correspond to chaotic regimes characterized by intermittent transitions between a discrete set of states. At any given time, the system is in one of these states characterized by a double quantization of size and angular momentum. A low dimensional intermittency determines their respective probabilities. They thus form an eigenstate basis of decomposition for what would be observed as a superposition of states if all measurements were intrusive.

Josephson coupling through one-dimensional ballistic channel in semiconductor-superconductor hybrid quantum point contacts

We study a superconducting quantum point contact made of a narrow In$_{0.75}% $Ga$_{0.25}$As channel with Nb proximity electrodes. The narrow channel is formed in a gate-fitted constriction of InGaAs/InAlAs/InP heterostructure hosting a two-dimensional electron gas. When the channel opening is varied with the gate, the Josephson critical current exhibits a discretized variation that arises from the quantization of the transverse momentum in the channel. The quantization of Josephson critical current persists down to the single-channel regime, providing an unambiguous demonstration of a semiconductor--superconductor hybrid Josephson junction involving only a single ballistic channel.

Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons

We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field-theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.

Polyhedral symmetry and quantum mechanics

A thorough study of regular and quasi-regular polyhedra shows that the symmetries of these polyhedra identically describe the quantization of orbital angular momentum, of spin, and of total angular momentum, a fact which permits one to assign quantum states at the vertices of these polyhedra assumed as the average particle positions. Furthermore, if the particles are fermions, their wave function is anti-symmetric and its maxima are identically the same as those of repulsive particles, e.g., on a sphere like the spherical shape of closed shells, which implies equilibrium of these particles having average positions at the aforementioned maxima. Such equilibria on a sphere are solely satisfied at the vertices of regular and quasi-regular polyhedra which can be associated with the most probable forms of shells both in Nuclear Physics and in Atomic Cluster Physics when the constituent atoms possess half integer spins. If the average sizes of the constituent particles are known, then the average sizes of the resulting shells become known as well. This association of Symmetry with Quantum Mechanics leads to many applications and excellent results.

High-energy cosmic rays and tests of basic principles of Physics

With the present understanding of data, the observed flux suppression for ultra-high energy cosmic rays (UHECR) at energies above 4.10E19 eV can be a signature of the Greisen-Zatsepin-Kuzmin (GZK) cutoff or be related to a similar mechanism. But it may also correspond, for instance, to the maximum energies available at the relevant sources. In both cases, violations of special relativity modifying cosmic-ray propagation or acceleration at very high energy can potentially play a role. Other violations of fundamental principles of standard particle physics (quantum mechanics, energy and momentum conservation, homogeneity and static properties, effective space dimensions, quark confinement...) can also be relevant at these energies. In particular, UHECR data would in principle allow to set bounds on Lorentz symmetry violation (LSV) in patterns incorporating a privileged local reference frame (the vacuum rest frame, VRF). But the precise analysis is far from trivial, and other effects can also be present. The effective parameters can be related to Planck-scale physics, or even to physics beyond Planck scale, as well as to the dynamics and effective symmetries of LSV for nucleons, quarks, leptons and the photon. LSV can also be at the origin of GZK-like effects. In the presence of a VRF, and contrary to a grand unification view, LSV and other violations of standard principles can modify the internal structure of particles at very high energy and conventional symmetries may cease to be valid at energies close to the Planck scale. We present an updated discussion of these topics, including experimental prospects, new potentialities for high-energy cosmic ray phenomenology and the possible link with unconventional pre-Big Bang scenarios, superbradyon (superluminal preon) patterns... The subject of a possible superluminal propagation of neutrinos at accelerator energies is also dealt with. (Contribution to the International Conference on New Frontiers in Physics, ICFP 2012, Kolymbari, Crete, June 10-16 2012)

Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots

We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum component exist, while non-integrable geometries lack confinement. We support these arguments with a calculation of the two-terminal conductance of a gate-defined graphene quantum dot, which shows resonances for a disc-shaped geometry and for a stadium-shaped geometry without flux tube, but no resonances for a stadium-shaped quantum dot with a $\pi$-flux tube.

Staggered Spin-Orbit Order: A New Paradigm of Broken Symmetry Phase of Matter

We propose a novel spin-orbit density wave order, which can arise in a variety of materials classes. In systems where the noninteracting wavefunctions are defined by an exotic quantum number such as total angular momentum, pseudospin, or helical quantum number owing to spin-orbit coupling of various natures, interaction can induce an emergent spin-orbit density wave even when time-reversal symmetry is intact. This density wave order is different from standard time-reversal breaking spin or orbital density wave. We apply this idea to explain the enigmatic “hidden order” phase in heavy fermion URu2Si2 as well as an unknown gapped quasiparticle state observed in two-dimensional electron gases, such as the surface state of BiAg2.

Efficient First-Principles Calculation of the Quantum Kinetic Energy and Momentum Distribution of Nuclei

Light nuclei at room temperature and below exhibit a kinetic energy which significantly deviates from the predictions of classical statistical mechanics. This quantum kinetic energy is responsible for a wide variety of isotope effects of interest in fields ranging from chemistry to climatology. It also furnishes the second moment of the nuclear momentum distribution, which contains subtle information about the chemical environment and has recently become accessible to deep inelastic neutron scattering experiments. Here, we show how, by combining imaginary time path integral dynamics with a carefully designed generalized Langevin equation, it is possible to dramatically reduce the expense of computing the quantum kinetic energy. We also introduce a transient anisotropic Gaussian approximation to the nuclear momentum distribution which can be calculated with negligible additional effort. As an example, we evaluate the structural properties, the quantum kinetic energy, and the nuclear momentum distribution for a first-principles simulation of liquid water.

SPATIAL PROPAGATION OF QUANTUM LIGHT IN NONLINEAR WAVEGUIDING DEVICES: THEORY AND APPLICATIONS

We present the main theoretical results on spatial propagation of quantum light in nonlinear waveguiding devices together with a few applications. We show that the quantization of the classical momentum provides a consistent quantum mechanical formulation of both the linear and the nonlinear quantum light propagation in waveguiding devices. The momentum operator allows us to derive the correct spatial Heisenberg's equations for the forward and backward absorption and emission operators and consequently to analyze the spatial propagation in the multimode optical-field strength space. For that purpose we use the Feynman's path integral method in order to derive the quantum spatial optical propagators of different nonlinear waveguiding devices and accordingly to calculate the spatial propagation of the optical-field strength probability amplitude of quantum states in these nonlinear devices. Likewise, we present a preliminary and heuristic formulation of quantum dissipation in order to take into account the losses under spatial quantum propagation in lossy nonlinear waveguiding devices. It must be stressed that these optical-field strength probabilities have the advantage of being measured by homodyne techniques and therefore their theoretical analysis is of a remarkable interest in the optical characterization of quantum states obtained under linear and nonlinear propagation in waveguiding devices.

Scattering by an oscillating barrier: Quantum, classical, and semiclassical comparison

We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the scattered particle, while also providing the foundation for semiclassical theory. We use the semiclassical approach to selectively add quantum-mechanical effects such as interference and diffraction. We find good agreement between the quantum and semiclassical momentum distributions. Our methods and results can be used to understand quantum and classical aspects of transport mechanisms involving time-varying potentials, such as quantum pumping.

Quantization of area for event and Cauchy horizons of the Kerr-Newman black hole

Based on various string theoretic constructions, and various string-inspired generalizations thereof, there have been repeated suggestions that the areas of black hole event horizons might be quantized in a quite specific manner, in terms of linear combinations of square roots of positive integers. It is important to realise that there are significant physical constraints on such integer-based proposals when one (somewhat speculatively) attempts to extend them outside their original extremal and supersymmetric framework. Specifically, in their most natural and direct physical interpretations, some of the more speculative integer-based proposals for the quantization of horizon areas fail for the ordinary Kerr-Newman black holes in (3+1) dimensions, essentially because the fine structure constant is not an integer. A more baroque interpretation involves asserting the fine structure constant is the square root of a rational number; but such a proposal has its own problems. Insofar as one takes (3+1) general relativity (plus the usual quantization of angular momentum and electric charge) as being paramount, the known explicitly calculable spectra of horizon areas for the physically compelling Kerr-Newman spacetimes indicate that some caution is called for when assessing the universality of some of the more speculative integer-based string-inspired proposals.

Classical vortex beams show their discrete side

Researchers twist sound, testing a fundamental law of the quantization of orbital angular momentum.

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum—classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than ħ is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

We study the quantum Hamilton–Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials, and show that the QHJ formalism reproduces the exact eigenvalues and the eigenfunctions. The fact that the eigenfunctions have zeros and poles in complex locations leads to an unconventional singularity structure of the quantum momentum function p(x), the logarithmic derivative of the wavefunction, which forms the crux of the QHJ approach to quantization. A comparison of the singularity structure for these systems with the known exactly solvable and quasi-exactly solvable models reveals interesting differences. We find that the singularity structure of the momentum function for these new potentials lies between the above two distinct models, sharing similarities with both of them. This prompted us to examine the exactness of the supersymmetric Wentzel–Kramers–Brillouin (SWKB) quantization condition. The interesting singularity structure of p(x) and of the superpotential for these models has important consequences for the SWKB rule and in our proof of its exactness for these quantal systems.

On the s-parameterized Quantization Scheme for Dirac’s Representation theory

Dirac is the founder of quantum mechanical representation theory. By virtue of the technique of integration within an ordered product (IWOP) of operators we introduce s-parameterized form of quantum mechanical coordinate and momentum representations, which are complete. We then point out that s-parameterized representation’s completeness relation is accompanied with operators’ s-ordering, the special cases s=1,0,−1 correspond to normal-ordering, Weyl ordering and antinormal-ordering, respectively. The s-parameterized form of the coherent state representation and the entangled state representation are also derived. In our view, the operators’ s-ordering should be traced back to s-parameterized form of the completeness relation of quantum mechanical coordinate and momentum representations, which is more fundamental. Many operator identities can be derived by virtue of the above mentioned s-parameterized representation’s completeness relations.