Quantum Phonon Optics: Coherent and Squeezed Atomic Displacements

In this paper we investigate coherent and squeezed quantum states of phonons. The latter allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent states. The expectation values and quantum fluctuations of both the atomic displacement and the lattice amplitude operators are calculated in these states---in some cases analytically. We also study the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach.Comment: 6 pages, RevTe

Analysis of quantum conductance of carbon nanotube junctions by the effective mass approximation

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.Comment: RevTe

Band structures of periodic carbon nanotube junctions and their symmetries analyzed by the effective mass approximation

The band structures of the periodic nanotube junctions are investigated by the effective mass theory and the tight binding model. The periodic junctions are constructed by introducing pairs of a pentagonal defect and a heptagonal defect periodically in the carbon nanotube. We treat the periodic junctions whose unit cell is composed by two kinds of metallic nanotubes with almost same radii, the ratio of which is between 0.7 and 1 . The discussed energy region is near the undoped Fermi level where the channel number is kept to two, so there are two bands. The energy bands are expressed with closed analytical forms by the effective mass theory with some assumptions, and they coincide well with the numerical results by the tight binding model. Differences between the two methods are also discussed. Origin of correspondence between the band structures and the phason pattern discussed in Phys. Rev. B {\bf 53}, 2114, is clarified. The width of the gap and the band are in inverse proportion to the length of the unit cell, which is the sum of the lengths measured along the tube axis in each tube part and along 'radial' direction in the junction part. The degeneracy and repulsion between the two bands are determined only from symmetries.Comment: RevTeX, gif fil

Phonon Transmission Rate, Fluctuations, and Localization in Random Semiconductor Superlattices: Green's Function Approach

We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.Comment: 36 pages, Late

Topological Phases in Graphitic Cones

The electronic structure of graphitic cones exhibits distinctive topological features associated with the apical disclinations. Aharonov-Bohm magnetoconductance oscillations (period Phi_0) are completely absent in rings fabricated from cones with a single pentagonal disclination. Close to the apex, the local density of states changes qualitatively, either developing a cusp which drops to zero at the Fermi energy, or forming a region of nonzero density across the Fermi energy, a local metalization of graphene.Comment: 4 pages, RevTeX 4, 3 PostScript figure

Squeezed Phonon States: Modulating Quantum Fluctuations of Atomic Displacements

We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, and also investigate the possibility of generating squeezed phonon states using a three-phonon parametric amplification process based on phonon-phonon interactions. Furthermore, we also propose a detection scheme based on reflectivity measurements.Comment: 4 pages, RevTeX. The previous entry had a wrong page number in the Journal-ref fiel

Disorder-induced phonon self-energy of semiconductors with binary isotopic composition

Self-energy effects of Raman phonons in isotopically disordered semiconductors are deduced by perturbation theory and compared to experimental data. In contrast to the acoustic frequency region, higher-order terms contribute significantly to the self-energy at optical phonon frequencies. The asymmetric dependence of the self-energy of a binary isotope system $m_{1-x} M_x$ on the concentration of the heavier isotope mass x can be explained by taking into account second- and third-order perturbation terms. For elemental semiconductors, the maximum of the self-energy occurs at concentrations with $0.5<x<0.7$, depending on the strength of the third-order term. Reasonable approximations are imposed that allow us to derive explicit expressions for the ratio of successive perturbation terms of the real and the imaginary part of the self-energy. This basic theoretical approach is compatible with Raman spectroscopic results on diamond and silicon, with calculations based on the coherent potential approximation, and with theoretical results obtained using {\it ab initio} electronic theory. The extension of the formalism to binary compounds, by taking into account the eigenvectors at the individual sublattices, is straightforward. In this manner, we interpret recent experimental results on the disorder-induced broadening of the TO (folded) modes of SiC with a $^{13}{\rm C}$-enriched carbon sublattice. \cite{Rohmfeld00,Rohmfeld01}Comment: 29 pages, 9 figures, 2 tables, submitted to PR

Topological quantum D-branes and wild embeddings from exotic smooth R^4

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge when there are non-trivial NS-NS H-fluxes where the topological classes are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher dimensional $p$-complexes into S^n correspond to Dp-branes. These wild embeddings as constructed by using gropes are basic objects to understand exotic smoothness as well Casson handles. Next we build C*-algebras corresponding to the embeddings. Finally we consider topological quantum D-branes as those which emerge from wild embeddings in question. We construct an action for these quantum D-branes and show that the classical limit agrees with the Born-Infeld action such that flat branes = usual embeddings.Comment: 18 pages, 1 figur