Opposite Parity Research Articles

Voltage-induced defect mode coupling in a one-dimensional photonic crystal with a twisted-nematic defect layer

Defect modes are investigated in a band gap of an electrically tunable one-dimensional photonic crystal infiltrated with a twisted-nematic liquid crystal. Their frequency shift and interference under applied voltage are studied both experimentally and theoretically. We deal with the case where the defect layer thickness is much larger than the wavelength (i.e., the Mauguin condition). It is shown theoretically that the defect modes could have a complex structure with elliptic polarization. Two series of polarized modes are coupled with each other and exhibit an avoided crossing phenomenon in the case of opposite parity.

A MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND THE RAMANUJAN'S SUM

AbstractLet q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with 1 ≤ a ≤ q − 1, it is clear that there exists one and only one b with 0 ≤ b ≤ q − 1 such that ab ≡ c (mod q). Let N(c, q) denotes the number of all solutions of the congruence equation ab ≡ c (mod q) for 1 ≤ a, b ≤ q − 1 in which a and b are of opposite parity, where b is defined by the congruence equation bb ≡ 1(modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving (N(c, q) − φ(q)) and Ramanujan's sum, and give two exact computational formulae.

Bound states of dissipative solitons in fiber lasers with a lumped saturable absorber

The interaction of ultrashort pulses and their bound states in fiber lasers with a saturable absorber are analyzed by numerical simulation. It is shown that the distance between two interacting pulses in the lasing mode established after a transient process can take a set of quantized values in which neighboring pulse separations correspond to steady bound states of opposite parity. Characteristic changes in the established states with a change in the parameters of the laser system are demonstrated. The developed model of passive laser mode locking and the results presented in the paper can be used to describe and interpret the lasing modes of fiber lasers with nonlinear losses due to different nanomaterials (media with quanta wells, nanotubes, graphene, etc.).

On Lehmer’s problem and Dedekind sums

Let p be an odd prime and c a fixed integer with (c, p) = 1. For each integer a with 1 ≤ a ≤ p − 1, it is clear that there exists one and only one b with 0 ⩽ b ⩽ p − 1 such that ab ≡ c (mod p). Let N(c, p) denote the number of all solutions of the congruence equation ab ≡ c (mod p) for 1 ⩽ a, b ⩽ p−1 in which a and \(\overline b \) are of opposite parity, where \(\overline b \) is defined by the congruence equation b\(\overline b \) ≡ 1 (mod p). The main purpose of this paper is to use the properties of Dedekind sums and the mean value theorem for Dirichlet L-functions to study the hybrid mean value problem involving N(c, p)−½φ(p) and the Dedekind sums S(c, p), and to establish a sharp asymptotic formula for it.

Topological semimetal in a fermionic optical lattice

Optical lattices have an important role in advancing our understandingof correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard1,2 and hexagonal3 optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2π, in sharp contrast to the π flux of Dirac points as in graphene. We show that the appearance of this topological liquid is universal for all lattices with D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.

Quasiequilibrium directed hopping in a time-dependent two-well periodic potential

We consider the directed motion of a Brownian particle in a two-well periodic potential with time-varying barriers and wells described by arbitrary periodic functions of time, v(t) and u(t), alternating with the period τ. In the framework of the low-temperature kinetic approach, we obtain explicit formulas for the probabilities of finding the particle in potential wells, average velocity of directed motion, input energy P(in) and useful work P(out) against additionally introduced stationary load force f. These formulas are considerably simplified by the assumption of the quasiequilibrium regime of motion corresponding to small values of u(t) and f. It is shown that depending on the same or opposite parity of the functions v(t) and u(t) with respect to time reversal, the motion direction of a Brownian particle is retained or reversed under the reversal of the direction of movement along the (v-u) loop in the phase space of the functions v(t) and u(t), and the nondiagonal kinetic coefficients are mutually symmetric or antisymmetric. In the adiabatic limit τ→∞, the average velocity is proportional to τ(-1) in two cases: (i) the above loop has a nonzero area, (ii) the functions v(t) and u(t) are proportional to each other (zero loop area) and include intervals of fast changes with small durations τ(0) on the period τ of their variations. In both of these cases, the efficiency of energy conversion, η=P(out)/P(in), tends to unity at large variations of the barriers v(t). In the second case, the deviation of η from unity can be split into two contributions: The former decreases exponentially with increasing amplitude v(0) of v(t), while the latter is a small nonadiabatic correction proportional to v(0)(-3/2). It is the nonadiabatic correction that limits high efficiencies at large variations of barriers.

Band gap energy comparison of lead iodide excited by an Nd:YAG laser

Photon density versus charge (( I p versus Q ))/lux–ampere characteristics of PbI 2 single crystals have been studied by using fundamental and frequency-doubled Nd:YAG lasers. The results are compared with those of similar photoconductivity studies of ZnS and CdI 2 crystals. The studies show the involvement of the Franck–Condon principle-process-effect rather than opposite parity valence bands for the appearance of two different frequencies: one in the case of photoluminescence/photoacoustics and the other in the case of transmittance/photoconductivity.

Valley Blockade Quantum Switching in Silicon Nanostructures

In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a novel kind of hybrid quantum based classical logic device.

Experimental and theoretical study of bound and quasibound states ofCe−

The negative ion of cerium is investigated experimentally with tunable infrared laser photodetachment spectroscopy and theoretically with relativistic configuration interaction in the continuum formalism. The relative cross section for neutral atom production is measured with a crossed ion-beam--laser-beam apparatus over the photon energy range of 0.54--0.75 eV. A rich resonance spectrum is revealed near the threshold with, at least, 12 peaks observed due to transitions from bound states of ${\mathrm{Ce}}^{\ensuremath{-}}$ to either bound or quasibound excited states of the negative ion. Theoretical calculations of the photodetachment cross sections enable identification of the transitions responsible for the measured peaks. Two of the peaks are due to electric dipole-allowed bound-bound transitions in ${\mathrm{Ce}}^{\ensuremath{-}}$, making cerium only the second atomic negative ion that has been demonstrated to support multiple bound states of opposite parity. In addition, combining the experimental data with the theoretical analysis determines the electron affinity of cerium to be 0.628(10) eV and the fine structure splitting of the ground state of ${\mathrm{Ce}}^{\ensuremath{-}}$ (${}^{4}\phantom{\rule{-0.16em}{0ex}}{H}_{7/2}--{}^{4}\phantom{\rule{-0.16em}{0ex}}{H}_{9/2}$) to be 0.097 75(4) eV.

Interplay between real and pseudomagnetic field in graphene with strain

We investigate electric and magnetic properties of graphene with rotationally symmetric strain. The strain generates a large pseudomagnetic field with alternating sign in space, which forms a strongly confined quantum dot connected to six chiral channels. The orbital magnetism, degeneracy, and channel opening can be understood from the interplay between the real and pseudomagnetic fields which have different parities under time reversal and mirror reflection. While the orbital magnetic response of the confined state is diamagnetic, it can be paramagnetic if there is an accidental degeneracy with opposite mirror reflection parity.

MIXING OF FERMION FIELDS OF OPPOSITE PARITIES AND BARYON RESONANCES

We consider a loop mixing of two fermion fields of opposite parities whereas the parity is conserved in Lagrangian. Such kind of mixing is specific for fermions and has no analogy in boson case. Possible applications of this effect may be related with physics of baryon resonances. The obtained matrix propagator defines a pair of unitary partial amplitudes which describe the production of resonances of spin J and different parity 1/2± or 3/2±. The use of our amplitudes for joint description of πN partial waves P13 and D13 shows that the discussed effect is clearly seen in these partial waves as the specific form of interference between resonance and background. Another interesting application of this effect may be related with partial waves S11 and P11, where the picture is more complicated due to presence of several resonance states.

Nonreciprocal switching thresholds in coupled nonlinear microcavities

A concept for the design of nonlinear optical diodes is proposed that uses the multistability of coupled nonlinear microcavities and the dependence of switching thresholds on the direction of incidence. A typical example of such a diode can be created by combining two mirror-symmetric microcavities where modes of the opposite parity dominate. It is shown that a strong nonreciprocal behavior can be achieved together with a negligible insertion loss. To describe the dynamical properties of such systems, a model based on the coupled-mode theory is developed, and a possible implementation in the form of multilayered structures is considered.

Indirect interband transition in hexagonal GaN

In this paper, we report on optical investigations with Raman experiment to underline a new ultraviolet (UV) luminescence band in hexagonal gallium nitride (GaN) at 4.56 eV. GaN is a direct band gap semiconductor, the photoluminescence peak corresponding to the energy gap at 3.43 eV dominates the spectrum. Nevertheless, other electronic interband transitions can appear on the spectrum: the electronic indirect interband transitions. We attribute one of them to the observed new photoluminescence band at 4.56 eV. This interpretation is supported by photoluminescence spectra obtained on three different samples at room temperature and at −50 °C with UV excitation source: mbd-266 nm solid laser (4.66 eV) and by the study of three criteria: the partly opposite parities of initial and final wave function, the implication of acoustic phonons and temperature control.

Electric-field-induced nuclear-spin flips mediated by enhanced spin–orbit coupling

Molecular hydrogen exists in two forms, which differ in the relative orientation of their nuclear spins. Interconversion between the two isomeric forms is extremely rare, unless there is an interaction breaking the symmetry between the two nuclei. Magnetic surfaces are known to act as such a catalyst, but this study finds that electric fields can also induce the spin flips necessary for the interconversion. Molecules made of identical nuclei of non-zero spin exist in nuclear-spin modifications, and the interconversion of these spin isomers is often forbidden for isolated states1,2,3. The interconversion between the nuclear-spin modifications, however, is promoted by inhomogeneous magnetic fields, such as those present on the surfaces of magnetic materials4. Nuclear-spin conversion on diamagnetic and insulating solid substances, on the other hand, is generally considered improbable. Here we present the observation of nuclear-spin flips of H2 and D2 occurring on amorphous solid water surfaces with time constants of 370−140+340 s and 1,220−580+2,980 s, respectively. To explain these unexpected conversion processes, we propose a model of electric-field-induced nuclear-spin flips. In this model, giant and inhomogeneous electric fields present on the ice surface5 mix the electronic states of opposite parities by the Stark effect6, and significantly enhance the spin–orbit couplings between the electronic singlet–triplet spin states of the molecules. By virtue of these effects, the intramolecular hyperfine contact interaction induces the nuclear-spin conversion. This concept should have implications for controlling nuclear magnetization using external electric fields7.

Hyperfine interaction effects on the (1s2p)3P1–(1s2s)1S0 energy splitting in He-like ions for parity nonconservation studiesThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

Accurate theoretical knowledge of the (1s2p)3P1–(1s2s)1S0 splitting in He-like ions is demanded for future experimental studies of the nuclear spin-dependent part of the weak interaction. In this paper we perform a calculation of the hyperfine structure of (1s2p)3P1–(1s2s)1S0 within 3 ≤ Z ≤ 35, Z being the atomic number. In this Z range parity nonconservation (PNC) effects are amplified by the close energy proximity of the opposite parity levels (1s2p)3P1 and (1s2s)1S0. We find that the hyperfine structure is relevant for Z > 12, and produces splitting among the hyperfine sublevels as large as 150 meV for medium Z He-like ions (Z ∼ 35).

Opposite parity packing arrangement for stereoscopic video coding

A frame-compatible opposite parity packing arrangement with a spatial and inter-view correlation-based interpolation is proposed for stereoscopic video coding. Experimental results demonstrate that the proposed algorithm is able to efficiently improve compression efficiency of stereoscopic video coding.

Influence of Glass Matrix on Magneto-Optical Activity of <i>f-f</i> Transitions in Dy<sup>3+</sup> Ion

The absorption and magnetic circular dichroism spectra of f-f transitions 6H15/2 → 6F3/2, 6F5/2 , 6(F7/2 +H5/2) and 6(F9/2+H7/2) in Dy3+ ion were studied in the glasses: Dy2O3-P2O5-SiO2-GeO2 and Dy2O3-La2O3-Al2O3-B2O3-SiO2-GeO2 with different concentrations of Dy3+ ions in temperature range 100-300 K. Basing on this data, absolute values and temperature dependences of the paramagnetic magneto-optical activity (MOA) of the transitions were determined. The origin of the MOA of f-f transitions was analyzed with the help of two models. In the first model, MOA is considered as a consequence of admixture of states with opposite parity by odd components of crystal field. The second approach is based on the Judd-Ofelt theory. The same f-f transitions reveal different values and temperature dependences in different glasses, what testifies to a different symmetry of the nearest environment of Dy3+ ions in these glasses.

Mechanisms of fluorescence enhancement in rare earth sol–gel glass containing Al3+

Abstract Analysis of glasses containing Eu and Tb dopants yields new insights about the role of Al 3+ co-doping in improving fluorescence yield of glasses containing rare earth (RE) dopants. Our work suggests that Al co-doping enhances fluorescence by two important mechanisms. (1) At low Al:RE ratio the site symmetry is lowered, allowing more admixture of opposite parity wavefunctions and increased transition probability. (2) At high Al:RE ratio, the highest frequency phonons are of lower energy; so nonradiative decay rates are reduced. In addition, a new technique – post-annealing immersion – is introduced, which allows the study of RE location in the sol–gel matrix. Al co-doping is observed to increase the tendency for RE ions to reside on pore surfaces.

Even-odd effects of Heisenberg chains on long-range interaction and entanglement

A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for qubits attached to an even chain, and (iii) the ability of chains of either parity to mediate qubit entanglement that is undiminished by distance.

Tunneling and inversion symmetry in single-molecule magnets: The case of theMn12wheel molecule

We present a detailed study of the influence of various interactions on the spin quantum tunneling in a Mn12 wheel molecule. The effects of single-ion and exchange (spin-orbit) anisotropy are first considered, followed by an analysis of the roles played by secondary influences, e.g. disorder, dipolar and hyperfine fields, and magnetoacoustic interactions. Special attention is paid to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is done within the framework of a 12-spin microscopic model, and also using simplified dimer and tetramer approximations in which the electronic spins are grouped in 2 or 4 blocks, respectively. If the molecule is inversion symmetric, the DM interaction between the dimer halves must be zero. In an inversion symmetric tetramer, two independent DM vectors are allowed, but no new tunneling transitions are generated by the DM interaction. Experiments on the Mn12 wheel can only be explained if the molecular inversion symmetry is broken, and we explore this in detail using both models, focussing on the asymmetric disposition and rounding of Berry phase minima associated with quantum interference between states of opposite parity. A remarkable behavior exists for the `Berry phase zeroes' as a function of the directions of the internal DM vectors and the external transverse field. A rather drastic breaking of the molecular inversion-symmetry is required to explain the experiments; in the tetramer model this requires a reorientation of the DM vectors on one half of the molecule by nearly 180 degrees. This cannot be attributed to sample disorder. These results are of general interest for the quantum dynamics of tunneling spins, and lead to some interesting experimental predictions.