Bloch oscillations of a soliton in a molecular chain

This paper presents the results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain subject to a constant electric field. By using as an example a homogeneous polynucleotide chain, it is shown that the system under consideration can exhibit complicated dynamical behaviour: when subject to field intensities less than a certain critical value, a soliton exhibits oscillations as a whole, while at field intensities exceeding this threshold, the soliton becomes a breather that oscillates. It is shown that the motion of a charge in a deformable chain is infinite, which in contrast to that in a rigid chain.     

Hole mobility in a homogeneous nucleotide chain

The conductivity of molecular DNA-based conductors has been calculated. Charge motion is described by quantum-mechanical equations, and macromolecular vibrations are described by classical equations of motion with dissipation and a source of temperature fluctuations. In a homogeneous sequence of G-C nucleotide pairs, the calculated hole mobility at T=300 K equals ≈2cm² V^?1 s^?1.     

Neutrino oscillations in a homogeneous moving medium

The quasi-classical equation that describes both neutrino flavor oscillations and spin rotation in dense matter is obtained in the framework of quantum field theory. The solution of this equation for homogeneous medium is found. The probabilities of the spin-flavor transitions in unpolarized moving matter are calculated in the two-flavor model. We show that if the medium is at rest the neutrino helicity is conserved and the flavor transition probabilities are equal to those obtained using the phenomenological approach.     

Optical Bloch oscillations in waveguide arrays

We show that optical Bloch oscillations can emerge in waveguide arrays with linearly varying propagation constants. The existence of localized modes (Wannier-Stark states) with equidistant wave-number spacing (Wannier-Stark ladder) that do not undergo diffraction is analytically proved. The evolution of arbitrary initial excitations is described, and potential applications are suggested.     

Topological optical Bloch oscillations in a deformed slab waveguide

Spatial Bloch oscillations of light waves of purely topological origin are theoretically shown to exist in weakly deformed slab waveguides. As the optical rays trapped in the deformed waveguide can roll freely, wave diffraction is strongly affected by the topology of the deformed surface, which can be tailored to simulate the effect of a tilted periodic refractive index.     

Bloch oscillations in optical dissipative lattices

We show that Bloch oscillations are possible in dissipative optical waveguide lattices with a linearly varying propagation constant. These oscillations occur in spite of the fact that the Bloch wave packet experiences coupling gain and (or) loss. Experimentally, this process can be observed in different settings, such as in laser arrays and lattices of semiconductor optical amplifiers. In addition, we demonstrate that these systems can suppress instabilities arising from preferential mode noise growth.     

Observation of anharmonic Bloch oscillations

We report on the experimental observation of Bloch oscillations of an optical wave packet in a lattice with second-order coupling. To this end, we employ zigzag waveguide arrays, in which the second-order coupling can be precisely tuned.     

Bloch oscillations of path-entangled photons

We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.     

Bloch oscillations of an acoustic field in a layered structure

This study is devoted to experimentally achieving the phenomenon of periodic modulation of the acoustic-wave intensity, which is observed upon passage of an acoustic signal through a quasi-periodic structure and is the acoustic analog of the effect of Bloch oscillations (BO). Ultrasound at a frequency of 1 MHz is used, and a layered structure that consists of alternate plane-parallel glass and water layers serves as a super-lattice. In order to create an analog of the external electric field, the thickness of the water layers was changed inversely with respect to their ordinals. It is shown that the transmission spectrum of such a structure has the form of narrow equidistant peaks (an analog of the Wannier-Stark ladder), and the envelope of a transmitted signal undergoes periodic oscillations (analogous to BO). The experimental results are in good agreement with theoretical calculations performed by the transfer-matrix method.     

Effective hamiltonian of Bloch electrons in a homogeneous electrical field

In order to construct a band mechanics of Bloch electrons in a homogeneous electrical field E with the interband interaction taken into account, a method of determining the exact single-band Hamiltonian $$H_q = \varepsilon _q^F (\kappa ) + Fi\frac{\partial }{{\partial \kappa }}$$ is proposed, where ε _q ^F (κ) is the renormalized (effective) electron dispersion law for R = 0 and the q-th Bloch band,F= ¦e¦·E. The function ε _q ^F (κ) is expressed in terms of the interband element coordinates as well as in terms of periodic solutions of the system of ordinary differential equations which degenerateinto a common Riccati equation in a two-band approximation. A solution of the system and the form of ε _q ^F (κ), in agreement with the Wanhier result, is found in the quasiclassical approximation.     

Magnetic Bloch oscillations in nanowire superlattice rings

The recent growth of semiconductor nanowire superlattices encourages hope that Bloch-like oscillations in such structures formed into rings may soon be observed in the presence of a time-dependent magnetic flux threading the ring. These magnetic Bloch oscillations are a consequence of Faraday's law; the time-dependent flux produces an electromotive force around the ring, thus leading to the Bloch-like oscillations. In the spectroscopic domain, generalized Wannier-Stark states are found that are manifestations of the emf-induced localization of the states.     

Super Bloch oscillations in the Peyrard-Bishop-Holstein model

Recently, polarons in the Peyrard-Bishop-Holstein model under DC electric fields were established to perform Bloch oscillations, provided the charge-lattice coupling is not large. In this work, we study this model when the charge is subjected to an applied field with both DC and AC components. Similarly to what happens in the rigid lattice, we find that the carrier undergoes a directed motion or coherent oscillations when the AC field is resonant or detuned with respect to the Bloch frequency, respectively. The electric density current and its Fourier spectrum are also studied to reveal the frequencies involved in the polaron dynamics.     

Photonic Bloch oscillations of correlated particles

A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.     

Rabi oscillations between dissipative Bloch bands

Within a two-band tight-binding model driven by DC–AC electric fields, we investigate the dynamics of electrons with Markoffian dephasing. We find that Rabi oscillations between the Bloch bands under the resonant condition may be destroyed by scattering from lattice imperfections. Through a perturbative calculation, we also obtain the effective decay time for the approach to equal Bloch band populations under conditions of small interband coupling and in the long-time limit. The decay rate shows characteristic sharp peaks at values of the parameters that give a signature of Rabi oscillations, and quasienergy spectra display avoided crossings at the same time.     

Bloch oscillations for circularly polarized light

All previous investigations on the Bloch oscillations of waves focus on scalar waves. Here we demonstrate, for the first time, the existence of Bloch oscillations of vector fields for circularly polarized light (CPL) propagating through a designed liquid crystal structure. To obtain the Wannier-Stark ladder of the CPL, we have designed a cholesteric liquid crystal structure with spatially varying pitch. The Bloch oscillations of the CPL have been observed in such a structure by exact numerical simulations. We have also shown that such a phenomenon can be easily detected in time-resolved reflection experiments.     

Bloch oscillations of quasispin polaritons in a magneto-optically controlled atomic ensemble

We consider the propagation of quantized polarized light in a magneto-optically-manipulated atomic ensemble with a tripod configuration. A polariton formalism is applied when the medium is subjected to a washboard magnetic field under electromagnetically-induced transparency. The dark-state polariton with multiple components is achieved. We analyze the quantum dynamics of the dark-state polariton using experimental data from the rubidium D1-line. It is found that one component propagates freely, however the wave packet trajectory of the other component performs Bloch oscillations.     

Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system

We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.