Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

Theoretical formalism for DC‐field polaron dynamics is extended to the dynamics of a 1D Holstein polaron in an external AC electric field using multiple Davydov trial states. Effects of carrier–phonon coupling on detuned and resonant scenarios are investigated for both phase and nonzero phase. For slightly off‐resonant or detuned cases, a beat between the usual Bloch oscillations and an AC driving force results in super Bloch oscillations, that is, rescaled Bloch oscillations in both the spatial and the temporal dimension. Super Bloch oscillations are damped by carrier–phonon coupling. For resonant cases, if the carrier is created on two nearest‐neighboring sites, the carrier wave packet spreads with small‐amplitude oscillations. Adding carrier–phonon coupling localizes the carrier wave packet. If an initial broad Gaussian wave packet is adopted, the centroid of the carrier wave packet moves with a certain velocity and with its shape unchanged. Adding carrier–phonon coupling broadens the carrier wave packet and slows down the carrier movement. Our findings may help provide guiding principles on how to manipulate the dynamics of the super Bloch oscillations of carriers in semiconductor superlattice and optical lattices by modifying DC and AC field strengths, AC phases, and detuning parameters.     

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.     

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.     

Bloch oscillations in a homogeneous nucleotide chain

It is shown that, at zero temperature, a hole placed in a homogeneous synthetic nucleotide chain with applied electric field demonstrates Bloch oscillations. The oscillations of the hole placed initially on one of the base pairs arise in response to disruption of the initial charge distribution caused by nucleotide vibrations. The finite temperature fluctuations result in degradation of coherent oscillations. The maximum permissible temperature for DNA “Bloch oscillator” occurrence is estimated.     

Anharmonic Bloch Oscillation of Electrons in Biased Superlattices

The oscillatory motion of electrons in a periodic potential under a constant applied electric field, known as Bloch oscillations (BO), is one of the most striking and intriguing quantum effects and was predicted more than eighty years ago. Oscillating electrons emit electromagnetic radiation and here we consider this BO effect for emission in the THz region. To date, it has been assumed that the Bloch oscillation of an electron is anharmonic oscillation, therefore with radiation emitted at the single Bloch frequency. We analyze scenarios when Bloch oscillations can be accompanied by the emission of radiation not only at the Bloch frequency but also with double and triple Bloch frequencies. The first scenario means that electrons could jump over neighboring Stark states. The second scenario of anharmonic emission is coupled to an opening of the minigap in the miniband.     

Anharmonicity of Bloch oscillations in GaAs/AlAs superlattices in the case of inhomogeneously broadened excitonic states in a weak electric field

The variation of the spectral shape of the four-wave mixing signal in GaAs/AlGaAs superlattices was studied experimentally and theoretically. It was shown that in an external electric field, leading to anti-crossing of the levels of heavy and light excitons, sawtooth oscillations of the energy position of the levels are observed. These oscillations are due to the inhomogeneous broadening of the states participating in the Bloch oscillations. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 820–825 (25 May 1998)     

Effects of strong electric fields in a polyacetylene chain

In this work, we study the effects related to the creation of electron/hole pairs via application of an external electric field that acts on a pristine trans-polyacetylene molecular chain at zero-temperature. This phenomenon is termed Schwinger–Landau–Zener (SLZ) effect and arises when a physical system, which can even be the vacuum, is under the action of a strong, static and spatially homogeneous electric field. Initially, we investigate how the electrical conductivity of the polyacetylene changes with the applied field, by considering the carriers production as well as the variation of the interband gap according to certain ab initio models. Next, we analyse the competition between the SLZ effect and another one associated with the incidence of an uniform electric field on one-dimensional crystals – the Bloch oscillations. We evaluate the conditions in which these latter can be destroyed by the particles created through the same field that induces them, and verify the possibility of occurrence of the Bloch oscillations inside the trans-polyacetylene with frequencies equal to or higher than the terahertz scale.     

Polarons in quantum chains with XY exchange and Dzyaloshinsky-Moriya interaction

Excitations of the polaron types are investigated in the spin-1/2 quantum chain with XY exchange and Dzyaloshinsky-Moriya interaction, both coupled to acoustic vibrations of the substrate lattice. The study is carried out via Jordan-Wigner transformation with the help of which the spin chain is mapped onto a chain of spinless fermions. From the resulting effective fermion-lattice Hamiltonian, the discrete equations of motion are derived. These equations are solved in the continuum limit for self-trapped states near the bottom of the fermion spectrum interacting with long-wavelength acoustic lattice modes. The associate polaron solution, which has a pulse shape, is shown to propagate bound to the induced lattice kink distortion by translation along the chain at a constant velocity v. The pair can also experience an additional acceleration ϑ₀ when the free fermion charge is excited above its groundstate. The polaron binding energy is strongly reduced, depending quadratically on the ratio D/J of the Dzyaloshinsky-Moriya interaction strength D to the isotropic XY exchange interaction J. It is also found that polaron parameters depend only on the XY spin-lattice coupling but not on the Dzyaloshinsky-Moriya contribution.     

Dispersive terahertz gain of a nonclassical oscillator: BLOCH oscillation in semiconductor superlattices

We have directly determined the spectral shape of the complex conductivities of Bloch oscillating electrons by using the time-domain terahertz (THz) electro-optic sampling technique, and presented experimental evidence for a dispersive Bloch gain in superlattices. This unique dispersive gain without population inversion arises from a nonclassical nature of Bloch oscillations; that is, the phase of the Bloch oscillation is shifted by pi/2 from that of the semiclassical charged harmonic oscillation when driven by the same ac field. By increasing the bias electric field, the gain bandwidth reached approximately 3 THz in our particular sample.     

Dynamics of polaron in a polymer chain with impurities

In a polymer chain, an extra electron or hole distorts the chain to form a charged polaron, which is the charge carrier being responsible for conductivity. When an intermediate-strength electric field is applied, the polaron will be accelerated for a short time and then move at a constant velocity. The dynamical process of polaron in a polymer chain with impurities is simulated within a non-adiabatic evolution method, in which the electron wave function is described by the time-dependent Schrödinger equation while the polymer lattice is treated classically by a Newtonian equation of motion. We have considered two kinds of dynamical processes, one is the field-induced depinning of a charged polaron, which is initially bound by an attractive impurity; and the other is the scattering of a polaron from an impurity. In the former process, the charged polaron will depart from the attractive impurity only for the applied field with strength over a threshold, otherwise, the polaron will oscillate around the impurity. In the latter process, the charged polaron moves through the impurity in the presence of an electric field while it will be bounced back for a repulsive impurity or trapped to oscillate around an attractive impurity in the case that the applied electric field is weak and just be present for the polaron acceleration.Received: 4 June 2004, Published online: 14 December 2004PACS: 71.38.-k Polarons and electron-phonon interactions - 72.80.Le Polymers; organic compounds (including organic semiconductors)     

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

Following the Dirac‐Frenkel time‐dependent variational principle, transient dynamics of a one‐dimensional Holstein polaron with diagonal and off‐diagonal exciton‐phonon coupling in an external electric field is studied by employing the multi‐D₂ Ansatz, also known as a superposition of the usual Davydov D₂ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton‐phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non‐zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton‐phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite‐sized ring within the anti‐adiabatic regime. For strong diagonal coupling, the multi‐ Anstaz is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations.

     

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.     

Dynamic localization and Bloch oscillations in the spectrum of a frequency mode-locked laser

It is shown that a frequency mode-locked laser with a sinusoidal sweep of modulation frequency around a mode-locking condition represents an ideal optical system for observing in the spectral domain the phenomena of dynamic localization and Bloch oscillations of electrons in an ideal solid placed in an external ac electric field.     

Chirped Bloch oscillations in strain-balanced InGaAs/InGaAs superlattices

Bloch oscillations excited in a strain-balanced In_xGa_1 − xAs/In_yGa_1 − yAs superlattice by fs optical pulses at 1.55 μ m are investigated in time-resolved transmission spectroscopy. The transition from the coherent oscillatory motion to an incoherent drift transport of the electrons is observed via a transient frequency shift of the Bloch oscillations due to the associated screening of the applied electric field. These electric field changes are analyzed quantitatively as a function of the initial field strengths and excitation densities. The incoherent transport can be described by a drift-diffusion model. As a result, the carrier mobility in the superlattice is obtained on a picosecond timescale.     

共轭高分子链中电荷迁移的热效应

从理论上研究了共轭高聚物链中在电场作用下极化子运动的热效应.基于SSH模型以及通过绝热动力学演化的方法,模拟了共轭高聚物链中极化子在电场作用下从链左端向右端运动的过程.晶格受到的热扰动作用假设为通过局域的晶格范围内原子位移的随机涨落来实现.结果发现,晶格中的局域热涨落对于运动中的极化子而言等效于一个势垒.势垒高度由高分子中受到热扰动的区域的范围大小以及该区域与其周围环境的温差来决定.当分子中存在热吸收不均匀的现象时,链内极化子迁移率在低电场范围内随电场的变化遵循对数曲线变化规律.     

Dynamics of Bloch–Zener Oscillations with Tuning Gap

In this study, the transient dynamics of Bloch–Zener oscillations (BZOs) in a 1D qubit chain with a controllable band gap are explored. The chain consists of alternating site energies and is subjected to a constant external field. Several tight-binding models were analyzed, including Bloch and Landau–Zener models, to understand the  BZOs mechanism. The findings revealed that the band gaps played a crucial role in bridging the intriguing interplay between Bloch oscillations and Landau–Zener transitions. The motion of carriers in real and quasi-momentum spaces is explored and the time evolution of occupancy in mini-bands is calculated. A linearly time-dependent way of tuning the gap is also proposed and non-periodic motion is observed. When the chain is coupled to dispersionless optical phonons, strong coupling leads to large phonon displacements and localizes the carrier wave packets of the qubit states. The findings provide new insights into the behavior of BZOs in complex systems and suggest avenues for future studies.     

共轭高聚物中极化子散射引起的激子迁移(英文)

基于Su-Schrieffer-Heeger(SSH)模型并考虑到Brazovskii-Kirova对称破缺项,研究了共轭聚合物中注入极化子和激子在外电场下的散射过程.研究发现在外场作用下极化子总是能通过激子,而激子的运动行为则密切依赖于电场的强度.如果电场大于临界电场3.0×10~5V/cm,那么激子与极化子散射后并不发生任何运动;然而当电场小于此临界值时,激子将在极化子运动的相反方向上有一个明显的位移.激子在弱电场下所发生的这种迁移运动,是由于同极化子发生了慢散射作用.     

Stationary polaron motion in a polymer chain at high electric fields

We study the stationary motion of a polaron in a conducting polymer in the presence of a high electric field. Using the Su-Schrieffer-Heeger model plus an electric field, we find that at polaron velocities not exceeding the sound velocity, the dissipation of the electronic energy into the lattice occurs via emission of phonons with single selected wave vector. For this case the corresponding contribution to the polaron mobility can be calculated analytically. We discuss the issue of the polaron stability with respect to dissociation in a very high field at supersonic velocities.     

Dynamical electron localization and self-induced transparency in semiconductor superlattices

The mechanisms of the occurrence of self-induced and selective transparencies of semiconductor superlattices in a strong time-dependent electric field are investigated. The association of these mechanisms with Bloch oscillations, dynamical localization, and collapse of electron quasi-energy minibands is analyzed, and a comparison with the properties of Josephson junctions is made. It is shown that the self-induced transparency is due to the fact that the current-contributing component of the electron distribution function is destroyed by collisions at discrete values of the amplitude of the time-harmonic field, while the selective transparency is associated with the nonmonotonic dependence of the spectrum of nonlinear electron oscillations in the electric field on the amplitude of the field. The dynamical localization and collapse of quasi-energy minibands lead to the field energy dissipation and are favorable to destruction of the transparency states of the superlattice.     

DNA-based tunable THz oscillator

The intrinsic helix conformation of the DNA strands is known to be the key ingredient of control of the electric current through the molecule by the perpendicular (gate) electric field. We show theoretically that Bloch oscillations in periodic systems with helical conformation are also strongly affected by such lateral field; the oscillation frequency splits into a manifold of several generally non-commensurate frequencies leading to a complicated pattern of the charge motion. For model parameters typical for the DNA the frequency of such oscillations falls in the THz domain, suggesting a possibility to design a DNA-based nano-scale source of THz radiation.