Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

We introduce and investigate a system that uses temporal resonance-induced phase-space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form weblike patterns, can by controlled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BEC’s center-of-mass kinetic energy to prespecified values. Surprisingly, the strength of the atom-lattice interaction and resulting BEC heating of the center-of-mass motion is enhanced by the repulsive interatomic interactions

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics

Using acoustic waves to induce high-frequency current oscillations in superlattices

We show that gigahertz acoustic waves in semiconductor superlattices can induce terahertz (THz) electron dynamics that depend critically on the wave amplitude. Below the threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-type oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localized electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular, the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends nonmonotonically on the strength of the acoustic wave, reflecting the variation in the single-electron drift velocity

Semiconductor charge transport driven by a picosecond strain pulse

We demonstrate that a picosecond strain pulse can be used to drive an electric current through both thin-film epilayer and heterostructure semiconductor crystals in the absence of an external electric field. By measuring the transient current pulses, we are able to clearly distinguish the effects of the coherent and incoherent components of the acoustic packet. The properties of the strain induced signal suggest a technique for exciting picosecond current pulses, which may be used to probe semiconductor devices

Lyapunov stability of charge transport in miniband semiconductor superlattices

We discuss a numerical method for the calculation of the spectrum of Lyapunov exponents for spatially extended systems described by coupled Poisson and continuity equations. This approach was applied to the model of collective charge transport in semiconductor superlattices operating in the miniband transport regime. The method is in very good agreement with analytical results obtained for the steady state. As an illustrative example, we consider the collective electron dynamics in the superlattice subjected to an ac voltage and a tilted magnetic field, and conclusively show that, depending on the field parameters, the dynamics can exhibit periodic, quasiperiodic, or chaotic behavior

ВЛИЯНИЕ МЕЖМИНИЗОННОГО ТУННЕЛИРОВАНИЯ НА ГЕНЕРАЦИЮ ТОКА В ПОЛУПРОВОДНИКОВОЙ СВЕРХРЕШЕТКЕ

В работе теоретически изучeнo влияние ширины запрещенной зоны между первой и второй энергетическими минизонами на транспорт заряда в полупроводниковой сверхрешетке, к которой приложены электрическое и наклонное магнитные поля. Были рассчитаны временные зависимости тока, протекающего через сверхрешетку, и построены зависимости амплитуды и частоты колебаний электрического тока от приложенного напряжения. Обнаружено, что межминизонное туннелирование электронов способствует уменьшению амплитуды колебаний тока, но в тоже время увеличивает их частоту

Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localized to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric-field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between the thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency

ИССЛЕДОВАНИЕ ПЕРЕХОДОВ МЕЖДУ РАЗЛИЧНЫМИ РЕЖИМАМИ ГЕНЕРАЦИИ КОЛЕБАНИЙ ТОКА В ПОЛУПРОВОДНИКОВОЙ СВЕРХРЕШЕТКЕ В ПРИСУТСТВИИ НАКЛОННОГО МАГНИТНОГО ПОЛЯ ПРИ РАЗЛИЧНЫХ ТЕМПЕРАТУРАХ [Studying transitions between different regimes of current oscillations generated in a semiconductor superlattice in the presence of a tilted magnetic field at various temperatures]

В настоящей работе исследуются механизмы переходов между различными режимами колебаний в полупроводниковой сверхрешетке в присутствии внешнего наклонного магнитного. В случае небольших температур с ростом напряжения в системе происходит бифуркация удвоения периода, обуславливающая смену динамического режима, тогда как с увеличением температуры переход осуществляется через срыв генерации колебаний тока. [The mechanisms of transitions between different regimes of current oscillations in a semiconductor superlattice in the presence of a tilted magnetic field at various temperatures have been studied. At relatively low temperatures, an increase in the applied voltage leads to a period -doubling bifurcation that causes a change in the dynamic regime. At increased temperatures, the transition takes place with the quenching of current oscillations.