F. M. S. Lima

Unexpected transition from single to double quantum well potential induced by intense laser fields in a semiconductor quantum well

When an electronic system is irradiated by an intense laser field, the potential “seen” by electrons is modified, which affects significantly the bound-state energy levels, a feature that has been observed in transition energy experiments. For lasers for which the dipole approximation applies, a nonperturbative approach based upon the Kramers–Henneberger translation transformation, followed by Floquet series expansions, yields, for sufficiently high frequencies, the so-called “laser-dressed” potential, which is taken for composing a time-independent Schrodinger equation whose solutions are the desired quasistationary states. This approach, developed originally for atoms, has been verified to be useful also for carriers in semiconductor nanostructures under intense laser fields. In quantum wells, analytical expressions for the dressed potential have been proposed in literature for a nonresonant, intense laser field polarized perpendicularly to the interfaces. By noting that they apply only for α0≤L/2, wher...

An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime

A simple approximate expression is derived for the dependence of the period of a simple pendulum on the amplitude. The approximation is more accurate than other simple relations. Good agreement with experimental data is verified.

Electric field effects on electron mobility in n-AlGaAs/GaAs/AlGaAs single asymmetric quantum wells

We calculated low-temperature electron mobility in n-AlGaAs/GaAs/AlGaAs single asymmetric quantum wells in the presence of a uniform electric field directed perpendicularly to the interfaces. The quantum well asymmetry is due to the doping profile (one-side modulation doping). Following a variational scheme, we solved both Schrodinger and Poisson equations simultaneously and the results were used to calculate the low-temperature (quasielastic) scattering rates. Only relevant scattering mechanisms were taken into account, namely ionized impurity, interface roughness, alloy disorder, and acoustic phonons (deformation potential and piezoelectric coupling). Our results show that both interface roughness and alloy disorder scattering rates are strongly dependent upon the electric field strength. We also show that there are interesting changes in the dominance of the mobility among different scattering processes, which leads to the formation of a maximum in the mobility dependence on the electric field strength...

Simple ‘log formulae’ for pendulum motion valid for any amplitude

By combining a logarithmic approximate formula for the pendulum period derived recently (valid for amplitudes below π/2 rad) with the Cromer asymptotic approximation (valid for amplitudes near to π rad), a new approximate formula accurate for all amplitudes between 0 and π rad is derived here. It is shown that this formula yields an error that tends to zero in both the small and large amplitude limits, a feature not found in any previous approximate formula. Some ways of refining this formula are also presented. Interestingly, when one of the improved expressions is taken for building a sinusoidal (harmonic) approximation to the solution of the pendulum equation of motion very good agreement is found. The simple log formulae derived here require only a few elementary function calls in a pocket calculator for accurate evaluations, being useful for analyzing pendulum experiments in introductory physics labs. They may also be of interest for those specialists working with nonlinear phenomena governed by pendulum-like differential equations, which arise in many fields of science and technology (e.g., analysis of acoustic vibrations, oscillations in small molecules, optically torqued nanorods, Josephson junctions, electronic filters, gravitational lensing in general relativity, advanced models in field theory, oscillations of buildings during earthquakes, and others).

Dichotomy of the exciton wave function in semiconductors under intense laser fields

We study the behavior of excitons in a semiconductor irradiated by a monochromatic, linearly polarized, intense laser field. By taking the finiteness of the hole effective mass into account and including the radiation field in a semiclassical manner, we solved the two-body quantum problem in the framework of a nonperturbative theory based upon the Kramers-Henneberger translation transformation for the Schrodinger equation. In the Kramers frame, the rapidly oscillating potential is expanded in a Fourier-Floquet series and, for laser frequencies high enough, only the zeroth-order term survives, the so-called “laser-dressed” potential. By applying the Ehlotzky’s approximation, this potential simplifies to a two-center potential that resembles that for the electronic motion in the H2+ molecule ion. The binding energy for an exciton in bulk GaAs under a nonresonant laser field is then computed by following a variational scheme we recently adapted from the linear combination of atomic orbitals-molecular orbital...

Magnetic field effect on the laser-driven density of states for electrons in a cylindrical quantum wire: transition from one-dimensional to zero-dimensional behavior

The influence of a uniform magnetic field on the density of states (DoS) for carriers confined in a cylindrical semiconductor quantum wire irradiated by a monochromatic, linearly polarized, intense laser field is computed here non-perturbatively, following the Greens function scheme introduced by some of the authors in a recent work (Lima et al 2009 Solid State Commun. 149 678). Besides the known changes in the DoS provoked by an intense terahertz laser field—namely, a significant reduction and the appearance of Franz–Keldysh-like oscillations—our model reveals that the inclusion of a longitudinal magnetic field induces additional blueshifts on the energy levels of the allowed states. Our results show that the increase of the blueshifts with the magnitude of the magnetic field depends only on the azimuthal quantum number m (m=0, 1, 2, ...), being more pronounced for states with higher values of m, which leads to some energy crossovers. For all states, we have obtained, even in the absence of a magnetic field, a localization effect that leads to a transition in the DoS from the usual profile of quasi-1D systems to a peaked profile typical of quasi-0D systems, as e.g. those found for electrons confined in a quantum dot.

Optical transitions involving impurities in semiconductors under additional infrared laser radiation

Abstract The influence of an intense infrared (IR) laser field on the optical absorption edge associated to acceptor impurities of a direct-gap semiconductor is discussed. It is shown that as the IR laser field intensity increases the absorption coefficient is modified so as to give rise to an absorption tail below the free-field forbidden gap. An application is made for the case of the GaAs irradiated by an intense CO2 laser.

Effect of a terahertz laser field on the electron-DOS in a GaAs/AlGaAs cylindrical quantum wire: finite well model

The influence of a linearly polarized terahertz laser field on the density of states (DOS) for carriers confined in a cylindrical semiconductor quantum wire is investigated here within a nonperturbative scheme, based on the Greens function approach introduced by Xu (1997 Semicond. Sci. Technol. 12 1559). In our finite potential well model, the functional dependence of the DOS on energy is significantly modified by a monochromatic, nonresonant, intense laser radiation polarized along the wire axis. Apart from a uniform blueshift with respect to the laser-free DOS, which is proportional to the laser intensity and to the inverse of the square of the frequency, a remarkable reduction of the DOS, followed by pronounced Franz–Keldysh-like oscillations above the bottom of each 1D sub-band, is obtained. The period of these oscillations is seen to depend more on the laser frequency than on the intensity. Interestingly, with an increase of the laser intensity and/or a reduction of the laser frequency, the DOS profile changes from the usual shape found in 1D electronic systems to a series of discrete peaks similar to that found in quasi-0D systems, such as quantum dots.

Analytical study of the critical behavior of the nonlinear pendulum

The dynamics of a simple pendulum consisting of a small bob and a massless rigid rod has three possible regimes depending on its total energy E: Oscillatory (when E is not enough for the pendulum to reach the top position), “perpetual ascent” when E is exactly the energy needed to reach the top, and nonoscillatory for greater energies. In the latter regime, the pendulum rotates periodically without velocity inversions. In contrast to the oscillatory regime, for which an exact analytic solution is known, the other two regimes are usually studied by solving the equation of motion numerically. By applying conservation of energy, I derive exact analytical solutions to both the perpetual ascent and nonoscillatory regimes and an exact expression for the pendulum period in the nonoscillatory regime. Based on Cromer’s approximation for the large-angle pendulum period, I find a simple approximate expression for the decrease of the period with the initial velocity in the nonoscillatory regime, valid near the critic...

Accurate measurement of the position and velocity of a falling object

A simple setup was assembled to study the motion of an object while it falls. The setup was used to determine the instantaneous velocity, terminal velocity and acceleration due to gravity. Also, since the whole project was done within