One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach

Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x ^2j 〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.     

Cyclotron resonance in asymmetric double quantum wells

Far-infrared magnetotransmission measurements in magnetic fields are carried out on asymmetric coupled double wells. We observe a splitting in the cyclotron resonance (CR) line for a wide range of intermediate magnetic fields and only one line at high magnetic fields. Two peaks observed in the CR spectra correspond to transitions between Landau levels in individual wells. We propose that phase transition between weak and strong coupling regimes may be responsible for the features. The characteristics of the transition are studied via an analysis of CR masses, CR splitting and line widths as a function of the magnetic field.     

Linear and nonlinear intersubband optical absorption in symmetric double semi-parabolic quantum wells

The linear and the nonlinear intersubband optical absorption in the symmetric double semi-parabolic quantum wells are investigated for typical GaAs/AlxGa1−xAs. Energy eigenvalues and eigenfunctions of an electron confined in finite potential double quantum wells are calculated by numerical methods from Schrödinger equation. Optical properties are obtained using the compact density matrix approach. In this work, the effects of the barrier width, the well width and the incident optical intensity on the optical properties of the symmetric double semi-parabolic quantum wells are investigated. Our results show that not only optical incident intensity but also structure parameters such as the barrier and the well width really affect the optical characteristics of these structures.     

Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method

Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.     

Tunnel transfer of excitons due to a Fano disintegration and an optical phonon emission in biased double quantum wells

We consider theoretically and experimentally the tunnel transfer of excitons in an asymmetric double quantum well structure. We interpret quantitatively the measured tunnel transfer time in terms of two intrinsic mechanisms for excitons: an inter-well Fano disintegration for excitons photocreated in an excited state and the inter-well emission of optical phonons.     

Binding energies of donor impurities in modulation-doped double quantum wells under an electric field

In this study, we have investigated theoretically the binding energies of shallow donor impurities in modulation-doped GaAs/Al_0.33Ga_0.67As double quantum wells (DQWs) under an electric field which is applied along the growth direction for different doping concentrations as a function of the impurity position. The electronic structure of modulation-doped DQWs under an electric field has been investigated by using a self-consistent calculation in the effective-mass approximation. The results obtained show that the carrier density and the depth of the quantum wells in semiconductors may be tuned by changing the doping concentration, the electric field and the structure parameters such as the well and barrier widths. This tunability gives a possibility of use in many electronic and optical devices.     

Anharmonic oscillators in higher dimension: Accurate energy eigenvalues and matrix elements

Energy eigenvalues and matrix elements of various anharmonic oscillators are determined to a high accuracy by applying a method for determining the eigenvalues and eigenvectors of real symmetric para-p diagonal matrices (described in the preceding paper). Our results for the 2- and 3-dimensional oscillators are new and complement similar accurate results for the one dimensional oscillators available in the literature.     

Electronic Raman scattering in double semi-parabolic quantum wells

The differential cross-section for electronic Raman scattering in double semi-parabolic quantum wells of typical GaAs/AlxGa1-x As is investigated numerically with the effective-mass approximation. The dependence of the differential cross-section on structural parameters such as the barrier width and the well widths is studied. Our results indicate that the electronic Raman scattering is affected by the geometrical size and can be negligible in the symmetric double-well case.     

A novel double quantum well device for THz range frequency detection

A novel device has been proposed which uses a double quantum well structure for the detection of signals in the THz range. The technology for the manufacturing of such devices at this point of time is significantly mature so that such a device may be easily fabricated. The detector frequency may be varied from 10 to 90 THz by changing the well widths from 10 to 30 Å.     

Laser field-driven potential profiles of double quantum wells

We study the potential profiles of double quantum wells with different geometries. The binding energy of an impurity under a laser field and its simultaneous application with a magnetic field is calculated by means of variational techniques. It is shown that the total potential of the structure suggests a strong control mechanism on the binding energy.     

Intersubband absorption in strained AlGaN/GaN double quantum wells

The intersubband absorption of the four-energy-level system in strained AlGaN/GaN double quantum wells is calculated by considering the polarization effect and the strain modification on material parameters (e.g., the conduction band offset, the electron effective mass and the static dielectric constant). It is found that the electron wavefunctions mainly locate at the left well and penetrate into the left barrier. The absorption spectrum exhibits multiple peaks contributed by different transitions. The position and height of absorption peaks are not very sensitive to the structural parameters (i.e., composition and thickness) of the central barrier because of the strong built-in electric field. However, the coupling between two wells can be enhanced by strain modulation.     

Optical second harmonic generation in asymmetric double triangular quantum wells

The second harmonic generation (SHG) in the asymmetric double triangular quantum wells (DTQWs) is investigated theoretically. The dependence of the SHG coefficient on the right-well width of the DTQWs is studied, and the influence of the applied electric field on SHG coefficient is also taken into account. The analytical expression of the SHG coefficient is analyzed by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for the typical GaAs/Al_xGa_1−xAs asymmetric DTQWs. The results show that the calculated SHG coefficient in this coupled system can reach the magnitude of 10⁻⁵ m/V, 1–2 orders of magnitude higher than that in step quantum well, and that in double square quantum wells. Moreover, the SHG coefficient is not a monotonic function of the right-well width, but has complex relationship with it. The calculated results also reveal that an applied electric field has a great influence on the SHG coefficient. Applying an appropriate electric field to a DTQW with a wider right well can induce a sharper peak of the SHG coefficient due to the double-resonant enhancement.     

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

For a large class of time-dependent non-Hermitian Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzed further and shown to be quasi-exactly solvable. Technically we constructed the Lewis–Riesenfeld invariants making use of the metric picture, which is an equivalent alternative to the Schrödinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.     

Magnetic field effect on transitions between direct and indirect excitons in diluted magnetic semiconductor double quantum wells

Transitions between direct and indirect excitons with change of magnetic field in double quantum well heterostructure Cd_1−xMg_xTe/Cd_1−yMg_yTe/Cd_1−xMg_xTe/Cd_1−zMn_zTe/Cd_1−xMg_xTe in external magnetic field are studied. The structure contains diluted magnetic semiconductor (Cd,Mn)Te layer that forms magnetic quantum well with the depth depending on the magnetic field intensity. Above some magnetic field the indirect exciton becomes the lowest excited state of the system. The indirect exciton lifetime exceeds by several orders of magnitude of the direct exciton one. The range of quantum well widths for which the indirect exciton is the exciton lowest state was estimated for the proposed system.     

LO-phonon assisted tunneling from spatially direct to indirect exciton in semimagnetic double quantum well structures

Relaxation from spatially direct to the spatially indirect exciton through ZnSe barriers of different thicknesses is investigated in (ZnCdMn)Se/ZnSe/(ZnCd)Se asymmetric double quantum wells by use of magneto-optical steady-state photoluminescence (PL) and PL excitation (PLE) experiments. The 1-LO-phonon scattering has been found to be the relevant mechanism for effective electron and hole tunneling.     

对称GaAs/Al0.3Ga0.7As双量子阱中激子的束缚能

在有效质量近似下采用简单的尝试波函数变分地计算了对称GaAs/Al_0.3Ga_0.7As双量子阱中激子体系束缚能，研究了体系束缚能随阱宽和垒宽的变化情况. 发现双量子阱中激子体系束缚能随阱宽变化同单量子阱情况类似，但束缚能的峰值出现在阱宽为10?左右，峰值位置小于单阱的情况；束缚能随垒宽的增加有一极小值，这与波函数向垒中的渗透有关.     

含时耦合谐振子系统的时间演化与双模压缩态

运用Lewis Riesenfeld不变量理论,通过适当地选取厄米不变量,得到了含驱动项和双模耦合项的含时耦合谐振子系统薛定谔方程的封闭解,给出了系统的演化算符及其产生双模光场的压缩态的条件,并得出系统压缩态的量子涨落与驱动项无关但与系统所处的初态有关的结论. 关键词： 含时耦合谐振子系统 Lewis Riesenfeld不变量理论 双模压缩态     

Linear and nonlinear intersubband optical absorption and refractive index changes of asymmetric double semi-parabolic quantum wells

The optical properties of the asymmetric double semi-parabolic quantum wells (DSPQWs) are investigated numerically for typical GaAs/Al_xGa_1−xAs. Optical properties are obtained using the compact density matrix approach. In this work, effects of the structure parameters such as the barrier width and the well widths on the optical properties of the asymmetric DSPQWs are investigated. The results show that the linear and nonlinear optical properties of asymmetric DSPQW are non-monotonic functions of these structure parameters. The behavior of the refractive index changes of asymmetric DSPQW with the variation of the barrier width is different substantially with that of symmetric DSPQW. Results reveal that the resonant peak values of the total absorption coefficient of asymmetric DSPQW is usually greater than that of symmetric DSPQW. Our calculations also show that the total absorption coefficient of asymmetric DSPQW is larger than that of asymmetric double square quantum well.     

Exciton behavior in GaAs/AlGaAs coupled double quantum wells with interface disorder

In this work, we present a detailed study on the optical properties of two GaAs/Al_0.35Ga_0.65As coupled double quantum wells (CDQWs) with inter-well barriers of different thicknesses, by using photoluminescence (PL) spectroscopy. The two CDQWs were grown in a single sample, assuring very similar experimental conditions for measurements of both. The PL spectrum of each CDQW exhibits two recombination channels which can be accurately identified as the excitonic e₁-hh₁ transitions originated from CDQWs of different effective dimensions. The PL spectra characteristics and the behavior of the emissions as a function of temperature and excitation power are interpreted in the scenario of the bimodal interface roughness model, taking into account the exciton migration between the two regions considered in this model and the difference in the potential fluctuation levels between those two regions. The details of the PL spectra behavior as a function of excitation power are explained in terms of the competition between the band gap renormalization (BGR) and the potential fluctuation effects. The results obtained for the two CDQWs, which have different degrees of potential fluctuation, are also compared and discussed.