‘Measurement of quantum mechanical operators’ revisited

The Wigner-Araki-Yanase (WAY) theorem states a remarkable limitation to quantum mechanical measurements in the presence of additive conserved quantities. Discovered by Wigner in 1952, this limitation is known to induce constraints on the control of individual quantum systems in the context of information processing. It is therefore important to understand the precise conditions and scope of the WAY theorem. Here we elucidate its crucial assumptions, briefly review some generalizations, and show how a particular extension can be obtained by a simple modification of the original proofs. We also describe the evolution of the WAY theorem from a strict no-go verdict for certain, highly idealized, precise measurements into a quantitative constraint on the accuracy and approximate repeatability of imprecise measurements.     

Magneto-optical studies of GainAsInP quantum wells

The optical properties of GainAsInP quantum wells are studied in magnetic fields of up to 16T. A comparison of the absorption and photoluminescence spectra of a series of multiple quantum wells provides evidence that the photoluminescence occurs from excitons in which the hole is localised. This localisation is shown to be present in a highly doped sample with a sheet carrier density of ∼10¹² cm⁻², indicating that the localisation is not screened out by high free carrier densities. A theoretical fit to measured Landau level transitions in a 100Å multiple quantum well allows values for the carrier masses, electron non-parabolicity and exciton binding energy to be determined.     

Index of refraction of GaAsAlxGa1−xAs superlattices and multiple quantum wells

Recent research of superlattices and multiple quantum wells has generated considerable interest in the optical waveguiding properties of these structures for optoelectronic applications. As a result we present a theoretical study of the index of refraction of superlattices and determine its variation as a function of frequency and the superlattice parameters, i.e., layer width and AlAs composition. Γ-region exciton and valence-band mixing effects are included in the model. It is found that these two effects have an important influence on the value of the index of refraction and that superstructure effects rapidly decrease for energies greater than the superlattice potential barriers. Because of the quasi-two-dimensional character of the Γ-region excitons, our results indicate that the superlattice index of refraction can vary by ∼ 2% at the quantized, bound-exciton, transition energies. Overall, the theoretical results are in good agreement with the experimental data.     

Light-emitting properties of GaAs/InGaAs quantum wells with a GaAs barrier δ-doped with Mn atoms

The structural, electric, and luminescence properties of quantum-confined InGaAs/GaAs heterostructures, modified by δ-Mn doping of the GaAs barrier, have been investigated. The structures were prepared by combination of metal-organic chemical vapor deposition and laser sputtering of solid targets. The structures had a high crystal quality and pronounced electroluminescence intensity. The Mn content in the δ-doped layer, providing enhanced electroluminescence intensity and reduced operating currents of light-emitting diodes, was experimentally determined.     

Impurity magneto-optical absorption with the participation of resonance states of D 2 − centers in quantum wells

The dependence of the average binding energy of the resonance g-state of a D ₂ ^? center on the induction of an external magnetic field in a quantum well with a parabolic confining potential is studied using the zero-range potential method. It has been shown that with an increasing exchange interaction, the character of the dependence of the average binding energy of the resonance g-state of the D ₂ ^? center on the induction of the external magnetic field changes. It has been assumed that in GaAs/AlGaAs quantum wells alloyed with small Si donors, resonance D ₂ ^? states can exist under conditions of exchange interaction. It has been found that in spectra of impurity magneto-optical absorption in multiwall quantum structures, exchange interaction manifests itself as oscillations of interference origin.     

Numerical simultation of quantum dots; quasi-periodic conductance fluctuations and ‘scarred’ wave-functions

Simulating ballistic transport through square quantum dots, we find quasi-periodic conductance fluctuations and power spectra containing few frequencies, indicating few periodic orbits participate, in very good agreement with some recent experiments. We also find corresponding scar-like features in the wave functions. To reproduce these effects classically, the electrons must be restricted to acollimated beamwhich enters the dot at anangle.     

Self-consistent inhomogeneity of quantum wells in II–VI semiconductors

An X-ray diffraction method that uses a slightly diverging (3′) beam and maximally attainable diffraction angles ? _B (as large as 77°) was developed to study quantum wells (QWs) with widths of 5–8 nm separated by wide (100–220 nm) barrier layers. The advantage of this method compared to the use of a parallel beam is an increase by two orders of magnitude in the intensity of the beam incident on the sample and an increase in the probability of diffraction for all QWs as a unified single crystal. It is found that the growth on GaAs substrates misoriented by 10° from the (001) plane in the [111]_II direction brings about monoclinization of crystal lattices of the QW layers and barrier layers in opposite directions. Inhomogeneity of composition over the thickness of each well is observed. In the case of growth of a ZnSe/ZnMgSSe structure in which the layers have a crystal-lattice period close to the lattice period of the GaAs substrate, the QWs are inhomogeneously doped with elements from the composition of the barrier layers. The inhomogeneity of QW composition observed in the growth of mismatched layers in ZnCdSe/ZnSSe and ZnCdS/ZnSSe structures is caused by the fact that mismatch between the lattice parameters of QWs and barriers stimulates the growth of self-consistent compositions; this occurs due to a decrease in the Cd concentration in the Zn_1?x Cd _x Se QW in the initial stages of growth compared to the Cd concentration in the flow of gases and an increase in the Zn concentration in the Cd_1?x Zn _x S QW at small values of x up to the concentration matching GaAs (x = 0.4). The mismatch stresses are partially relaxed via dislocations with the (111)_II glide planes, as a result of which is observed the combination of rotation of the crystal planes of the layers and QW around the [1\(\overline 1 \)0] axis and almost cylindrical bending of the entire sample around the perpendicular [110] axis. Mismatch between lattice parameters of the ZnMgSSe barrier layers and the substrate brings about decomposition of these layers into two phases; this decomposition is caused by thermodynamic instability of the alloy.     

Effects of an anisotropic parabolic potential and Coulomb’s impurity potential on the energy characteristics of asymmetrical semi-exponential CsI quantum wells

Because of its unique optoelectronic properties,people have studied the characteristics of polarons in various quantum well(QW)models.Among them,the asymmetrical semiexponential QW(ASEQW)is a new model for studying the structure of QWs in recent years.It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential(APCP)on the crystal’s properties,because some of the impurities,usually regarded as Coulomb’s impurity potential(CIP),will exist in the crystal more or less,and the APCP has flexible adjustment parameters.However,the energy characteristics of the ASEQW under the combined actions of impurities and APCP have not been studied,which is the motivation of this paper.Using the linear combination operation and Lee-Low-Pines unitary transformation methods,we investigate the vibrational frequency and the ground state energy of the strong coupling polaron in an ASEQW with the influences of the CIP at the origin of coordinates and APCP,and make a comparison between our results and previous literature’s.Our numerical results about the energy properties in the ASEQW influenced by the CIP and APCP may have important significances for experimental design and device preparation.     

On the relation of Manin’s quantum plane and quantum Clifford algebras

In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined and interpreted in Clifford algebraic terms. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

The symmetry of donor–bound electron wavefunctions in quantum wells

In order to investigate the symmetry (i.e. sphericity) of donor–bound electron wavefunctions in quantum wells, we have invoked a two-parameter trial wavefunction. One parameter is the Bohr radius λ, whilst the other is the eccentricity parameter ζ. The latter incorporates the effect of the quantum well (QW) on the carrier motion in the growth (i.e. the z) direction. Working within the envelope function approximation it is shown that the donor wavefunction has the form of a prolate spheroid. However, calculations of the ratio λ/ζ shows that it is the value of λ which determines the essential symmetry of the wavefunction.     

Combined exciton–electron excitation in quantum wells with a two-dimensional electron gas of low density

A combined exciton–cyclotron resonance is found in the photoluminescence excitation and reflectivity spectra of semiconductor quantum wells with an electron gas of low density. In external magnetic fields an incident photon creates an exciton in the ground state and simultaneously excites an electron between Landau levels. A theoretical model is developed and suggests the dominating contribution of the exchange exciton–electron interaction.     

Elaboration and characterization of organic–inorganic quantum wells impregnated on porous anodic alumina nanostructures

An organic–inorganic quantum well embedded on porous anodic alumina was synthesized and studied by MEB, AFM, optical absorption and photoluminescence. The morphology determined by the MEB and the AFM, shows that the size of the pores is about 10 nm for alumina evaporated on glass substrate and about 35 nm for alumina template prepared in sulfuric acid (H₂SO₄). The optical properties are characterized from absorption and photoluminescence spectra measured at room and low temperature. The measured spectral characteristics demonstrate the influence of the pore size on the emission of the organic–inorganic quantum well ((C₁₂H₂₅NH₃)₂PbI₄). An obvious blueshifted photoluminescence (PL) of (C₁₂H₂₅NH₃)₂PbI₄ in nanometer-sized pores was observed. It results in a better quantum confinement.     

Growth of strain-compensated InGaAs/GaAsP multiple quantum wells by MOVPE

InGaAs/GaAsP strain-compensated multiple quantum wells (SCMQWs) and strained InGaAs/GaAsmultiple quantum wells (MQWs) were grown on GaAs substrates by metal organic vapor phase epitaxy(MOVPE). The results of double crystal X-ray diffraction (DCXRD) revealed that strain relief had beenpartly accommodated by the misfit dislocation formation in the strained MQW material. It led to thatthe full width half maximums (FWHMs) of superlattice satellite peaks are broader than those of SCMQWstructures, and there was no detectable room temperature photoluminecence(RT-PL)for the strained     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

Properties of InGaAs/GaAs quantum wells with a δ〈Mn〉-doped layer in GaAs

A method of formation of two-dimensional structures containing a δ〈Mn〉-doped layer in GaAs and an In_xGa_1?x As quantum well (QW) separated by a GaAs spacer of thickness d = 4–6 nm is developed using laser evaporation of a metallic target during MOS hydride epitaxy. It is shown that, up to room temperature, these structures have ferromagnetic properties most likely caused by MnAs clusters. At low temperatures (T _m ～ 30 K), the anomalous Hall effect is revealed to occur. This effect is related to hole scattering by Mn ions in GaAs and to the magnetic exchange between these ions and QW holes, which determines the spin polarization of the holes. The behavior of the negative magnetoresistance of these structures at low temperatures indicates the key role of quantum interference effects.     

Dynamics on reactive potential energy surfaces: hyperspherical view and signatures of ‘quantum chaos’

Adiabatic energy levels for two prototypical reactions, F + H₂ → HF + H and He + H⁺ ₂ → HeH⁺ + H, are analysed by means of statistical tests. These levels result from quantum mechanical calculations of dynamics based on the hyperspherical approach, and are given as a function of the total inertia of the system measured by the hyperradius ρ The nearest neighbour level spacing distributions of Brody and of Berry and Robnik, the spectral rigidity δ₃ of Dyson and Mehta and the correlation coefficient are reported, together with other properties, such as variance, skewness and kurtosis of the distributions. Trends are studied as a function of ρ, proposed as a natural control variable. For low ρ, which correspond to the transition state, evidence is found of Wigner-like behaviour, which is interpreted as the signature of quantum chaos. On the passage of the systems through intermediate ρ a mixture of Wigner- and Poisson-like behaviour emerges. The situation for high ρ where reactants and products of the reactions are well separated, is characterized by a tendency towards regular Poisson-like behaviour. A comparison between the two investigated systems shows that the chaotic regime in the transition state region is more pronounced for the He reaction, which proceeds through a deep well and whose dynamics are characterized by a rich resonance pattern.     

Photoluminescence and dark current of p-doped InGaAs/AlxGa1−xAs strained multiple quantum wells

We report the temperature dependence of the photoluminescence spectra and current-voltage (I_d-V) characteristics of p-doped In_0.15Ga_0.85As/AlGaAs quantum well infrared photodetectors (QWIPs) with different barrier heights grown by molecular beam epitaxy (MBE). The dark current at low temperatures is found to be about three orders of magnitude lower than that reported for the n- and p-doped QWIPs made of other material systems. The PL spectra show two emission peaks which correspond to an intersubband absorption and are tunable by changing the mole fraction of Al. The low energy emission peak of the In_0.15Ga_0.85As/Al_0.45Ga_0.55As QWIP is found to be much lower in intensity than that of the high one, due possibly to excess Al which may result in defects or imperfection at/or near well-barrier interfaces.