Coherent state polarons in quantum wells

We investigate the polaronic effects of an electron confined in a quantum well, which we describe through its algebraic properties using su(1,1), taking into account the electron-bulk longitudinal-optical phonon interaction. We construct the variational wave function as the direct product of an electronic part and a part describing coherent phonons generated by the Low–Lee–Pines transformation from the vacuum state. We use two explicit forms of coherent states, Perelomov and Barut-Girardello states, to represent the electronic part in the quantum well spectrum. Our results show that in a coherent state basis for electrons the basic polaron parameters such as the energy gap shift and effective mass are further enhanced compared to those obtained with the conventional sinusoidal form of the basis. The difference between the two types of quantum well coherent states appears in polaronic interactions in quantum wells. We extend the calculations in order to estimate polaron lifetimes for a variety of different material systems.     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Effects of tunneling coupling on plasmon modes in asymmetric double-quantum-well structures

The collective charge density excitations in asymmetric double-quantum-well (DQW) structures with different tunneling strengths are systematically studied. In particular, the damping properties of the plasmon modes in various tunneling strengths are investigated in detail. It is shown that plasmon modes in asymmetric DQW structures are quite different from those in symmetric DQW systems. In weak tunneling regime, an intra-subband mode ω _- with an acoustic-like dispersion relation which is damped in symmetric DQW structures arises and coexists with the optical-like mode ω ₊ while the inter-subband mode ω ₁₀ is highly damped. With the tunneling strength being increased, the ω ₁₀ branch gradually becomes undamped and emerges out of the (1-0) single-particle continuum, whereas the ω _- branch gradually approaches the (0-0) single-particle continuum. In intermediate coupling regime, these three branches of modes coexist undamped. In strong tunneling regime, ω _- enters the (0-0) single-particle continuum and becomes damped. Consequently, only the ω ₊ and ω ₁₀ modes exist in this regime. Received 10 July 2001 and Received in final form 17 September 2001     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Propagation of electrons in coupled quantum wells

Summary We study propagation of an electron wave in a double-quantum-well structure formed by alternate layers of GaAlAs and GaAs. In such a structure, electron states parallel to the layers are described by 2D plane waves and in the perpendicular direction by the bound states of the confining potential. We show that an electron, initially introduced in one well, will execute oscillations between the two wells of the structure. Although the frequency of oscillations depends primarily on the distance separating the wells and the confining potential, it is shown in this paper that the frequency also depends on the effective mass of the electron, if it is different within and outside the well. Expressions are derived for the frequency of oscillations, taking into account the difference in the effective mass of the electron.     

Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from theelectron-longitudinal optical phonon interaction on the energyspectrum of a two-dimensional electron system with a one-dimensionalperiodic antidot array geometry created by a weak electrostaticmodulation potential, and subjected to a weak magnetic fieldmodulation as well as a uniform strong perpendicular staticmagnetic field. To incorporate the effects of electron-phononinteractions within the framework of Fröhlich polaron theory, wefirst apply a displaced-oscillator type unitary transformation todiagonalise the relevant Fröhlich Hamiltonian, and we thendetermine the parameters of this transformation together with theparameter included in the electronic trial wave function . On thebasis of this technique, it has been shown that the polaroniccorrections have non-negligible effects on the electronic spectrumof a two-dimensional electron system with a quantum antidot array,since switching such an interaction results in shifting thedegeneracy restoring points of Landau levels wherein the flatbandcondition is fulfilled, thus suppressing the Weiss oscillations.     

The role of layer-thickness deviation in dispersion and structure of plasmons in finite superlattices

We study the effects of layer thickness variations on the collective plasmon excitation modes of finite superlattices. Unlike other symmetry lowering mechanisms, thickness variation does not strongly localize the surface modes. We find that the reason for this insensitivity lies in the fact that the collective modes of a given finite structure must evolve continuously from the single-finite-superlattice at zero thickness deviation into modes of a pair of uncoupled finite structures at large thickness variation. We also show that this behavior is analogous to the evolution of molecular orbitals from atomic orbitals as the internuclear separation is reduced, in contrast to the analogy of the superlattice modes as a stack of coupled quantum wells. This emphasizes the difference between the electromagnetic symmetry of the finite superlattice and the structural symmetry. Received 16 April 2001 and Received in final form 6 July 2001     

Plasmons in asymmetric double quantum well structures

We investigate the effects of spatial asymmetry, tunneling coupling, and exchange-correlation correction on the plasmon modes in asymmetric double quantum well (DQW) structures in a time-dependent local-density approximation. Special attention is paid to the properties of the ω _- mode which is always damped in symmetric DQW systems. In addition, the results on the spectral weight of the excitations are also presented. In general, all the modes carry finite spectral weights and should be observable in resonant inelastic light scattering experiments for the specified values of the parameters. Received 2 July 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: c412-1@aphy.iphy.ac.cn     

Influence of the quantum dot shape on the determination of the electronic structure and electron decoherence

Theoretical calculations of electron–phonon scattering rates in AlGaN/GaN quantum dots (QDs) have been performed by means of effective mass approximation in the frame of finite element method. The influence of a symmetry breaking of the carrier's wave function on the electron dephasing time is investigated for various QDs shapes. In a QD system the electron energy increases when the QD shape changes from a spherical to a non-spherical form. In addition, the influence of the QD shape upon the electronic structure can be modulated by external magnetic fields. We also show that the electron–acoustic phonon scattering rates strongly depend upon both the QD shape and the applied magnetic field. As an additional parameter, the QD shape can be used to modify the electron–acoustic phonon interaction in a wide range. Moreover, the scattering rate of different transitions, such as Δm=0(1), presents distinct magnetic field dependency.     

Triggered single photons and entangled photons from a quantum dot microcavity

Current quantum cryptography systems are limited by the attenuated coherent pulses they use as light sources: a security loophole is opened up by the possibility of multiple-photon pulses. By replacing the source with a single-photon emitter, transmission rates of secure information can be improved. We have investigated the use of single self-assembled InAs/GaAs quantum dots as such single-photon sources, and have seen a tenfold reduction in the multi-photon probability as compared to Poissonian pulses. An extension of our experiment should also allow for the generation of triggered, polarization-entangled photon pairs. The utility of these light sources is currently limited by the low efficiency with which photons are collected. However, by fabricating an optical microcavity containing a single quantum dot, the spontaneous emission rate into a single mode can be enhanced. Using this method, we have seen 78% coupling of single-dot radiation into a single cavity resonance. The enhanced spontaneous decay should also allow for higher photon pulse rates, up to about 3 GHz. Received 8 July 2001 and Received in final form 25 August 2001     

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport

We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions (determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample boundaries. Received 19 August 2002 Published online 19 November 2002     

Fractional-dimensional polaron corrections in asymmetric GaAs-Ga1−xAlxAs quantum wells

Polaron effects in asymmetric GaAs-Ga_1−xAl_xAs quantum wells (QWs) are investigated within the framework of the fractional-dimensional space approach and by using second-order perturbation theory. A well-width dependence of the polaron corrections with a dip and a peak is obtained for both symmetric and asymmetric QWs. The dip and the peak occur in the case of asymmetric QWs for larger well widths than in the case of symmetric QWs. An enhancement of the contrast between the dip and the peak of the polaron energy shift is found for the case of asymmetric QWs. These results show the convenience of using asymmetric QWs instead of symmetric ones in any experimental attempt of detecting the dip and the peak of the polaron energy shift.     

A bound polaron in a spherical quantum dot

The binding energy of a bound polaron in a spherical quantum dot has been investigated by using the variational method. The influence of LO and SO phonons have taken into consideration. Result shows that the phonon contribution to the binding energy is dependent on the size of the quantum dot as well as the position of the impurity in the quantum dot. Numerical calculation on the ZnSe quantum dot shows that such contribution is about 5% to 20% of the total binding energy. Received: 13 October 1997 / Revised: 4 March 1998 / Accepted: 26 May 1998     

Weak and strong coupling regimes, vacuum Rabi splitting and two types of resonances

For two discrete-level quantum systems in interaction, we follow the displacement in the complex plane of the eigen-energies of the compound system when the excited level of one of the two systems is enlarged. These new points are usually called resonances and describe mixed unstable states. This allows us to define and to calculate a critical value of the coupling constant which separates two well-known coupling regimes. These two regimes are thus described in a unified way. In the study, resonances which are usually not taken into account occur. They are studied in the large continuum case provided by the coupling of the hydrogen atom to the states of the transverse electromagnetic field in the vacuum. We justify that some of these resonances be neglected in this case.     

Bound polaron in a wurtzite GaN/AlxGa1 − xN ellipsoidal finite-potential quantum dot

A variational method is used to study the ground state of a bound polaron in a weakly oblate wurtzite GaN/Al_xGa_1 − xN ellipsoidal quantum dot. The binding energy of the bound polaron is calculated by taking the electron couples with both branches of LO-like and TO-like phonons due to the anisotropic effect into account. The interaction between impurity and phonons has also been considered to obtain the binding energy of a bound polaron. The results show that the binding energy of bound polaron reaches a peak value as the quantum dot radius increases and then diminishes for the finite potential well. We found that the binding energy of bound polaron is reduced by the phonons effect on the impurity states, the contribution of LO-like phonon to the binding energy is dominant, the anisotropic angle and ellipticity influence on the binding energy are small.     

Influence of acoustic phonons on dephasing of free excitons in quantum wells

A theory of the dephasing rate of quasi-2D free excitons due to acoustic phonon interaction at low exciton densities is presented. Both deformation potential and piezoelectric couplings are considered for the exciton–phonon interaction in quantum wells. Using the derived interaction Hamiltonian obtained recently by us, exciton linewidth and dephasing rate are calculated as a function of the exciton density, exciton temperature, exciton momentum and lattice temperature.     

Intersubband scattering of cold electrons in a coupled quantum well with subband spacing below

We report measurements of the intersubband scattering rate between the first and second subband in a quantum-well structure with subband spacing (11 meV) smaller than the optical phonon energy. We measure the electron population in the second subband under CW excitation by a far-infrared laser tuned to the intersubband absorption frequency. This allows us to determine the intersubband relaxation rate using detailed balance. These measurements are novel because they are performed at very low excitation densities (I10 μW/cm²). In this regime the heating of the electron gas is negligible, so that the optically excited population in the upper subband greatly exceeds any thermal population induced by laser heating. Therefore, the relaxation rate we measure is controlled by intersubband scattering rather than carrier cooling. At low temperature we obtain an intersubband lifetime of which is power independent below 10⁻¹ W/cm², and approximately temperature independent for lattice temperatures between T=10 and 2.5 K.     

Effect of electron-phonon interaction on surface states in a ternary mixed crystal

A variational theory is proposed to study the surface states of electrons in a semi-infinite ternary mixed crystal, by taking the effect of electron-surface optical (SO) phonon interaction into account. The energy and the wave function of the electronic surface-states are calculated. The numerical results of the energies of the surface states of the polarons and the self-trapping energies are obtained as functions of the composition x and surface potential V₀ for several ternary mixed crystal materials. The results show that the electron-phonon interaction lowers the surface-state levels with the energies from several to scores of meV. It is also found that the self-trapping energy of the surface polaron has a minimum at some middle value of the composition x. It is indicated that the electron-phonon coupling effect can not be neglected. Received 4 January 1999 and Received in final form 7 January 2000     

Creation of entanglement between two electron spins induced by many spin ensemble excitations

We theoretically explore the possibility of creating spin entanglement by simultaneously coupling two electronic spins to a nuclear ensemble. By microscopically modeling the spin ensemble as a single mode boson field, we use the time-dependent Fr?hlich transformation (TDFT) method developed recently [Y. Li, C. Bruder, C.P. Sun, Phys. Rev. A 75, 032302 (2007)] to calculate the effective coupling between the two spins. Our investigation shows that the total system realizes a solid state based architecture for cavity QED. Exchanging such kind of effective boson in a virtual process can result in an effective interaction between two spins. It is discovered that a maximum entangled state can be obtained when the velocity of the electrons matches the initial distance between them in a suitable way. Moreover, we also study how the number of collective excitations influences the entanglement. It is shown that the larger the number of excitation is, the less the two spins entangle each other.