Multiphonon processes in a model quantum dot (QD) containing two electronic states and several optical phonon modes are considered taking into account both intra-and inter-level terms. The Hamiltonian is exactly diagonalized including a finite number of multi-phonon processes, large enough as to guarantee that the result can be considered exact in the physically important region of energies. The physical properties are studied by calculating the electronic Green's function and the QD dielectric function. When both the intra-and inter-level interactions are included, the calculated spectra allow for explanation of several previously published experimental results obtained for spherical and self-assembled QDs, such as enhanced 2LO phonon replica in absorption spectra and up-converted photoluminescence. An explicit calculation of the spectral line shape due to intra-level interaction with a continuum of acoustic phonons is presented, where the multi-phonon processes also are shown to be important. It is pointed out that such an interaction, under certain conditions, can lead to relaxation in the otherwise stationary polaron system. PACS numbers: 78.67.De; 63.22.+m; 63.20.Kr Keywords: quantum dot, phonon, exciton, absorption, emission Rule, the broadening could be a lifetime effect owing to the electron (or exciton) transition to another state with emission or absorption of an optical phonon. However, it would require strict energy conservation in the electronphonon scattering, i.e. exact resonance between the optical phonon energy and level spacing, which should be rather accidental. This kind of argument also justified the theoretical concept of "phonon bottleneck", a very slow carrier relaxation which should be inherent to small QDs 2 . Nevertheless, an efficient phonon-mediated carrier relaxation has been reported in a number of works 21,28,30 . All these experimental results imply that multiphonon processes are important and that the e-ph interaction in QDs must be treated in a non-perturbative way, even for the moderate values of the coupling constants coming out from the calculations 31 . An important ingredient to be included is the non-adiabaticity of this interaction 2,7,22 leading to a phonon-mediated coupling of different electronic levels, even if they are separated by an energy quite different from the optical phonon energy. This is essential for understanding those experimental results which are in clear disagreement with the single level-generated Franck-Condon progression.Polaron effects in QDs have been studied theoretically in several recent papers 32,33,34,35 . The model considered in these works included two electronic levels and several Einstein phonon modes. The one-electron spectral function was obtained applying either self-consistent perturbation theory approximations 32,33 or exactly, using a combined analytical and numerical approach 34 . The results calculated using the perturbation theory approaches show shift and broadening of the levels, even for a sufficiently large detuning (defined ...

Phonon-assisted tunneling in a double barrier resonant tunneling device can be seen as a resonance in the electron-phonon Fock space which is tuned by the applied voltage. We show that the geometrical parameters can induce a symmetry condition in this space that can strongly enhance the emission of longitudinal optical phonons. For devices with thin emitter barriers this is achieved by a wider collector barrier.Progress in mesoscopic semiconductor devices [1] and molecular electronics [2] is driven by the need of miniaturization and the wealth of new physics provided by coherent quantum phenomena. A fundamental idea behind these advances was Landauer's view that conductance is transmittance [3,4]. Hence, the typical conductance peaks and valleys, observed when some control parameter is changed, are seen as fringes in an interferometer. However, the many-body electron-electron (ee) and electron-phonon (e-ph) interactions restrict the use of this picture. The e-e effects received much attention in different contexts [1]. While interest on e-ph interaction remained mainly focused on double barrier Resonant Tunneling Devices (RTD) [5], where phononassisted tunneling shows up as a satellite peak in a valley of the current-voltage (I-V) curve, recent observation of electro-mechanical effects in molecular electronics [6] requires a reconsideration of the e-ph problem. Theory evolved from a many-body Green's function in a simplified model for the polaronic states [7] to quantum and classical rate equations approach [8]. The latter uses an incoherent description of the e-ph interaction by adopting an imaginary self-energy correction to the electronic states [9,10].In this article, we analyze a quantum coherent solution of transport with e-ph interaction. We resort to a mapping of the many-body problem into a one-body scattering system where each phonon mode adds a new dimension to the electronic variable [11,12]. Transmission of electrons between incoming and outgoing channels with different number of phonons are then used in a Landauer's picture where the only incoherent processes occur inside the electrodes. This allows to develop the concept of resonance in the e-ph Fock space and the identification of the control parameters that optimize the coherent processes leading to a maximized phonon emission. It also gives a clue as to how "decoherence" arise within an exact many-body description. As an application, we consider a RTD phonon emitter where the relevant parameters are best known. There, the first polaronic excitation serves as an "intermediate" state for the phonon emission. An electron with kinetic energy ε ≤ ε F and potential energy eV in the emitter decays through tunneling into an electron with energy ε + eV−hω 0 in the collector plus a longitudinal optical (LO) phonon. The tuning parameter is the applied voltage while the optimization of phonon emission requires the tailoring of the tunneling rates.Let us consider a minimal Hamiltonian:where c + j and c j are electron creation and annihilation operators at s...

Resonant tunnelling in a double-barrier heterostructure (DBHS) designed in order to produce an intense coherent emission of phonons is studied theoretically. This emission is achieved when the energy difference between the first excited level and the ground state in the well is close to the LO-phonon energy. The LO phonons emitted during the electron transition decay into a pair of (LO and TA) phonons that leave the well in the [111] direction. These secondary TA phonons are coherent and form a beam that we call a SASER (by analogy with 'laser'). The circulating current and the populations of phonons and electrons in the well are calculated by solving appropriate kinetic equations. Some possible applications of this system are discussed.

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