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A quantum theory of spectral parameters and oscillator strengths of quantum transitions in an active region, which contains cascades of wide quantum wells with a complicated potential profile is developed. A new spatial design of the cascade is calculated and proposed with such an asymmetric arrangement of the wells and barriers, in which, without an applied electric bias, the magnitudes of oscillator strengths are considerable and one-way resonant-tunneling transport of electrons is observed. As a result, it becomes possible to ensure a successful functioning of the broadband photodetector in the far IR range., Comment: 13 pages, 2 figures, 3 tables

Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at $T=0$ K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed., Comment: 8 pages, 1 figure

The theory of renormalized energy spectrum of a multi-level quasiparticle interacting with polarization phonons at $T=0$ K is developed within the Feynman-Pines diagram technique in a new approach. It permits a successive separation of multiplicative diagrams from non-multiplicative ones for all orders of mass operator, and their partial summing as well. The obtained mass operator is presented as a sum of branched chain fractions, which effectively take into account the multi-phonon processes. For the two-level quasiparticle it is shown that just the interlevel (non-diagonal) interaction with phonons fundamentally changes the properties of the spectrum. In the vicinity of all threshold energies, the quasi-equidistant phonon satellite bands (i.e., groups of energy levels) are formed. They correspond to the complexes of bound states of a quasi-particle with many phonons., Comment: 15 pages, 3 figures

Theory of the spectrum of localized two-level quasi-particle renormalized due to interaction with polarization phonons at cryogenic temperature is developed using the generalized method of Feynman-Pines diagram technique. Using the procedure of partial summing of infinite ranges of the main diagrams, mass operator is obtained as a compact branched chain fraction, which effectively takes into account multi-phonon processes. It is shown that multi-phonon processes and interlevel interaction of quasiparticle and phonons cardinally change the renormalized spectrum of the system depending on the difference of energies of two states, which either resonates with phonon energy or does not. The spectrum of non-resonant system contains renormalized energies of the main states and two similar infinite series of groups of phonon satellite levels. The spectrum of a resonant system contains a renormalized ground state and infinite series of satellite groups., Comment: 14 pages, 2 figures, 1 table

The theory of renormalized energy spectrum of localized quasi-particle interacting with polarization phonons at finite temperature is developed within the Feynman-Pines diagram technique. The created computer program effectively takes into account multi-phonon processes, exactly defining all diagrams of mass operator together with their analytical expressions in arbitrary order over the coupling constant. Now it is possible to separate the pole and non-pole mass operator terms and perform a partial summing of their main terms. The renormalized spectrum of the system is obtained within the solution of dispersion equation in the vicinity of the main state where the high- and low-energy complexes of bound states are observed. The properties of the spectrum are analyzed depending on the coupling constant and the temperature., Comment: 16 pages, 3 figures, 3 tables

Using the Feynman-Pines diagram technique, the energy spectrum of localized quasi-particles interacting with polarization phonons is calculated and analyzed in the wide range of energies at the finite temperature of the system. It is established that the general model of the system, besides the bound states known from the simplified model with an additional condition for the operator of quasi-particles number, contains the new bound states even for the systems with weak coupling. The contribution of multi-phonon processes into the formation of renormalized spectrum of the system is analyzed. The reasons of the appearance, behaviour and disappearance of separate pairs of bound states depending on the coupling constant and temperature are revealed., Comment: 13 pages, 4 figures

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant., Comment: 12 pages, 5 figures

The Hamiltonian of electrons interacting with interface phonons in three-barrier resonant tunneling structure is established using the first principles within the models of effective mass and polarization continuum. Using the Green's functions method, the temperature shifts and decay rates of operating electron states are calculated depending on geometric design of three-barrier nano-structure GaAs/Al$_{x}$Ga$_{1-x}$As which is an active region of quantum cascade detector. It is established that independently of the temperature, the energy of quantum transition during the process of electromagnetic field absorption is a nonlinear weakly varying function of the position of the inner barrier with respect to the outer barriers of the structure., Comment: 10 pages, 5 figures

Using the effective mass and rectangular potential approximations, the theory of electron dynamic conductivity is developed for the plane multilayer resonance tunnel structure placed into a constant electric field within the model of open nanosystem, and oscillator forces of quantum transitions within the model of closed nanosystem. For the experimentally produced quantum cascade laser with four-barrier active band of separate cascade, it is proven that just the theory of dynamic conductivity in the model of open cascade most adequately describes the radiation of high frequency electromagnetic field while the electrons transport through the resonance tunnel structure driven by a constant electric field., Comment: 10 pages, 2 figures

An exact solution of non-stationary Schrodinger equation is obtained for a one-dimensional movement of electrons in an electromagnetic field with arbitrary intensity and frequency. Using it, the permeability coefficient is calculated for a two-barrier resonance tunnel nano-structure placed into a high-frequency electromagnetic field. It is shown that a nano-structure contains quasi-stationary states the spectrum of which consists of the main and satellite energies. The properties of resonance and non-resonance channels of permeability are displayed., Comment: 8 pages, 3 figures

The non-perturbation theory of electronic dynamic conductivity for open two-barrier resonance tunnel structure is established for the first time within the model of rectangular potentials and different effective masses of electrons in the elements of nano-structure and the wave function linear over the intensity of electromagnetic field. It is proven that the results of the theory of dynamic conductivity, developed earlier in weak signal approximation within the perturbation method, qualitatively and quantitatively correlate with the obtained results. The advantage of non-perturbation theory is that it can be extended to the case of electronic currents interacting with strong electromagnetic fields in open multi-shell resonance tunnel nano-structures, as active elements of quantum cascade lasers and detectors., Comment: 10 pages, 2 figures

Within the model of rectangular potentials and different effective masses of electrons in different elements of plane two-barrier resonance tunnel structure there is developed a theory of spectral parameters of quasi-stationary states and active conductivity for the case of mono-energetic electronic current interacting with electromagnetic field. It is shown that the two-barrier resonance tunnel structure can be utilized as a separate or active element of quantum cascade laser or detector. For the experimentally studied In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As nano-system it is established that the two-barrier resonance tunnel structure, in detector and laser regimes, optimally operates (with the biggest conductivity at the smallest exciting current) at the quantum transitions between the lowest quasi-stationary states., Comment: 11 pages, 4 figures

The theory of dynamic conductivity of nanosystem is developed within the model of rectangular potentials and different effective masses of electron in open three-barrier resonance-tunnel structure in a constant homogeneous electric field. The application of this theory for the improvement of operating characteristics of quantum cascade laser active region (for the experimentally investigated In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As heterosystem) proves that for a certain geometric design of nanosystem there exists such minimal magnitude of constant electric field intensity, at which the electromagnetic field radiation power together with the density of current flowing through the separate cascade of quantum laser becomes maximal., Comment: 7 pages, 2 figures