Modèle s'excite
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Modèle s'excite
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2: évolution temporelle de la population de l'état excité dans le cadre du modèle d'Einstein
... [97][98][99] and on the lecture notes in Refs. [100, 101] . ...
In recent years, the field of quantum optics has thrived thanks to the possibility of controlling light-matter interaction at the quantum level.This is relevant for the study of fundamental quantum phenomena, the generation of artificial quantum systems, and for quantum information applications.In particular, it has been possible to considerably increase the intensity of light-matter interaction and to shape the coupling of quantum systems to the environment, so to realise unconventional and highly nonclassical states.However, in order to exploit these quantum states for technological applications, the question of how to measure and control these systems is crucial.Our work is focused on proposing and exploring new protocols for the measurement and the control of quantum systems, in which strong interactions and peculiar symmetries lead to the generation of highly nonclassical states.The first situation that we consider is the ultrastrong coupling regime in cavity (circuit) quantum electrodynamics.In this regime, it becomes energetically favourable to have photons and atomic excitations in the ground state, that is no more represented by the standard vacuum.In particular, in case of parity symmetry, the ground state is given by a light-matter Schrödinger cat state.However, according to energy conservation, the photons contained in these exotic vacua are bound to the cavity, and cannot be emitted into the environment.This means that we can not explore and control them by simple photodetection.In our work we propose a protocol that is especially designed to overcome this issue.We show that we can infer the photonic properties of the ground state from the Lamb shift of an ancillary two-level system.Another class of systems in which the fundamental parity symmetry leads to very unconventional quantum states is given by two-photon driven-dissipative resonators.Thanks to the reservoir engineering, it is today possible to shape the interaction with the environment to stabilize the system in particularly interesting quantum states.When a resonator (an optical cavity) exchanges with the environment by pairs of photons, it has been possible to observe the presence of optical Schrödinger cat states in the transient dynamics of the system.However, the quantum correlations of these states quickly decays due to the unavoidable presence of one-photon dissipation.Protecting the system against this perturbation is the goal of the parity triggered feedback protocol that we present in this thesis
... These loads are likely to move under the action of the electric field of an electromagnetic wave. In our study, one is interested has to determine the optical properties of the medium while being based on the Lorentz model [5] and to study the influence of the electrons number on the index of the vapor. ...
Optical properties of a dielectric medium consisting of an atomic vapor are investigated theoretically using the model of elastically bound electrons. This model describes the interaction of an electromagnetic field with the bound electrons to the vapor atoms [7]. In this paper, we propose a formalism which takes into accurate the effect of the number of electrons on the vapor index. We use the approximation of free electrons (no interaction between free electrons).
... These loads are likely to move under the action of the electric field of an electromagnetic wave. In our study, one is interested has to determine the optical properties of the medium while being based on the Lorentz model [5] and to study the influence of the electrons number on the index of the vapor. 1) Model of the elastically bound electron: Within the framework of this model, the electron is subjected to: An elastic force of recall, proportional to its displacement r compared to its position of balance: . ...
Optical properties of a dielectric medium consisting of an atomic vapor are investigated theoretically using the model of elastically bound electrons. This model describes the interaction of an electromagnetic field with the bound electrons to the vapor atoms [7]. In this paper, we propose a formalism which takes into accurate the effect of the number of electrons on the vapor index. We use the approximation of free electrons (no interaction between free electrons).
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From Wikipedia, the free encyclopedia
Quasiparticle which is a bound state of an electron and an electron hole
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An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force . It is an electrically neutral quasiparticle that exists in insulators , semiconductors and some liquids. The exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge. [1] [2] [3]
An exciton can form when a material absorbs a photon of higher energy than its bandgap . [4] This excites an electron from the valence band into the conduction band . In turn, this leaves behind a positively charged electron hole (an abstraction for the location from which an electron was moved). The electron in the conduction band is then less attracted to this localized hole due to the repulsive Coulomb forces from large numbers of electrons surrounding the hole and excited electron. These repulsive forces provide a stabilizing energy balance. Consequently, the exciton has slightly less energy than the unbound electron and hole. The wavefunction of the bound state is said to be hydrogenic , an exotic atom state akin to that of a hydrogen atom . However, the binding energy is much smaller and the particle's size much larger than a hydrogen atom. This is because of both the screening of the Coulomb force by other electrons in the semiconductor (i.e., its relative permittivity ), and the small effective masses of the excited electron and hole. The recombination of the electron and hole, i.e., the decay of the exciton, is limited by resonance stabilization due to the overlap of the electron and hole wave functions, resulting in an extended lifetime for the exciton.
The electron and hole may have either parallel or anti-parallel spins . The spins are coupled by the exchange interaction , giving rise to exciton fine structure . In periodic lattices, the properties of an exciton show momentum (k-vector) dependence.
The concept of excitons was first proposed by Yakov Frenkel in 1931, [5] when he described the excitation of atoms in a lattice of insulators. He proposed that this excited state would be able to travel in a particle-like fashion through the lattice without the net transfer of charge.
Excitons are often treated in the two limiting cases of small dielectric constant versus large dielectric constant; corresponding to Frenkel exciton and Wannier–Mott exciton respectively.
In materials with a relatively small dielectric constant , the Coulomb interaction between an electron and a hole may be strong and the excitons thus tend to be small, of the same order as the size of the unit cell. Molecular excitons may even be entirely located on the same molecule, as in fullerenes . This Frenkel exciton , named after Yakov Frenkel , has a typical binding energy on the order of 0.1 to 1 eV . Frenkel excitons are typically found in alkali halide crystals and in organic molecular crystals composed of aromatic molecules, such as anthracene and tetracene . Another example of Frenkel exciton includes on-site d - d excitations in transition metal compounds with partially-filled d -shells. While d - d transitions are in principle forbidden by symmetry, they become weakly-allowed in a crystal when the symmetry is broken by structural relaxations or other effects. Absorption of a photon resonant with a d - d transition leads to the creation of an electron-hole pair on a single atomic site, which can be treated as a Frenkel exciton.
In semiconductors, the dielectric constant is generally large. Consequently, electric field screening tends to reduce the Coulomb interaction between electrons and holes. The result is a Wannier–Mott exciton , [6] which has a radius larger than the lattice spacing. Small effective mass of electrons that is typical of semiconductors also favors large exciton radii. As a result, the effect of the lattice potential can be incorporated into the effective masses of the electron and hole. Likewise, because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than that of a hydrogen atom, typically on the order of 0.01 eV . This type of exciton was named for Gregory Wannier and Nevill Francis Mott . Wannier–Mott excitons are typically found in semiconductor crystals with small energy gaps and high dielectric constants, but have also been identified in liquids, such as liquid xenon . They are also known as large excitons .
In single-wall carbon nanotubes , excitons have both Wannier–Mott and Frenkel character. This is due to the nature of the Coulomb interaction between electrons and holes in one-dimension. The dielectric function of the nanotube itself is large enough to allow for the spatial extent of the wave function to extend over a few to several nanometers along the tube axis, while poor screening in the vacuum or dielectric environment outside of the nanotube allows for large (0.4 to 1.0 eV ) binding energies.
Often more than one band can be chosen as source for the electron and the hole, leading to different types of excitons in the same material. Even high-lying bands can be effective as femtosecond two-photon experiments have shown. At cryogenic temperatures, many higher excitonic levels can be observed approaching the edge of the band, [7] forming a series of spectral absorption lines that are in principle similar to hydrogen spectral series .
In a bulk semiconductor, a Wannier exciton has an energy a
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