| Quantum dots and photonic crystals are now two man-made materials in the forefront of international research。However,participation of these materials has induced the the electron-phonon interaction along with the phonon bath that arose some intresting features, although different effects of which on the Quantum dots and photonic crystals。The work what we have done is mainly included of three parts as follow。First,in the Chapter Ⅱ, We theoretically investigate the influence of the phonon-mediated coupling on the properties of the laser generated by a single red-detuned quantum dot (QD), where the QD is coherently driven and coupled to a microscopic cavity which can be engineered in a photonic band-gap (PBG) material。In the low-temperature limit, the phonon-mediated coupling is deleterious to the emission of photon into cavity field and the threshold behavior of the laser persists after the inclusion of the phonon-mediated processes。Without being engineered in the PBG material, if the damping rate κ of the cavity is close to but smaller than the phonon-mediated spontaneous emission rate y of the dot, the photon statistics of the cavity field change from super-Poissonian to sub-Poissonian。The nonclassical effect can be achieved due to the phonon-mediated processes induced by the electron-phonon interaction and the off-resonant dot-cavity coupling。The nonclassical effect can be enhanced by the PBG material。When the effect of the thermal phonon is taken into account, the cavity field exhibits the super-Poissonian property。If κ is much smaller than y, the phonon-mediated processes can lead to the increase (decrease) of the photons provided that the incoherent pumping rate is lower (higher) than the effective phonon-mediated threshold。But, if κ is close to or larger than y, the emission of the photon may dominate the absorption process, strengthening the intensity of the cavity field。Then, in the Chapter III, We propose a scheme for the quadrature squeezing of the cavity field via dissipative processes and investigate the effect of the electron-phonon interaction (EPI) on the squeezing, where the cavity is off-resonantly coupled with a coherently-driven quantum dot (QD) which is allowed to interact with an acoustic-phonon reservoir。Under certain conditions, the participation of the phonon induced by both the EPI and the off-resonant coupling of the cavity with the QD enables the dissipative processes to occur resonantly in the dressed state of the QD。The cavity-mode photons emitted or absorbed during the phonon-mediated dissipative processes are correlated, thus leading to the squeezing of the cavity field。A squeezed vacuum reservoir for the cavity field is built up due to the EPI plus the off-resonant coupling between the cavity and the QD。The numerical results indicate that the degree of squeezing is maximal in low temperature limit, but the increasing temperature of the phonon reservoir could hinder the squeezing and degrade the degree of the squeezing of the cavity field。In addition, the photonic crystal could enhance the quadrature squeezing of the cavity field。The third part of work is illusrated in the Chaper IV that we investigate the effects of a low-frequency (acoustic) phonon bath on the dynamics of a quantum dot modeled as a cascade three-level system。We show that the phonon bath appears to the upper transition of the cascade system as a broadband reservoir of inverted rather than conventional harmonic oscillators。The action of the annihilation and creation operators of the inverted oscillator are interchanges relative to those of the usual harmonic oscillator that it serves as a linear amplifier to the system, and thereby gives rise to unusual features in the dynamics of the quantum dot。We find that the phonon bath, although being in a thermal state, affects the quantum dot as a correlated-type reservoir which results in the decay of the system to a correlated two-photon state with the population distribution no longer obeying a Boltzmann distribution。It is particularly interesting that even for a zero-temperature phonon reservoir, the steady state is a correlated state which, under appropriate conditions on the Rabi frequencies and the damping rates, can reduce to a strongly correlated pure state。It is shown that the two-photon correlations result in a significant squeezing and strong two-photon correlations in the radiation field emitted by the quantum dot。The presence of the correlations in the system is manifest in the presence of quantum beats in the time evolution of the populations and the radiation intensity。The effect of the ordinary spontaneous emission on the features induced by the phonon bath is also discussed。... |
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