Ground-state Cooling Of A Mechanical Resonator Coupled With The Quantum Dots

Laser cooling of an atom, a trapped ion or microscopic systems, is a recent rapidly-developed topic about quantum optics, laser physics and quantum information science. Cooling a trapped ion, an atom or a mechanical resonator down to their ground-state not only offers a good platform to test the postulate of quantum mechanics and exploit their quantum behaviors, but also has important applications in high-precision detection of mass, spin, mechanical dis-placement and quantum information processing, thereby has attracted considerable attentions. Moreover, the semiconductor-quantum-dot (known as "artificial atom") systems offer promis-ing applications for this topic. Therefore, how to effectively cool the trapped ions down to their ground state, during the transport of the electron, is one of the interesting topic.This thesis is devoted to the investigation of the schemes for the ground-state cooling of a mechanical resonator coupled to different coupled quantum-dots systems from the following instructions (1) how to solve the problem that the cooling efficiency of the cooling is limited due to the off-resonant transition in traditional sideband cooling schemes;(2) whether the presence of the two-electron dark state can improve the cooling properties;(3) how to cancel both the carrier transitions and the blue sideband transitions.Firstly, in the strong Coulomb-blockade regime, we propose a scheme for ground-state cooling of a mechanical resonator coupled to two coupled quantum dots forming an effective A-type three-level structure and driven by one microwave field and two light fields respectively. For the first case, under certain conditions, the electronic state in the right dot can be modulated to be resonant with the upper dressed state, thereby the electron can be trapped in the lower one of the two dressed states. For the second case, the coupled quantum dots are driven by two light fields. It is found that the electron can be trapped in the dark state of the system. The mechanical resonator is cooled by absorbing phonons of the electron and jumping from dark state to bright state or one of the dressed states and then tunneling out of the two coupled dots. For both case, since the electron is almost trapped in the lower state of the cooling transition and the heating(cooling) transitions are resonant(far-off resonant), the cooling rate and the cooling efficiency are greatly improved. The resonator can be cooled via two-phonon process to its non-classical state.Then, we consider the ground-state cooling scheme of a resonator coupled to a triple quan-tum dot in the weak Coulomb-blockade regime. We obtained the general conditions for the cooling to the ground state with single and two-electron dark states. The results show that in the case of the interaction of the resonator with a single-electron dark state, no cooling of the res- onator occurs unless the quantum dots are not identical. The detuning has the effect of unequal shifting of the effective dressed states of the system that the cooling and heating processes occur at different frequencies. For the case of two electrons injected to the quantum dot system, the results predict that with the two-particle dark state, an effective cooling can be achieved even with identical quantum dots subject of an asymmetry only in the charging potential energies cou-pling the injected electrons. It is found that similar to the case of the single-electron dark state, the asymmetries result in the cooling and heating processes to occur at different frequencies. However, an important difference between the single and two-particle dark state cases is that the cooling process occurs at significantly different frequencies. This indicates that the frequency at which the resonator could be cooled to its ground state can be changed by switching from the one-electron to the two-electron Coulomb blockade processIn order to break the cooling limit of sideband cooling approach, we then employ the double quantum interference to propose a ground-state cooling scheme for a nanomechanical resonator coupled to a triple quantum dot possessing a four-level configuration. In this scheme, the carri-er transition is diminished by the destructive interference (the occurrence of dark state) arising from the coherent tunnelings of electron among the three dots. Furthermore, under certain con-ditions, the processes which might increase one phonon through the blue sideband transitions are prohibited due to the double destructive interference analogue to double electromagnetically induced transparency (EIT) mechanism. Thus, both the carrier and blue sideband transitions are canceled. The cooling process occurs when the electron trapped in the dark state absorbs one phonon of the resonator through the transition from the dark state to bright state and then to excited state, finally tunnels to the drain. As a result, the phonon occupation can be reduced to zero in the ideal case.