Theoretical Study Of Quantum Dissipative Dynamics In Semiconductor Quantum Dot Systems

Quantum information processing,as an interdisciplinary subject of both quantumphysics and computer science,has received considerable attention in the past twodecades.Because of the advantage in scalability,quantum computing based on semi-conductor quantum dots (QD's) becomes one of the frontier subjects in quantum infor-mation science.Not only important in the potential applications,studies of quantumcoherent effects in confined systems can also give us a better understanding of the basicprinciples in quantum mechanics.In this Ph.D thesis,we study the quantum dissipativedynamics of the QD systems.Chapter 1 gives an overview of the fabrication,dissipative phenomena,and quantumcoherent effects of the QD systems.In Chapter 2,we describe the master equation approach used in this thesis.Aftertaking the trace over the environmental degrees of freedom,the master equation of aconfined system can be used to characterize the dynamics of the system.Also,infor-mation of the system,for example,the state probability,the relaxation time (T₁) andthe decoherence time (T₂) of the system,can be obtained using the master equation.In Chapter 3,we study electron transport through a quantum dot,connected to non-magnetic leads,in a magnetic field.A super-Poissonian electron noise due to the effectsof both interacting localized states and dynamic channel blockade is found when theCoulomb blockade is partially lifted.This is sharp contrast to the sub-Poissonian shotnoise found in the previous studies for a large bias voltage,where the Coulomb block-ade is completely lifted.Moreover,we show that the super-Poissonian shot noise canbe suppressed and will change to be sub-Poissonian by applying a sufficiently strongelectron spin resonance (ESR) driving field.In Chapter 4,we investigate shot noise in tunneling current through a double quan-tum dot (DQD) connected to two electric leads.We derive two master equations inthe occupation-state basis and the eigenstate basis to study the shot-noise propertiesof currents through the DQD.The approach based on the occupation-state basis,de-spite widely used in many previous studies,is valid only when the interdot couplingstrength is much smaller than the energy difference between the two dots.In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling.Using realistic model parameters,we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdotcoupling is not small.Furthermore,properties of the shot noise predicted using theeigenstate basis successfully reproduce qualitative features found in a recent experi-ment.In Chapter 5,we investigate the dissipative dynamics of a solid-state qubit with anextra electron confined to either one of two coupled QDs.Previous theoretical workbased on Bloch-type rate equations gave an unphysical uniform occupation probabilityof the electron in the QDs even for non-identical dots.We show that this is due toneglecting higher order interactions in the analysis.By including higher order terms,we obtain expected asymmetric occupation probabilities for non-identical dots.Ourwork demonstrates that the high order interaction terms can lead to important qualitativeimpacts on the operation of the qubit.In Chapter 6,we study the cooling of a mechanical resonator (MR) that is capaci-tively coupled to a DQD.The MR is cooled by the dynamical backaction induced by thecapacitive coupling between the DQD and the MR.The transition between the two dotsof the DQD is excited by an a.c.field and afterwards a tunneling event results in the de-cay of the excited state of the DQD.An important advantage of this system is that boththe energy level splitting and the decay rate of the DQD can be well tuned by varyingthe gate voltage.We find that the steady average occupancy,below unity,of the MR canbe achieved by changing both the decay rate of the excited state and the red-detuningbetween the transition frequency of the DQD and the microwave frequency,in analogyto the laser sideband cooling of an atom or trapped ion in atomic physics.Our resultsshow that the cooling of the MR to the ground state is experimentally implementable.