Decoherence And Quantum Control In Solid-State System

Quantum mechanics has inspired the rapid development of science and technology for one hundred years. Using the parallelism of quantum system with the coherence, quantum computation and quantum information have far more power than the classi-cal computer. But there are many rigorous requirements to realize them. Solid-state system becomes an important physical platform, such as superconducting system and quantum dot system, which can be scaled, integrated and tunable easily. At the same time, the noise in control parameters or the interaction between the system and the bath leads to decoherence of quantum system. For the Berry phase of quantum control, the geometric dephasing makes the phase unmeasurable. How many quantum logic gate operations can be done in the decoherence time is the most important factor to measure the performance of quantum system. Decoherence can be suppressed by quantum error correcting code, decoherence free subspace, dynamical decoupling, and so on.In this thesis, we study on decoherence and quantum control in solid-state system with the main aspects as follow:1. We introduce quantum bit and quantum logic gate in quantum computing and quantum information. The common physical platforms of quantum computer are pre-sented. We use master equation to deal with open quantum system, where Markovian master equation and non-Markovian master equation are derived briefly. We mainly discuss the concept of the Berry phase and its generalization. The related background knowledge of this thesis is given briefly.2. Charge qubit in solid-state quantum system shows the best coherence at the degeneracy point (sweet spot). But the longest decoherence time is observed at large positive bias in some recent double dot experiments. We consider three-level system with the excitation level in the right dot to reveal the mechanism of decoherence theo-retically. Spin-boson model is used to describe the interaction between the system and bath. In large positive bias region, two lowest levels make up a decoherence free sub-space. However, the σx interaction between the noise and two lowest levels at the de-generacy point causes the extra relaxation, which leads to the stronger decoherence than the large positive bias region. The results calculated by the master equation agree very well with the unexplained experiments. We analyze the coherent control via adiabatic-impulse model, which simplifies the applied pulse as optical interference device. Then we realize the high visibility of coherent oscillations by "hat-shape" pulse.3. Classical fluctuation field brings the random variable to the dynamic phase and causes the dynamic dephasing of quantum system. For the process of realizing the Berry phase, it also disturbs the closed loop and gives rise to the geometric dephasing. The tradition dynamical decoupling sequence is useful to cancel the dynamic phase and suppress the dynamic dephasing, but it doesn’t work for the geometric dephasing. In this thesis, we design two dynamical decoupling sequences to suppress the residual geometric dephasing. Results from the numerical simulations verify the validity of our designed sequences, which suppress the geometric dephasing successfully. Berry phase can be recovered from the chaos with the very high coherence. The improvement of the coherence decreases as the correlation time of the fluctuation field becomes short. In addition, the control in reality doesn’t harm the efficiency of the designed sequences when the width of applied π pulse is short enough.4. We show that the artificial two-level system interacts with one-dimensional coupled-resonator array, which functions as quantum switch. The coherent transport of single-photon is well controlled by the state of two-level system. Spin up and spin down correspond to switch on and switch off respectively, or vice versa. We improve the fi-delity of quantum switch by pre-adjusting the frequency of resonators around two-level system. Quantum switch realizes quantum beam splitter when two-level system is in the superposition state. The single-photon reflected wave-packet and transmitted wave-packet with the information of two-level system propagate to the remote resonators.