Theory Research On Quantum Control Of Multiple Degrees Of Freedom In Solid-state Spin System

The intersection of quantum mechanics and information science has produced a new field,quantum information and quantum computing which has attracted much attention because of its powerful ability solving some important problems.Among many platforms used to realize quantum information process,solid state system is considered as a promising candidate by the international academic community due to its unique advantages.Common solid-state systems include superconducting quantum bits,semiconductor quantum dots,rare-earth ion doped in crystals and nitrogen vacancy centers in diamond.Among them,the nitrogen vacancy center in diamond,semiconductor quantum dots,rare-earth-doped ion crystals are all used to bind the electron spin or nuclear spin in a certain way in the solid state system,which are typical solid state spin systems.Superconducting quantum bit is a solid-state circuit device.As an artificial atom,it can also be seen as an artificial solid-state spin system.These different solid-state spin systerms have different advantages and can play different important roles in the quantum information process.For example,superconducting quantum bits have mature integrability and high-fidelity gate operation,which can be used as an ideal carrier for quantum processors.The nuclear spin coherence time in the rare-earth ion doped in crystals is extremely long.Under suitable operations,the coherence time can reach the order of hours,which can be used as an excellent carrier for quantum memory.A remarkable feature of solid state spin system is that it has various degrees of freedom,such as electron spin,nuclear spin,multi-level structure,etc.These rich degrees of freedom,on the one hand,provide an ideal physical carrier for the quantum information process,on the other hand,they also bring complex coupling and interaction,and various decoherence mechanisms of the external environment.These new features are not only an unknown field that has not been fully explored,but also bring new challenges to the development of the corresponding quantum control methods.To realize a practical quantum information process on the solid-state spin system,we will face many key and important problems:how to use the multiple degrees of freedom of the solid-state system to design various quantum information processors and quantum information memories,how to realize the high-fidelity quantum manipulation of multiple degrees of freedom in the complex solid-state environment,how to realize the high-fidelity state transfer between different quantum information units,and so on.The above important issues are the forefront of the scientific community’s attention,and are in the ascendant period and pregnant with important breakthroughs.In view of the above important problems,this thesis has carried out the research of quantum control based on multiple degrees of freedom of solid state spin system.The content of this thesis is mainly divided into two parts:The first part is to design new quantum control schemes for common solid-state spin systems,including electronic spin,nuclear spin and other degrees of freedom.These schemes include adiabatic methods,geometric phase methods,etc.Using new control methods can effectively improve some characteristics of the solid-state spin system,such as quantum storage efficiency,gate operation fidelity,and so on.In the second part,we introduce phonon,an important degree of freedom in the solid state system,to explore the special contribution of phonon to the hybrid spin system.This is a new field that has not been explored before.We found that the phonon superradiance has a completely different dynamics and scaling law from the traditional photon superradiance,and the radiative cooling of phonons can also have a completely different new process and mechanism from the traditional radiative cooling of photons.The main innovations of this thesis are:1.For quantum memory based on solid state spin,a novel modulated adiabatic pulse is designed,which cancels the non-adiabatic transition of the evolution process and effectively improves the performance of quantum memory.At present,the highest storage efficiency reported in the experiment is only 67%,while our scheme can significantly improve it to 93%.2.For quantum nodes based on solid state spin,a new geometric gate operation is designed,which achieves high fidelity by utilizing the robustness of geometric phase.At present,the highest door operation fidelity reported in the experiment is only 86%,while our scheme can significantly improve it to 98%.3.For the quantum register based on solid state spin,a new geometric LandauZener Stü kelberg-Majorana interference process is designed.We find that there is a geometric phase accumulated in each autorotation space,and the high-fidelity state transmission of the electron spin state and the nuclear spin state is realized.At present,the highest transmission fidelity reported in the experiment is 88%,while our scheme can significantly improve it to 98.5%.4.For the hybrid system composed of superconducting qubits and phonon fields,we find that superconducting qubits have giant atom effect at this time,which can realize multi-point coupling with phonon fields,thus changing the dynamics and scaling law of phonon superradiance.This is a completely different phenomenon from the traditional photon superradiance and represents a new direction of quantum acoustics.5.For the complex hybrid system composed of spin ensemble,phonon bath and optical cavity field,we find that the spin system can not only radiate photons,but also radiate phonons and photons simultaneously.This is a completely different phenomenon from the traditional laser cooling of atoms.It is a new field with rich physical content and has not been explored.