| Quantum mechanics possesses various unique properties beyond the frame of classical physics,such as the tunneling of particles through potential barriers,the interference of particles,as well as the quantum entanglement.Quantum entanglement plays an important role in the development of quantum computing,quantum measurement and quantum information processing,etc.Both the fundamental research and the development of new applications require the preparation and manipulation of multi-qubit entangled states.There are mainly two approaches to construct multi-qubit entangled states.One approach is through the multi-particle entanglement,the other is through multiple degrees of freedom(DOFs)entanglement.Entanglement in multiple DOFs becomes the research hotspots thanks to many unique benefits,such as that it can increase the efficiency quantum information processing and the compatibility of quantum networks,etc.Ultracold atoms in optical lattices have become a promising quantum platform.Quantum entanglement has been studied in ultracold atoms confined in optical lattices,but these studies mainly focus on entanglement in single DOF and two DOFs.Investigation on entanglement in multiple DOFs has not been fully developed.In my doctoral thesis,I have carried out the theoretical investigation for the preparation and application of entanglement in multiple DOFs.Our research focus on the spin,orbital and spatial mode DOF in lattice cold atomic systems,etc.My doctoral project is carried out in two steps:(I)Theoretical research for preparation and properties of entanglement in orbital DOF based on ultracold atoms in optical lattice.(II)Theoretical research for the preparation scheme and physical properties of entanglement in multiple DOFs contributed by the orbital and spin DOFs of ultracold atoms in optical lattice.In the first step,the focus is mainly on the following two points:(1)The research for the rapid preparation of orbital entanglement.We used the special spatial symmetry of orbital DOF and have developed a symmetry-protected resonant shaking scheme to selectively excite degenerate entangled states.(2)The study for the dynamical evolution properties of the entangled state in orbital DOF,including the dynamic transformation between the Valencebond and Triplet-bond entanglement,and the dynamic processes of many-body correlation induced tunneling under a specific driving Hamiltonian.Moreover,we utilized this correlation induced tunneling to distinguish the four Bell-basis encoded within the orbital DOF and perform quantum metrology with precision reaching beyond 1/N-scaling.In the second step,we turn to the following subjects:(1)Based on the study of photons entangled states in multiple DOFs,we determined the property of the ultracold atoms entangled states in multiple DOFs,including orbital and spin DOF,and decided the target form of the hyper entanglement and hyper-hybrid entanglement in multiple DOFs.(2)We proposed a scheme to generate scalable hyper entanglement and hyper-hybrid entanglement in multiple DOFs through symmetry-protected resonant lattice shaking and spin-dependent symmetry-protected resonant lattice shaking,respectively.(3)We further explore the unique advantages of multiple DOFs entanglement of ultracold atomic lattice in manipulation,transfer and detection.We constructed different single-body and two-body quantum logic gate operations under the combination of different DOFs,transferred the entangled states from the double-well superlattice to the plaquette superlattice,and quickly detect entanglement in plaquette superlattice.Utilized above unique advantages,we designed a theoretical scheme to verify the Mermin’s inequalities for hyper-hybrid entanglement of ultracold atoms in optical superlattices.We simplified the verification steps by utilizing the unique advantages of different DOFs in operation and detection,the traditional 256 measurements is greatly reduced to 16 measurements. |
