Quantum control of Bose-Einstein-Condensates (BEC) had been found for one and two dimension cases. Firstly in this paper, we want to control BEC at electro-magnetic field in three dimension optical lattice theoretically. The trapped particles in constructed lattices can be made and controlled by optical pulse, and known as molasses. It is evident that quantum control theory is worked for physical particles in BEC status. It is a survey with system control and quantum particle physics. Future work is to focus on collaborating with real laboratory.
Quantum control of Bose-Einstein-Condensates (BEC) had been found for one and two dimension cases. Firstly in this paper, we want to control BEC at electro-magnetic field in three dimension optical lattice theoretically. The trapped particles in constructed lattices can be made and controlled by optical pulse, and known as molasses. It is evident that quantum control theory is worked for physical particles in BEC status. It is a survey with system control and quantum particle physics. Future work is to focus on collaborating with real laboratory.
Quantum control of Bose-Einstein-Condensates (BEC) had been found for one and two dimension cases. Firstly in this paper, we want to control BEC at electro-magnetic field in three dimension optical lattice theoretically. The trapped particles in constructed lattices can be made and controlled by optical pulse, and known as molasses. It is evident that quantum control theory is worked for physical particles in BEC status. It is a survey with system control and quantum particle physics. Future work is to focus on collaborating with real laboratory.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
In this theoretic work, trapped particles at matter surface to be considered as target system of quantum control. At the framework of variational method in Hilbert space, it would be quite interesting for us to explore particles which is trapped via optical lattice or other kinds of constraints at a matter surface (metal, crystal). The aim of this task is to survey theoretical control for quantum particles as they are appeared and trapped at matter surface (cf. [1]). The physical background of this work is laying on the specified particles motion or reaction under a certain chemical surface. As is well known, one can move a particle at surface smoothly through a point force above it or according to a proper angle, such quantum mechanical motion had already been achieved by the IBM team several years ago. At the viewpoint of quantum control, what is theoretic support? Can we make these control theoretically, computationally or experimentally? In fact, free trapped particles had been considered by scientists and researchers at worldwide scale. The most exciting things in this study is to take particle as target as it constrained on a surface. Theoretically, this work is to describe quantum control system consisting of time-varying Schrodinger equation at physical constraints condition. Then to apply control theory to quantum system of trapped particles, find and characterize optimal quantum control. Further, to compose optimality system (Euler-Lagrange system). Comprising of control free trapped particle, this work is focusing on control taking place at matter surface (on it particle is trapped), that is, try to discuss the external force constrain (e.g. optical lattice) and surface constrain are acting at particle together. Amazing result is desired in control of different multi-forces as control inputs, what would be happened as a particle changing its position, displacement or status under trapped situation? can we make a trapped chemical quantum well, or a physical optical lattice which worked using external force? what is extension of such kind of works at a variety of fields? whether the general quantum control is worked in this case? It is the purpose to solve these mysteries in this work, and report the initial conclusion of theoretic aspect for trapped particle at matter surface.