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.
Optimal control of the transport of Bose-Einstein condensates with atom chips
