Born-Oppenheimer approximation for an atom in constant magnetic fields

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. In Martinez-Sordoni \cite{MaSo2} such a case is also studied but their reduced Hamiltonian includes the vector potential terms. In this paper, using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields

Diffraction-Unlimited Position Measurement of Ultracold Atoms in an Optical Lattice

We consider a method of high-fidelity, spatially resolved position measurement of ultracold atoms in an optical lattice. We show that the atom-number distribution can be nondestructively determined at a spatial resolution beyond the diffraction limit by tracking the progressive evolution of the many-body wavefunction collapse into a Fock state. We predict that the Pauli exclusion principle accelerates the rate of wavefunction collapse of fermions in comparison with bosons. A possible application of our principle of surpassing the diffraction limit to other imaging systems is discussed.Comment: 6+6 pages, 3+3 figures, PRL accepted versio