Atom-number filter in an optical latticeThis paper is dedicated to Peter Lambropoulos on the occasion of his jubilee.

Georgios M Nikolopoulos (1) , David Petrosyan (1)

1 Institute of Electronic Structure and Laser

We present an efficient procedure to filter out from an optical lattice, having inhomogeneous site occupation number, only preselected number of bosonic atoms per site and place them into another internal atomic state, creating thereby a lattice with desired site occupation number. Atom number filter in an optical lattice 2 Ultracold atoms in optical lattices [ 1 ] represent a remarkably clean and controllable system [ 2, 3 ] to realize the fundamental Bose-Hubbard model [ 4 ]. Its two main ingredients are the atom tunneling, or hopping J, between the neighbouring lattice sites and the on-site atom-atom interaction U. In a homogeneous lattice, when the kinetic energy due to the inter-site hopping dominates, J ? U, the atoms are delocalized over the entire lattice yielding a superfluid (SF) phase, while in the opposite regime of strong on-site interaction, U ? J, the hopping is energetically suppressed resulting in a Mott insulator (MI) phase with fixed integer number n of localized atoms at each lattice site. When a deep optical lattice is superimposed by a shallow confining potential, there can be MI phases with occupation numbers of n = 0, 1, 2,... in successive spatial shells [ 5, 6, 7, 8 ], separated by SF phases with intermediate mean occupation number corresponding to delocalized atoms on top of the filled MI shell. Experimentally [ 3 ], the quantum phase transition between the SF and MI phases is implemented by adiabatically increasing the lattice depth which results in the reduction of intersite tunneling amplitude and simultaneous increase of the on-site interaction [ 2 ]. If, however, the lattice potential is raised quickly, so that the tunneling is suddenly switched off, each site occupation " freezes " to whatever atom-number distribution it corresponded to just before the switching off, be it a SF, a MI, or a spatially-dependent combination of the two phases. In this paper, we propose a very efficient method to filter out from such a frozen (J = 0) optical lattice only the desired number N of atoms per site. This is achieved by using an external field which couples the initially populated internal atomic state |a? to another internal state |b? trapped by a second optical lattice potential. We show that, for strong enough state- (or lattice-) dependent on-site interactions, the coupling field with properly tuned frequency will selectively transfer to the second lattice only the singles (N = 1), the pairs (N = 2), or the triples (N = 3) of atoms, via the corresponding Nphoton resonant transition. Hence, after the transfer, the second lattice will only have the desired site occupation number N = 1, 2, or 3, while the first lattice will contain all the other occupation numbers n ? = N. Before proceeding, we note related, but different, earlier work. Rabl et al [ 9 ] proposed to reduce the site occupation number defects in an optical lattice by adiabatically transferring a chosen number of atoms to another internal state. DeMarco et al [ 5 ] studied similar systems employing rapid adiabatic transfer of atoms to the second internal state, or inducing resonant single-photon Rabi oscillations between the atomic states with occupation number-dependent Rabi frequencies. Mohring et al [ 10 ] discussed coherent extraction of atoms from a BEC reservoir into the quantum tweezers--tight trap--using adiabatic and resonant transfer techniques. del Campo et al [ 11 ] described the preparation of number states of strongly interacting atoms by reducing the depth and width of a one-dimensional trap.

Mots clés: Physical Sciences

Georgios M Nikolopoulos, David Petrosyan. Atom-number filter in an optical latticeThis paper is dedicated to Peter Lambropoulos on the occasion of his jubilee.. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010, 43 (13), pp.131001. ⟨10.1088/0953-4075/43/13/131001⟩. ⟨hal-00630005⟩