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Europhysics Letters (EPL)

Interference of cold atoms released from an optical lattice

Andrey R. Kolovsky

Published Oct 19, 2004• 7 citations
Publisher

Abstract

We study interference of the cold atoms which are released out of the quasi–one-dimensional optical lattice, for the different initial states of the system. In particular, in the case of the Mott-insulator initial state, the atomic-density distribution is shown to exhibit a non-trivial interference pattern, similar to that observed for BEC in double-well potential in the experiment by Andrews et al. ( Science 275 (1997) 637).

DOI
10.1209/epl/i2004-10212-8

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We study interference of the cold atoms which are released out of the quasi–one-dimensional optical lattice, for the different initial states of the system. In particular, in the case of the Mott-insulator initial state, the atomic-density distribution is shown to exhibit a non-trivial interference pattern, similar to that observed for BEC in double-well potential in the experiment by Andrews et al. ( Science 275 (1997) 637).
Motivated by the experimental observation of collapses and revivals of Bose matter wave field, we investigate correlation functions of cold bosons in an optical lattice. Within a simple model we examine two kinds of states: one that employs the commonly used notion of coherent states, and one that obeys the total number of atoms conservation. We identify rare situations at which these states behave differently. Typically, however, their predictions coincide and so: As a function of ``interaction time'' the interference pattern in the density undergoes collapse and revival. Exactly at revival times the system mimics the ideal gas case, in which all correlation functions factorize, while in the collapsed phase of the evolution the system effectively behaves as if initially there was no long-range coherence. Even in the latter case though, an interference pattern should be seen in a single experiment. We stress the role of column averaging, which in fact corresponds to an averaged observation of an ensemble of two-dimensional realizations. We also note that, contrary to the common belief, an interference pattern should also be seen in a single observation of a Mott state.
We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter–wave interference patterns. We complement these findings by self-consistent Hartree–Fock–Bogoliubov–Popov calculations for one-dimensional lattices, including the effects of a parabolic trapping potential.
The transition from a superfluid to a Mott-insulator (MI) phase has been observed in a Bose-Einstein condensate (BEC) of ytterbium (Yb) atoms in an optical lattice. An all-optically produced BEC of 174Yb^{174}\text{Y}\text{b}174Yb atoms was loaded into three-dimensional optical lattices produced by a 532 nm laser beam. The interference pattern was measured after releasing the quantum gas from the trapping potential. As increasing the optical lattice depth, we observed the disappearance of the interference patterns, which is a signature of entering the MI regime. This result is an important step into studies by using a combination of the MI state and the ultranarrow optical transition of ultracold alkaline-earth-metal-like atoms.
We present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions. We compare the superfluid fraction to other physical quantities, i.e., the interference pattern after ballistic expansion, the quasimomentum distribution, and number fluctuations. We have performed exact numerical calculations of all these quantities for small one-dimensional systems. We show that the superfluid fraction alone exhibits a clear signature of the Mott-insulator transition. Observables like the fringe visibility, which probe only ground-state properties, do not provide direct information on superfluidity and the Mott-insulator transition.
Abstract We have studied the interference of degenerate quantum gases in a vertical optical lattice. The coherence of the atoms leads to an interference pattern when the atoms are released from the lattice. This has been shown for a Bose‐Einstein condensate in early experiments. Here we demonstrate that also for fermions an interference pattern can be observed provided that the momentum distribution is smaller than the recoil momentum of the lattice. Special attention is given to the role of interactions which wash out the interference pattern for a condensate trapped in the lattice but do not affect a spin polarized Fermi gas, where collisions at ultra cold temperatures are forbidden. Comparing the interference of the two quantum gases we find a clear superiority of fermions for trapped atom interferometry.