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arXiv:quant-ph/0701110 · Physical Review Letters

Preparing and Probing Atomic Number States with an Atom Interferometer

Jennifer Sebby-Strabley, Benjamin L. Brown, Marco Anderlini, Patricia J. Lee, William D. Phillips, J. V. Porto, Philip Johnson

Published May 17, 2007• 149 citations
arXivHTMLPDF

Abstract

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state.

DOI
10.1103/physrevlett.98.200405

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We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state.
We describe the design and implementation of a two-dimensional optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms in an optical lattice. Atoms in the square lattice can be placed in a double well with any of their four nearest neighbors. The properties of the double well (the barrier height and relative energy offset of the paired sites) can be dynamically controlled. The topology of the lattice is phase stable against phase noise imparted by vibrational noise on mirrors. We demonstrate the dynamic control of the lattice by showing the coherent splitting of atoms from single wells into double wells and observing the resulting double-slit atom diffraction pattern. This lattice can be used to test controlled neutral atom motion among lattice sites and should allow for testing controlled two-qubit gates.
Interference patterns produced by binomially splitting atom states in a double well optical lattice can be used to probe many important properties of this system, including double well tilt (and tilt inhomogeneities), the on-site interaction energy U, atom number distribution across the lattice, vibrational excitation, and lattice state coherence, making atom interferometry a powerful tool to analyze and characterize the structure and states of optical lattice systems, an essential task if they are to realize their potential for quantum information and for a variety of other proposed uses.
Using the quantum collapse and revival phenomenon of a Bose--Einstein condensate in three-dimensional optical lattices, the atom number statistics on each lattice site are experimentally investigated. We observe an interaction driven time evolution of on-site number fluctuations in a constant lattice potential with the collapse and revival time ratio as the figure of merit. Through a shortcut loading procedure, we prepare a three-dimensional array of coherent states with Poissonian number fluctuations. The following dynamics clearly show the interaction effect on the evolution of the number fluctuations from Poissonian to sub-Poissonian. Our method can be used to create squeezed states, which are important in precision measurement.
A multiwave atom interferometer using multiple Wannier-Stark states is experimentally realized in a vertical optical lattice. Atoms are coherently driven by stimulated Raman transitions into a superposition of several adjacent lattice sites, in which they evolve at multiples of Bloch frequency in the same internal state to form an interference pattern. We observe coherent evolution for more than 500 Bloch periods. The noise analysis shows that the phase resolution of this interferometer is detection noise limited. This multiwave interferometer could be a potential instrument for gravimetry and short-range forces measurement.
We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.