Mach-Zehnder Interference of Boson Flavor States in the Excited Band of a 2D Optical Lattice*

Bosons promoted to the first excited Bloch band of an optical lattice have two important properties: they are metastable, having lifetimes long compared to the nearest neighbor hopping rate, and they carry a ``flavor'' quantum number which controls the direction of highly anisotropic hopping in the lattice \footnote{A Isacsson and SM Girvin. Phys. Rev. A 72, 053604 (2005) }. For a 2D optical lattice where the laser beams are not quite perpendicular, there is a small energy which causes the flavors to mix. The two flavor states can be treated as a two-level system with an avoided crossing, with the relative intensity of the two laser beams serving as a tuning parameter controlling the energy difference between the two flavors. When the tuning parameter is varied sinusoidally around some nonzero offset, the avoided crossing acts like a beam splitter in a Mach-Zehnder interferometer \footnote{WD Oliver et al. Science Vol. 310, Issue 5754, pp. 1653-1657(2005)}. Since this offset is momentum dependent, the rate of flavor change varies throughout the Brillouin Zone. This fact leads to interesting time-dependent momentum distributions which should be readily observable experimentally by free expansion of the bosons.