Lattice Thermodynamics for Ultra-Cold Atoms

We measure the temperature of ultra-cold Rb-87 gases transferred into an optical lattice and compare to non-interacting thermodynamics for a combined lattice--parabolic potential. Absolute temperature is determined at low temperature by fitting quasimomentum distributions obtained using bandmapping, i.e., turning off the lattice potential slowly compared with the bandgap. We show that distributions obtained at high temperature employing this technique are not quasimomentum distributions through numerical simulations. To overcome this limitation, we extract temperature using the in-trap size of the gas.