Light scattering for thermometry of fermionic atoms in an optical lattice

We propose a method for measuring the temperature of fermionic atoms in an optical lattice potential from the intensity of the scattered light in the far-field diffraction pattern. We consider a single-component gas in a tightly-confined two-dimensional lattice, illuminated by far off-resonant light driving a cycling transition. Our calculations show that thermal correlations of the fermionic atoms generate fluctuations in the intensity of the diffraction pattern of light scattered from the atomic lattice array and that this signal can be accurately detected above the shot noise using a lens to collect photons scattered in a forward direction (with the diffraction maxima blocked). The sensitivity of the thermometer is enhanced by an additional harmonic trapping potential.