Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide the first quantitative description of the full momentum distribution measurements of Van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008). We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry.