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At present, many laboratories are performing experiments to simulatetheoretical models of strongly correlated systems using cold atoms in opticallattices, a program referred to as "Quantum Simulation". It is hoped that theseexperiments will shed light on some long standing problems in condensed matterphysics. The goal of Quantum Simulation is to obtain information of homogenousbulk systems. However, experiments are performed in confining traps. Thenon-uniformity of the trapping potential inevitably introduces different phasesin the sample, making it difficult to deduce the properties of a single bulkphase. So far, there are no algorithms to use the experimental data to map outphase diagrams and important thermodynamic quantities. Here, we present analgorithm to achieve this goal. Apart from phase diagram, it also maps outentropy density, superfluid density of superfluids, and staggeredmagnetizations of anti-ferromagnets. Our scheme is exact within local densityapproximation.

Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases