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For a Bose system with Bose-Einstein condensation, the interatomic interaction can have nontrivial effect on the time-of-flight images and cause a broadening of the condensate peak. In such a case, since the condensate and thermal parts can be separated in the images through a bimodal fit, this interaction effect can be addressed by numerically evolving the time-dependent Gross-Pitaevskii equation for the condensate, while leaving the momentum correlation of the thermal part almost unchanged. See, e.g., 10.1103/PhysRevA.77.043626
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What one measures in experiments is the atomic density integrated along the imaging direction. However, for the quasi-one-dimensional case or the 3D case with spherical symmetry as discussed in this paper, one can reconstruct the density profile from its column integration. See 10.1103/PhysRevLett.97.030401
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For 2D Bose gases, time-reversal symmetry can be spontaneously broken by creating vortex-antivortex pairs below the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. However, since the excitation energy increases logarithmically with the vortex pair size, for temperature not too close to the transition temperature, vortex pairs are tightly combined and we can resume a time-reversal symmetry for the coarse-grained wave function.
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For 2D Bose gases, time-reversal symmetry can be spontaneously broken by creating vortex-antivortex pairs below the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. However, since the excitation energy increases logarithmically with the vortex pair size, for temperature not too close to the transition temperature, vortex pairs are tightly combined and we can resume a time-reversal symmetry for the coarse-grained wave function.
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