Seminarium Fizyki Materii Skondensowanej

Motivated by the possibility of imaging density profiles of ultracold quantum gases with high resolution, e.g. at the single-atom level with quantum gas microscopes, we investigate the effect of measuring the number of particles in an extended subsystem, and of post-selecting those rare measurements outcomes where the subsystem particle number differs significantly from its mean value. In a gas of non-interacting bosons, the effect of that protocol is clear: the measured state is a tensor product of the equilibrium state at the measured density inside the substem, and at the complementary density (so that the total number of particles in the full system is conserved) in its complement. The natural expectation about interacting systems would then be that this picture would be mildly modified only in a small region around the interface between the subsystem and its complement. However, this expectation turns out to be completely wrong, and the density profiles are drastically different even in simple systems like the ground state of non-interacting fermions. I will discuss a few examples combining analytical techniques and results from quantum Monte Carlo, and argue that the emergence of limit shapes in the density profile of such measured systems is a generic phenomenon. I will also discuss correlations in such measured quantum states, and their relation with 'symmetry-resolved entanglement entropy' and argue that 'entanglement equipartition', generically expected in the regime of small deviations, breaks down and is replaced by an area law in the large deviation regime.