Quantized squeezing and even-odd asymmetry of trapped bosons

We investigate the exact nature of the superfluid-to-Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional, harmonic trap by high-precision density-matrix renormalization-group calculations. The results reveal an intermediate regime characterized by a cascade of microscopic steps. These arise as a consequence of individual boson "squeezing" events and display an even-odd alternation dependent on the trap symmetry. We discuss the experimental observation of this behavior, which is generic in an external trapping potential.