ABSTRACT
This work reports the different information theoretic measures, i.e., Shannon information entropy, order, disorder, complexity, and their dynamical measure for the interacting bosons in an optical lattice with both commensurate and incommensurate filling factor. We solve the many-body Schrödinger equation from first principles by multiconfigurational time-dependent Hartree method which calculates all the measures with high level of accuracy. We find for both relaxed state as well as quenched state the López-Ruiz-Mancini-Calbet (LMC) measure of complexity is the most efficient depictor of superfluid (SF) to Mott-insulator transition. In the quench dynamics, the distinct structure of LMC complexity can be used as a "figure of merit" to obtain the timescale of SF to Mott state entry, Mott holding time, and the Mott state to SF state entry in the successive cycles. We also find that fluctuations in the dynamics of LMC complexity measure for incommensurate filling clearly establish that superfluid to Mott-insulator transition is incomplete. We overall conclude that distinct structure in the complexity makes it more sensitive than the standard use of Shannon information entropy.
ABSTRACT
Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases - due to their repulsion - the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.
