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Sorting Fermionization from Crystallization in Many-Boson Wavefunctions.

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Summary
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Fermionization and crystallization in one-dimensional bosons both cause particles to spread out due to repulsion. Distinctive density patterns reveal these phases, aiding experimental differentiation.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Atomic physics

Background:

  • Strongly interacting repulsive bosons in one spatial dimension exhibit distinct quantum phases.
  • Fermionization and crystallization are two such phases characterized by particle repulsion and spatial overlap minimization.

Purpose of the Study:

  • To investigate the ground state properties of one-dimensional bosonic systems undergoing fermionization and crystallization.
  • To differentiate between these two phases using one- and two-body density matrices.
  • To provide experimental signatures for distinguishing fermionization from crystallization.

Main Methods:

  • Solving the N-body Schrödinger equation from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method.
  • Utilizing the one- and two-body density matrices to analyze particle behavior in position space.
  • Comparing results with complementary calculations for fermions using the MCTDHF method.

Main Results:

  • A unique N-fold splitting pattern in the one- and two-body density is observed for both fermionization and crystallization.
  • This splitting is incomplete for fermionized bosons, influenced by confinement potential, unlike the complete splitting in crystalline bosons.
  • The spreading of density in crystalline bosons diverges as a power law with increasing dipolar interaction strength.

Conclusions:

  • The incomplete splitting of density patterns serves as a key differentiator between fermionization and crystallization in bosonic systems.
  • Experimental measurements of one- and two-body densities can distinguish these two quantum phases.
  • The study provides a theoretical framework and experimental guidance for understanding strongly correlated quantum systems.