Order parameter and detection for a finite ensemble of crystallized one-dimensional dipolar bosons in optical lattices

Abstract

We explore the ground-state properties of bosons with dipole-dipole interactions in a onedimensional optical lattice. For strong interactions, the interesting phenomenon of crystallization takes place. Herein, we provide a detailed characterization and a way to measure the resulting crystal phase. Using the eigenvalues of the reduced one-body density matrix we define an order parameter that yields a phase diagram in agreement with an analysis of the density and two-body density. We demonstrate that the phase diagram can be detected experimentally using the variance of single-shot measurements. arXiv:1708.07409v4 [cond-mat.quant-gas]

Correlations of strongly interacting one-dimensional ultracold dipolar few-boson systems in optical lattices

“…Unidimensional dipolar atoms have been predicted to exhibit Luttinger liquid-like behavior [22][23][24][25] as well as anisotropic effects in curved and ring geometries [26][27][28]. Moreover, for very strong dipolar interactions a remarkable crystallization effect takes place where the dipolar atoms themselves form a crystal lattice structure irrespective of the geometry of their external confinements [22,26,[29][30][31][32][33].Optical lattices often serve as a controllable toolbox to understand and simulate a large variety of condensed matter systems. For dipolar atoms, the additional existence of the long-range anisotropic interactions leads to a plethora of interesting quantum phases arising from the interplay of the kinetic energy, the short and long-range interactions, each dominating different energy scales [2].…”

“…This dipolar Bose-Fermi map implies that bosons with strong dipolar interactions and fermions with strong dipolar interactions have identical one-body densities and identical onebody momentum densities. Last, for even higher interaction strengths, the long-range tail of the interaction dominates and leads to the formation of the so-called crystal phase [22,26,[29][30][31][32][33].Herein we follow the same strategy as [47-49] and theoretically investigate, the physics of a larger manybody system by studying in detail its few-body building blocks. Although few-body systems with dipole-dipole interactions have not been studied experimentally as of yet, the experimental realization of tunable few-fermion systems [47-49] motivates our theoretical study of a small ensemble of dipolar bosons.…”

“…We observe distinct structural changes in the correlations that accompany the phase transitions and clearly characterize the phases and their transitions. We stress here that the focus of this work is different from that of [33]. While in [33], an order parameter and its experimental detection via single-shot images was the prime motivation, here we take the emergence of these phases as the starting point and focus on their correlation and coherence properties in coordinate and momentum space.We remark that the few-body finite-size system studied here cannot exhibit true phase transitions in the macroscopic sense.…”

“…We stress here that the focus of this work is different from that of [33]. While in [33], an order parameter and its experimental detection via single-shot images was the prime motivation, here we take the emergence of these phases as the starting point and focus on their correlation and coherence properties in coordinate and momentum space.We remark that the few-body finite-size system studied here cannot exhibit true phase transitions in the macroscopic sense. What we obtain are ground states that are the finite-size precursors to the macroscopic thermodynamic phases [66].…”

“…This dipolar Bose-Fermi map implies that bosons with strong dipolar interactions and fermions with strong dipolar interactions have identical one-body densities and identical onebody momentum densities. Last, for even higher interaction strengths, the long-range tail of the interaction dominates and leads to the formation of the so-called crystal phase [22,26,[29][30][31][32][33].…”