Abstract
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 []). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
Highlights
Ultracold atoms with dipole–dipole interactions have become a popular tool to simulate and understand the physics of long-range interacting systems [1, 2]
We investigate a system of dipolar bosons in an optical lattice by studying the triple-well potential
We have explored the many-body correlations of interacting ultracold dipolar bosons in optical lattices
Summary
Ultracold atoms with dipole–dipole interactions have become a popular tool to simulate and understand the physics of long-range interacting systems [1, 2]. The MCTDH for bosons (MCTDHB) [57, 105] is such a general many-body method capable of addressing strong interaction regimes [58,59,60,61,62] and its implementation in the MCTDH-X software [63,64,65] has been employed in [33] to establish an order parameter and an experimental method to classify and detect all the quantum phases of dipolar atoms in optical lattices via single-shot images. For strong dipolar interactions, the interaction energy dominates the potential energy; the crystal formed by the bosons can have a ‘lattice constant’ that depends on the interaction strength The physics of such a crystal cannot be cast into a model where the basis is localized in space and the corresponding lattice constant is fixed irrespective of the interaction strength, as done in the single-band and multi-band BHM. The crystal phase is realized by the equal contribution of N natural orbitals [33]
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