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arXiv:2502.04429 · Physical Review Research

Stability of dipolar bosons in a quasiperiodic potential

Paolo Molignini, Barnali Chakrabarti

Published Jun 9, 2025• 10 citations
arXivHTMLPDF

Abstract

Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.

DOI
10.1103/physrevresearch.7.023237

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Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.
Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(παi)\cos(παj), where n=α=(\sqrt{5}-1)/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.
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 [ 33 ]). 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.
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases under these long-range interactions. In this work, we study repulsive ultracold dipolar fermions in a quasiperiodic optical lattice to characterize the behavior of interacting quasicrystals. We simulate the full time evolution of the typical experimental protocols used to probe quasicrystalline order and localization properties. We extract experimentally measurable dynamical observables and correlation functions to characterize the three phases observed in the noninteracting setting: localized, intermediate, and extended. We then study the stability of such phases to repulsive dipolar interactions. We find that dipolar interactions can completely alter the shape of the phase diagram by stabilizing the intermediate phase, mostly at the expense of the extended phase. Moreover, in the strongly interacting regime, a resonance-like behavior characterized by density oscillations appears. Remarkably, strong dipolar repulsions can also localize particles even in the absence of quasiperiodicity if the primary lattice is sufficiently deep. Our work shows that dipolar interactions in a quasiperiodic potential can give rise to a complex, tunable coexistence of localized and extended quantum states.
We explore the ground-states of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one-and two-body densities. We probe their transitions and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We demonstrate that the crystal state orders can be observed using the full distribution functions of the particle number which we extract from simulated single-shot images.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
We explore the ground states of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one- and two-body densities. We probe the transitions between these orders and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We show that the crystal state orders can be observed using the full distribution functions of the particle number extracted from simulated single-shot images.