A controlled twist between separate potentials can drastically influence localization properties of quantum particles between ordered and (quasi)disordered limits. Transport properties of single-particle and correlated fermionic materials have been extensively studied in connection with twisted bilayer graphene, but their bosonic counterpart remains largely unexplored. Here, we study bosonic matter in twisted potentials. We use continuous-space quantum Monte Carlo simulations to determine the unique phase diagrams of strongly correlated ultracold bosons in twisted optical lattices. For commensurate twisting angles, spectral gaps govern the formation of insulators, separated by thin superfluid domains. These domains form weak superfluids; with low superfluid fraction at zero temperature and high sensitivity to thermal fluctuations, but may be stabilized under appropriate parameter control. In contrast, slightly changing the twisting angle to an incommensurate value destroys most spectral gaps, leaving behind a prominent Bose glass phase. Our results are directly applicable to current generation experiments that quantum simulate moiré physics. Published by the American Physical Society 2024
A controlled twist between separate potentials can drastically influence localization properties of quantum particles between ordered and (quasi)disordered limits. Transport properties of single-particle and correlated fermionic materials have been extensively studied in connection with twisted bilayer graphene, but their bosonic counterpart remains largely unexplored. Here, we study bosonic matter in twisted potentials. We use continuous-space quantum Monte Carlo simulations to determine the unique phase diagrams of strongly correlated ultracold bosons in twisted optical lattices. For commensurate twisting angles, spectral gaps govern the formation of insulators, separated by thin superfluid domains. These domains form weak superfluids; with low superfluid fraction at zero temperature and high sensitivity to thermal fluctuations, but may be stabilized under appropriate parameter control. In contrast, slightly changing the twisting angle to an incommensurate value destroys most spectral gaps, leaving behind a prominent Bose glass phase. Our results are directly applicable to current generation experiments that quantum simulate moiré physics. Published by the American Physical Society 2024
In recent years, twisted bilayer systems such as bilayer graphene attracted a great deal of attention as the twist angle introduced a degree of freedom which can be used to nontrivially modify system properties. This idea has been picked up in the cold atom community, first with a theoretical proposal to simulate twisted bilayers in state-dependent optical lattices, and, more recently, with an experimental realization of twisted bilayers with bosonic atoms in two different spin states. In this article, we theoretically investigate dipolar bosons in a twisted bilayer geometry. The interplay between dipolar interaction and the twist between the layers results in the emergence of quantum states not observed in the absence of twist. We study how system properties vary as we change the twist angle at fixed distance between the layers and fixed dipolar interaction. We find that at a twist angle $\ensuremath{\theta}=0.{1}^{\ensuremath{\circ}}$, the observed quantum phases are consistent with those seen in the absence of twist angle, i.e., paired superfluid, paired supersolid, and paired solid phases. However, a slight increase in the twist angle to $\ensuremath{\theta}=0.{2}^{\ensuremath{\circ}}$ disrupts these paired phases in favor of a phase separation between checkerboard solid and superfluid regions. Notably, at a twist angle of $\ensuremath{\theta}=5.{21}^{\ensuremath{\circ}}$, the local occupation number follows the moir\'e pattern of the underlying moir\'e bilayers so that a periodic structure of insulating islands is formed. These insulating islands are surrounded by a superfluid.
Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.
Recent experiments have realized ultracold gases in twisted-bilayer optical lattices. We show that interacting bosons in these lattices present a highly nontrivial ground-state physics resulting from the interplay between inter- and intralayer hopping and interactions. This physics is crucially determined by site clusterization, which we properly take into account by developing a specifically tailored cluster Gutzwiller approach. Clusterization results in a large variety of different Mott-like phases characterized by typically different occupations of the clusters, and in the appearance of pockets of sites in between which particles can freely move, but which remain for any practical purposes disconnected from the rest of the sites. This peculiar phase, which resembles the well-known Bose glass phase, may occur even for commensurate twist angles and is further enhanced when the twisting is incommensurate. Moreover, in the incommensurate case, the formation of mobility islands may occur even without interlayer hopping solely due to interlayer interactions.
Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order 10−3ER, corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.
Moiré superlattices, a twisted functional structure crossing the periodic and nonperiodic potentials, have recently attracted great interest in multidisciplinary fields, including optics and ultracold atoms, because of their unique band structures, physical properties, and potential implications. Driven by recent experiments on quantum phenomena of bosonic gases, the atomic Bose–Einstein condensates in moiré optical lattices, by which other quantum gases such as ultracold fermionic atoms are trapped, could be readily achieved in ultracold atom laboratories, whereas the associated nonlinear localization mechanism remains unexploited. Here, we report the nonlinear localization theory of ultracold atomic Fermi gases in two-dimensional moiré optical lattices. The linear Bloch-wave spectrum of such a twisted structure exhibits rich nontrivial flat bands, which are separated by different finite bandgaps wherein the existence, properties, and dynamics of localized superfluid Fermi gas structures of two types, gap solitons and gap vortices (topological modes) with vortex charge S=1, are studied numerically. Our results demonstrate the wide stability regions and robustness of these localized structures, opening up a new avenue for studying soliton physics and moiré physics in ultracold atoms beyond bosonic gases.