Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly-correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground state polar molecules and weakly bound molecules of strongly magnetic atoms trapped in a weak optical lattice in a two-dimensional configuration. By tuning the lattice depth, defect interactions turn repulsive, which allows us to deterministically design a novel supersolid phase in the continuum limit.Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly-correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground state polar molecules and weakly bound molecules of strongly magnetic atoms trapped in a weak optical lattice in a two-dimensional configuration. By tuning the lattice depth, defect interactions turn repulsive, which allows us to deterministically design a novel supersolid phase in the continuum limit.

Feb 16, 20150 citations

Mesoscopic dipolar quantum crystals

Massimo Boninsegni

The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to 30 polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., $N=12$ and $N=19$ ) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to 30 polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., $N=12$ and $N=19$) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.

arXiv:1306.1266Physical Review AJun 5, 201312 citations

Flux Magnetism in a Strongly Interacting Dipolar Lattice Supersolid under Tunable Gauge Fields

Anonymous, Pietro Lombardi, Giovanni Ferioli +4 more

Supersolidity and magnetism are fundamental phenomena characterizing strongly correlated matter. Here we unveil a mechanism that directly connects these two regimes and can be experimentally accessed in ultracold atomic systems. Specifically, we exploit the distinctive properties of magnetic lanthanide atoms trapped in a one-dimensional antimagic wavelength optical lattice. This platform enables a realistic implementation of a triangular Bose-Hubbard ladder featuring two key ingredients: strong long-range interactions and tunable gauge fields. Owing to these properties, our numerical analysis reveals a robust lattice supersolid regime with finite fluxes in each triangular plaquette. Remarkably, we show that the density modulation of the supersolid phase and a finite gauge field induce magnetic ordering of the fluxes, forming ferromagnetic and ferrimagnetic patterns. Our results thus reveal a quantum effect that bridges supersolidity and magnetism.Supersolidity and magnetism are fundamental phenomena characterizing strongly correlated matter. Here we unveil a mechanism that directly connects these two regimes and can be experimentally accessed in ultracold atomic systems. Specifically, we exploit the distinctive properties of magnetic lanthanide atoms trapped in a one-dimensional antimagic wavelength optical lattice. This platform enables a realistic implementation of a triangular Bose-Hubbard ladder featuring two key ingredients: strong long-range interactions and tunable gauge fields. Owing to these properties, our numerical analysis reveals a robust lattice supersolid regime with finite fluxes in each triangular plaquette. Remarkably, we show that the density modulation of the supersolid phase and a finite gauge field induce magnetic ordering of the fluxes, forming ferromagnetic and ferrimagnetic patterns. Our results thus reveal a quantum effect that bridges supersolidity and magnetism.

arXiv:2509.05058Physical Review LettersJun 12, 20260 citations

Bosonic quantum mixtures with competing interactions: quantum liquid droplets and supersolids

Sarah Hirthe, Leticia Tarruell

These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.

cond-mat.quant-gasCross-listedarXiv:2603.17745Mar 19, 20260 citations

Quantum simulations of extended Hubbard models with dipolar crystals

Michael Ortner, Andrea Micheli, Guido Pupillo +1 more

In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.

arXiv:0903.2710New Journal of PhysicsMay 14, 200955 citations

Supersolid Stripe Crystal from Finite-Range Interactions on a Lattice

Guido Masella, Adriano Angelone, Fabio Mezzacapo +2 more

Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.

arXiv:1909.09082Physical Review LettersJul 26, 201932 citations

N=12

and

N=19

) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.