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arXiv:1612.08019 · Physical Review A

Phases of dipolar bosons in a bilayer geometry

Fabio Cinti, Daw-Wei Wang, Massimo Boninsegni

Published Feb 22, 2017• 31 citations
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Abstract

We study, by first-principles computer simulations, the low-temperature phase diagram of bosonic dipolar gases in a bilayer geometry as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely, paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.

DOI
10.1103/physreva.95.023622

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We study, by first-principles computer simulations, the low-temperature phase diagram of bosonic dipolar gases in a bilayer geometry as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely, paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.
We consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid is characterized by a finite value of both the atomic condensate and the super-counterfluid density. The pair superfluid phase is found to be stable against formation of many-body cluster states and features a gap in the spectrum of elementary excitations.
We predict that ultracold bosonic dipolar gases, confined within a multilayer geometry, may undergo self-assembling processes, leading to the formation of chain gases and solids. These dipolar chains, with dipoles aligned across different layers, emerge at low densities and resemble phases observed in liquid crystals, such as nematic and smectic phases. We calculate the phase diagram using quantum Monte Carlo methods, introducing a newly devised trial wave function designed for describing the chain gas, where dipoles from different layers form chains without in-plane long-range order. We find gas, solid, and chain phases, along with quantum phase transitions between these states. Specifically, we predict the existence of quantum phase transitions from gaseous to self-ordered phases, as the interlayer distance is decreased. Remarkably, in the self-organized phases, the mean interparticle distance can significantly exceed the characteristic length of the interaction potential, yielding solids and chain gases with densities several orders of magnitude lower than those of conventional quantum solids.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform path-integral quantum Monte Carlo simulations using the worm algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighbor interaction, supersolid phases are stabilized by doping the solids not only with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and we suggest experimental conditions under which the pair checkerboard phase can be observed.
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.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed.
A two-component, two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, and the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure factor for the in-phase (symmetric) and out-of-phase (antisymmetric) collective modes during the dimerization is studied in detail with the stochastic reconstruction method and the method of moments. The antisymmetric mode spectrum is most strongly influenced by suppression of the inlayer superfluidity (specified by the superfluid fraction ${\ensuremath{\gamma}}_{s}={\ensuremath{\rho}}_{s}/\ensuremath{\rho}$). In a pure superfluid (normal fluid) phase, only an acoustic [optical (gapped)] mode is recovered. In a partially superfluid phase, both are present simultaneously, and the dispersion splits into two branches corresponding to a normal and a superfluid component. The spectral weight of the acoustic mode scales linearly with ${\ensuremath{\gamma}}_{s}$. This weight transfers to the optical branch when ${\ensuremath{\gamma}}_{s}$ is reduced due to formation of dimer states. In summary, we demonstrate how the interlayer dimerization in dipolar bilayers can be uniquely identified by static and dynamic properties.