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arXiv:1301.0343 · Physical Review A

Stability and excitations of a bilayer of strongly correlated dipolar bosons

Diana Hufnagl, Robert E. Zillich

Published Mar 25, 2013• 16 citations
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Abstract

We study correlation effects and excitations in a dipolar Bose gas bilayer which is modeled by a one-dimensional double-well trap that determines the width of an individual layer, the distance between the two layers, and the height of the barrier between them. For the ground-state calculations we use the hypernetted-chain Euler-Lagrange method, and for the calculation of the excitations we use the correlated basis function method. We observe instabilities both for wide, well-separated layers dominated by intralayer attraction of the dipoles, and for narrow layers that are close to each other dominated by interlayer attraction. The behavior of the pair distribution function leads to the interpretation that the monomer phase becomes unstable when pairing of two dipoles becomes energetically favorable between or within layers, respectively. In both cases we observe a tendency towards ``rotonization,'' i.e., the appearance of a soft mode with finite momentum in the excitation spectrum. The dynamic structure function is not simply characterized by a single excitation mode but has a nontrivial multipeak structure that is not captured by the Bijl-Feynman approximation. The dipole-dipole interaction between different layers leads to additional damping compared to the damping obtained for uncoupled layers.

DOI
10.1103/physreva.87.033624

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We study correlation effects and excitations in a dipolar Bose gas bilayer which is modeled by a one-dimensional double-well trap that determines the width of an individual layer, the distance between the two layers, and the height of the barrier between them. For the ground-state calculations we use the hypernetted-chain Euler-Lagrange method, and for the calculation of the excitations we use the correlated basis function method. We observe instabilities both for wide, well-separated layers dominated by intralayer attraction of the dipoles, and for narrow layers that are close to each other dominated by interlayer attraction. The behavior of the pair distribution function leads to the interpretation that the monomer phase becomes unstable when pairing of two dipoles becomes energetically favorable between or within layers, respectively. In both cases we observe a tendency towards ``rotonization,'' i.e., the appearance of a soft mode with finite momentum in the excitation spectrum. The dynamic structure function is not simply characterized by a single excitation mode but has a nontrivial multipeak structure that is not captured by the Bijl-Feynman approximation. The dipole-dipole interaction between different layers leads to additional damping compared to the damping obtained for uncoupled layers.
We study the pair correlations and excitations of a dipolar Bose gas layer. The anisotropy of the dipole-dipole interaction allows us to tune the strength of pair correlations from strong to weak perpendicular and weak to strong parallel to the layer by increasing the perpendicular trap frequency. This change is accompanied by a roton-roton crossover in the spectrum of collective excitations, from a roton caused by the head-to-tail attraction of dipoles to a roton caused by the side-by-side repulsion, while there is no roton excitation for intermediate trap frequencies. We discuss the nature of these two kinds of rotons and the relation to instabilities of dipolar Bose gases. In both regimes of trap frequencies where rotons occur, we observe strong damping of collective excitations by decay into two rotons.
We consider a bilayer of dipolar bosons in which the polarization of dipoles are perpendicular to the planes. Using accurate static structure factor S(q)S(q)S(q) data from hypernetted-chain calculation for single layer dipolar bosons we construct effective screened interactions for intralayer particles. We adopt the random-phase approximation for interlayer interactions. We study the instability of the homogeneous bilayer system against the formation of density waves by investigating the poles of the density-density response function. The dispersion of collective modes of this system also signals the density-wave instability. We also investigate the effect of counterflow on the collective mode dispersion and on the density-wave instability and discuss the dissipationless superfluid drag effect in the presence of a background velocity.
We present a method for calculating the dynamics of a bosonic mixture, the multicomponent correlated-basis-function (CBF) method. For a single component, CBF results for the excitation energies agree quite well with experimental results, even for highly correlated systems like 4He^{4}\mathrm{He}4He, and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multicomponent CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider the case of strong coupling, leading to large positive interlayer correlations. We calculate the spectrum for a system of eight layers and show that the strong coupling can lead to a simpler spectrum than in the uncoupled case, with a single peak carrying most of the spectral weight.
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.
We consider a bilayer of dipolar particles in which the polarization of dipoles is perpendicular to the planes, in the antiparallel configuration. Using accurate static structure factor data from hypernetted-chain (HNC) and Fermi HNC calculations, respectively for an isolated layer of dipolar bosons and dipolar fermions, we construct effective screened intralayer interactions. Adopting the random-phase approximation for interlayer interactions, we investigate the instability of these homogeneous bilayer systems towards the formation of density waves by studying the poles of the density–density response function. We have also studied the collective modes of these systems and find that the dispersion of their antisymmetric collective mode signals the emergence of the density wave instability as well.
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.