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arXiv:1604.08110 · Physical Review A

Correlation effects and collective excitations in bosonic bilayers: Role of quantum statistics, superfluidity, and the dimerization transition

Alexey V. Filinov

Published Jul 11, 2016• 36 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.013603

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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 \ensuremathγs=\ensuremathρs/\ensuremathρ{\ensuremath{\gamma}}_{s}={\ensuremath{\rho}}_{s}/\ensuremath{\rho}\ensuremathγs​=\ensuremathρs​/\ensuremathρ). 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 \ensuremathγs{\ensuremath{\gamma}}_{s}\ensuremathγs​. This weight transfers to the optical branch when \ensuremathγs{\ensuremath{\gamma}}_{s}\ensuremathγs​ 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 study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum on both sides of this transition by using two microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both the density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value.
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 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.
Controlling the coupling between different degrees of freedom in many-body systems is a powerful technique for engineering novel phases of matter. We create a bilayer system of two-dimensional (2D) ultracold Bose gases and demonstrate the controlled generation of bulk coherence through tunable interlayer Josephson coupling. We probe the resulting correlation properties of both phase modes of the bilayer system: the symmetric phase mode is studied via a noise-correlation method, while the antisymmetric phase fluctuations are directly captured by matter-wave interferometry. The measured correlation functions for both of these modes exhibit a crossover from short-range to quasi-long-range order above a coupling-dependent critical point, thus providing direct evidence of bilayer superfluidity mediated by interlayer coupling. We map out the phase diagram and interpret it with renormalization-group theory and Monte Carlo simulations. Additionally, we elucidate the underlying mechanism through the observation of suppressed vortex excitations in the antisymmetric mode.
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.
The Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar systems has been studied recently by path integral Monte Carlo simulations [A. Filinov et al., Phys. Rev. Lett. 105, 070401 (2010)]. Here, we complement this analysis and study temperature-coupling strength dependence of the density (particle-hole) and single-particle (SP) excitation spectra both in superfluid and normal phases. The dynamic structure factor, $S(q,\ensuremath{\omega})$, of the longitudinal excitations is rigorously reconstructed with full information on damping. The SP spectral function, $A(q,\ensuremath{\omega})$, is worked out from the one-particle Matsubara Green's function. A stochastic optimization method is applied for reconstruction from imaginary times. In the superfluid regime sharp energy resonances are observed in both the density and SP excitations. The involved hybridization of both spectra is discussed. In contrast, in the normal phase, when there is no coupling, the density modes, beyond acoustic phonons, are significantly damped. Our results generalize previous zero-temperature analyses based on variational many-body wave functions [F. Mazzanti et al., Phys. Rev. Lett. 102, 110405 (2009); D. Hufnagl et al., Phys. Rev. Lett. 107, 065303 (2011)], where the underlying physics of the excitation spectrum and the role of the condensate has not been addressed.