Excitation spectra of strongly correlated ultra-cold dipolar gases from first-principle thermodynamic simulations
Theoretical Condensed Matter Physics
Final Report Abstract
Static properties of dipolar bosons have been analyzed quite extensively in recent years using quantum Monte Carlo techniques. This includes strongly correlated phases in a harmonic confinement and 2D homogeneous geometry, the gas-solid phase transition, superfluid response in incommensurate crystals and the Berezinskii-Kosterlitz-Thouless transition. On the other hand, theoretical predictions for dynamic properties, in particular, excitation spectra of density fluctuations are more challenging if performed on a microscopic level. Beyond the mean-field regime, up to date there exist only few analyses. The main focus of the present project was to demonstrate how information on the realtime dynamics can be extracted from quantum many-body simulations in thermodynamic equilibrium and the imaginary-time correlation functions in the framework of the linear response. Within the statistical errors, the reconstructed spectra contain full information on the dynamics and damping of the collective modes. In the first part of the project we investigated the quantum breathing mode (BM) of trapped bosons. We have developed a set of accurate procedures to study elementary excitation energies and full spectral density of the excitation operator. The sum-rules formalism has been applied for accurate calculations of the upper bounds to the BM-frequency in terms of equilibrium expectation values which are directly accessible with PIMC. Several dependencies of the sum-rule estimators, i.e on temperature, particle number and interaction type [dipole/Coulomb], have been analyzed in detail. We have also focused on general properties of confined bosons in 2D/3D, such as the reduction of the moment of inertia due to the superfluid-normal fluid phase transition [a crossover in finite systems]. A strong inhomogeneity of density suggests consideration of spatially resolved information provided by a local superfluid density estimator. We have demonstrated that with an increase in temperature the trap center stays superfluid, while the boundary starts to behave classically. A strong localization of particles in this region reduces the many-body exchange and suppresses the superfluidity. The role of disorder, in confinements with different geometries, has been also addressed. We studied the stability/melting of a Wigner molecule [a finite cluster of quantum particles]. Several independent melting criteria has been introduced and allowed to reconstruct the full phase diagram [classical liquid – Wigner molecule – quantum liquid] on the temperaturedensity plane. In the second part, a two-component two-dimensional dipolar bosonic system in the bilayer geometry was considered. By performing PIMC simulations in a wide range of layer spacings we analyzed in detail the pair correlation functions, the static response function, 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, was 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 γs = ρs /ρ). Our main finding is that in a partially superfluid phase, the dispersion relation splits into two branches (optical and acoustic one) corresponding to a normal and a superfluid component. The spectral weight of the acoustic mode scales linearly with γs . This weight transfers to the optical branch when γs is reduced due to formation of dimer states. Our results clearly demonstrate how the interlayer dimerization in dipolar bilayers can be uniquely identified by static and dynamic properties.
Publications
- Influence of the nature of confinement on the melting of Wigner molecules in quantum dots, Europ. Phys. J. B 89, 60 (2015)
D. Bhattacharya, A.V. Filinov, Amit Ghosal, and M. Bonitz
(See online at https://doi.org/10.1140/epjb/e2016-60448-5) - Superfluidity of trapped quantum systems in two and three dimensions, Phys. Rev. B 91, 054503 (2015)
T. Dornheim, A. Filinov, M. Bonitz
(See online at https://doi.org/10.1103/PhysRevB.91.054503) - Correlation effects and collective excitations in bosonic bilayers: role of quantum statistics, superfluidity and dimerization transition, Phys. Rev. A 94, 013603 (2016)
A. Filinov
(See online at https://doi.org/10.1103/PhysRevA.94.013603)
