Quantum Phase Transition in a Two-Dimensional System of Dipoles

Abstract

The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from gas to solid phase when the density increases. In the gas phase the condensate fraction is calculated as a function of the density. Using Feynman approximation, the collective excitation branch is studied and appearance of a roton minimum is observed. Results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindeman ratio at the transition point comes to be γ = 0.230(6). The condensate fraction in the gas phase is estimated as a function of the density.The chromium atom has exceptionally large permanent dipole moment and recent realization of Bose-Einstein condensation of 52 Cr[1] has stimulated great interest in properties of dipolar systems at low temperatures. It was observed[2] that dipolar forces lead to anisotropic deformation during expansion of the condensate. In the experiments [1,2], the dipolar forces were competing with short-range scattering. The latter, in principle, can be removed by tuning the s-wave scattering length to zero by Feshbach resonance [3]. This would lead to an essentially pure system of dipoles. On the other hand, lowdimensional systems can be realized by making the confinement in one (or two) directions so tight, that no excitations of the levels of the tight confinement are possible and the system is dynamically two-(or one-) dimensional.A major development has also been done in the present years towards the realization of excitons at temperatures close to the Bose-Einstein condensation temperature [4]. An exciton is much more stable if the electron is spatially separated from the hole (spatially separated excitons). Such an exciton can be modeled as a dipole. If the excitons are in two coupled quantum wells they can be treated effectively as two-dimensional if the size of an exciton is small compared to the mean distance between excitons.One might expect to find a phase transition from gas phase to a crystal one at large density. As the condensate fraction is small at the transition point, perturbative theories, like Gross-Pitaevskii [5] or Bogoliubov [6,7] approaches, will fail to describe accurately this transition. One has to use ab initio numerical methods to address this quantum many-body problem. Recently a trapped system of two-dimensional dipoles has been studied by Path Integral Monte Carlo method [8] and mesoscopic analog of crystallization has been found. Trapped dipoles with s-wave scattering were investigated [9]. So far, there have been no full quantum microscopic computations of the properties of a homogeneous system of dipoles.The Hamiltonian of a homogeneous system of N bosonic dipoles has the formwhere M is the dipole mass and r i , i = 1, N are the positions of dipoles. The expression for the coupling constant C dd depends on the nature of the dipole-dipole interaction. Two possible physical realizations of a twodim...

High-temperature superfluidity with indirect excitons in van der Waals heterostructures

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Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

“…In a very dilute system, na 2 < ∼ 10 −7 , the dipoledipole scattering length is well approximated by its value at zero scattering momentum, a dd (0) = e 2γ r d = 3.17222 · · · r d , where r d is a characteristic length scale for the dipole-dipole interaction potential [43]. We solve the s-wave scattering problem numerically and find that the following fit describes well the numerical data for the value of the s-wave scattering length at low energies:…”

“…A series of our previous works has been devoted to the study of the equation of state of dilute 2D Bose gases [24,[42][43][44][45][46][47]. A number of interaction potentials (dipolar, hard disks, etc.)…”

Dipolar bilayer with antiparallel polarization: A self-bound liquid

“…An anisotropic 2D quantum gas can be realized by tilting the polarization dipoles in a deep trap, and a stripe phase can form spontaneously 20,21 . For r D r s , dipoles will crystallize without imposing an optical lattice [22][23][24] . A bilayered dipolar Bose gas can dimerize if the polarization direction in the two layers is the same 25 .…”