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arXiv:1410.8716

Twisted behavior of dipolar BECs: Dipole-dipole interaction beyond the self-consistent field approximation and exchange electric dipole interaction

Pavel A. Andreev

Published Oct 31, 2014• 0 citations
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Abstract

Dipole-dipole interaction is a long-range interaction, hence we could expect that the self-consistent field approximation might be applied. In most cases it is correct, but dipolar BECs reveal a surprise. Structure of the self-consistent field term requires that interacting particles are in different quantum states, while in BECs all particles in a single quantum state. This fact requires to consider the two-particle polarisation, which describes dipole-dipole interaction, in more details. We present this consideration and show an astonishing result that the two-particle quantum correlation in dipolar BECs reveals in the same form as the self-consistent field term.

DOI
10.48550/arxiv.1410.8716

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Dipole-dipole interaction is a long-range interaction, hence we could expect that the self-consistent field approximation might be applied. In most cases it is correct, but dipolar BECs reveal a surprise. Structure of the self-consistent field term requires that interacting particles are in different quantum states, while in BECs all particles in a single quantum state. This fact requires to consider the two-particle polarisation, which describes dipole-dipole interaction, in more details. We present this consideration and show an astonishing result that the two-particle quantum correlation in dipolar BECs reveals in the same form as the self-consistent field term.
The self-consistent field approach for the electric dipolar ultracold spin-1/2 fermions is discussed. Contribution of the exchange part of the electric dipole interaction is found. Hence we obtain a model of dipolar fermions beyond the self-consistent field approximation. It is shown that the exchange interaction of electric dipolar fermions depends on the spin-polarisation of the system. For instance the electric dipole exchange interaction equals to zero for spin-unpolarised systems, namely all low laying quantum states occupied by two-particles with opposite spins. In opposite limit of the full spin polarisation of the degenerate fermions, then we have one particle in each quantum states, the exchange interaction has maximum value, which is comparable with the self-consistent field part of the dipole-dipole interaction. The self-consistent part of the electric dipole-dipole interaction gives a positive contribution into the spectrum of collective excitations, while the exchange part of the dipole-dipole interaction leads to a negative term in the spectrum. At angles between the equilibrium polarisation and the direction of wave propagation close to π/2π/2π/2 the full dipolar part of the spectrum becomes negative. At the electric dipole moment of fermions of order of several Debay the dipolar part is large enough to exceed the Fermi pressure, that reveals in an instability.
We apply the Hartree-Fock-Bogoliubov-Popov (HFBP) method to two problems. The first is the phenomenon of Anderson localisation of a BEC in a two-dimensional bichromatic lattice. The second is the case of a harmonically trapped BEC with an-isotropic, long-range, dipolar interactions between particles. The HFBP method allows us to calculate the condensate properties and excitation spectrum of the sys-tem at finite temperature. For the bichromatic lattice, we examine the effects of in-teractions and finite temperature on the the localisation of the condensate. We also include a synthetic magnetic field and determine its effect. For the dipolar BEC, we examine the effect of the dipolar interactions on the condensate and thermal cloud as well as the excitation spectrum of the system. At finite temperature, we calculate the effects of both direct and exchange dipolar interactions of the thermal cloud on the condensate. The exchange interactions are numerically intensive to calculate and have been excluded from most previous studies. i
Summary form only given. Approaching temperatures near the absolute zero, i.e. the lowest temperature in the whole universe, the atoms develop extreme behaviors, which challenge our understanding. In this extreme regime, the atoms assume exceptional behaviors and form a new type of matter, which is now governed by the laws of quantum mechanics.In this regime, the interactions between many particles dictate the quantum behavior. Highly magnetic atoms, such a s Erbium, feature a novel type of interaction, which i s of long-range nature and isotropic character. This magnetic dipole-dipole interaction (DDI) imprints genuinely novel properties to quantum manyand few-body ultracold systems. The behavior of these systems i s fundamental to understand nature and quantum physics, and reserves u s every day fascinating and counterintuitive surprises. This talk will provide an overview of the fascinating dipolar phenomena from the Innsbruck prospective, ranging from the first-produced quantum gas of Er, to the observation of long-range nearest-neighbor interaction in lattice confined system, and the formation of a quasi self-bound droplet state in analogy with the He case.
We present the Gross–Pitaevskii equation for Bose–Einstein condensates (BECs) possessing the electric dipole and the electric quadrupole moments in a non-integral form. These equations are coupled with the Maxwell equations. The model under consideration includes the dipole–dipole, the dipole–quadrupole, and the quadrupole–quadrupole interactions in terms of the electric field created by the dipoles and quadrupoles. We apply this model to obtain the Bogoliubov spectrum for three-dimensional BECs with a repulsive short-range interaction. We obtain an extra term in the Bogoliubov spectrum in comparison with the dipolar BECs. We show that the quadrupole–quadrupole interaction gives a positive contribution in the Bogoliubov spectrum. Hence, this spectrum is stable.
We analyze the physics of self-bound droplets in a doubly dipolar Bose-Einstein condensate composed by particles with both electric and magnetic dipole moments. Using the particularly relevant case of dysprosium, we show that the anisotropy of the doubly dipolar interaction potential is highly versatile and nontrivial, depending critically on the relative orientation and strength between the two dipole moments. This opens novel possibilities for exploring intriguing quantum many-body physics. Interestingly, by varying the angle between the two dipoles we find a dimensional crossover from quasi-one-dimensional to quasi-two-dimensional self-bound droplets. This opens a so far unique scenario in condensate physics, in which a dimensional crossover is solely driven by interactions in the absence of any confinement.