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arXiv:cond-mat/0310672 · Journal of Physics B Atomic Molecular and Optical Physics

Depletion of a Bose–Einstein condensate by laser-induced dipole–dipole interactions

I. E. Mazets, Duncan H J O’Dell, G Kurizki, Nir Davidson, W P Schleich

Published Mar 24, 2004• 31 citations
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Abstract

We study a gaseous atomic Bose–Einstein condensate with laser-induced dipole–dipole interactions using the Hartree–Fock–Bogoliubov theory within the Popov approximation. The dipolar interactions introduce long-range atom–atom correlations which manifest themselves as increased depletion at momenta similar to that of the laser wavelength, as well as a ‘roton’ dip in the excitation spectrum. Surprisingly, the roton dip and the corresponding peak in the depletion are enhanced by raising the temperature above absolute zero.

DOI
10.1088/0953-4075/37/7/061

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We study a gaseous atomic Bose–Einstein condensate with laser-induced dipole–dipole interactions using the Hartree–Fock–Bogoliubov theory within the Popov approximation. The dipolar interactions introduce long-range atom–atom correlations which manifest themselves as increased depletion at momenta similar to that of the laser wavelength, as well as a ‘roton’ dip in the excitation spectrum. Surprisingly, the roton dip and the corresponding peak in the depletion are enhanced by raising the temperature above absolute zero.
We study a Bose-Einstein condensate of a dilute gas with dipolar interactions, at finite temperature, using the Hartree-Fock-Bogoliubov theory within the Popov approximation. An additional approximation involving the dipolar exchange interaction is made to facilitate the computation. We calculate the temperature dependence of the condensate fraction of a condensate confined in a cylindrically symmetric harmonic trap. We show that the biconcave-shaped condensates found in [Ronen et al. Phys. Rev. Lett. 98, 30406 (2007)] in certain pancake traps at zero temperature are also stable at finite temperature. Surprisingly, the dip in the central density of these structured condensates is actually enhanced at low finite temperatures. We explain this effect.
We investigate the dynamics of a three-dimensional Bose-Einstein condensate of ultracold atomic gases with a soft-core-shaped long-range interaction, which is induced by laser dressing the atoms to a highly excited Rydberg state. For a homogeneous condensate, the long-range interaction drastically alters the dispersion relation of the excitation, supporting both roton and maxon modes. Rotons are typically responsible for the creation of supersolids, while maxons are normally dynamically unstable in BECs with dipolar interactions. We show that maxon modes in the Rydberg-dressed condensate, on the contrary, are dynamically stable. We find that the maxon modes can be excited through an interaction quench, i.e., turning on the soft-core interaction instantaneously. The emergence of the maxon modes is accompanied by oscillations at high frequencies in the quantum depletion, while rotons lead to much slower oscillations. The dynamically stable excitation of the roton and maxon modes leads to persistent oscillations in the quantum depletion. Through a self-consistent Bogoliubov approach, we identify the dependence of the maxon mode on the soft-core interaction. Our study shows that maxon and roton modes can be excited dynamically and simultaneously by quenching Rydberg-dressed long-range interactions. This is relevant to current studies in creating and probing exotic states of matter with ultracold atomic gases.
Several authors have recently discussed the existence of roton excitations in Bose–Einstein condensates (BECs) and considered how a roton dip in the dispersion curve of elementary excitations may be related to the formation of a spatially modulated ground state. Here attention is drawn to a theoretical study of Minguzzi et al. on interatomic correlations in a BEC from dipole–dipole interactions induced by laser light of increasing intensity. Attractive interactions in superfluid 4He and repulsive interactions in ‘untuned’ BECs are then compared and contrasted, the experiments of Woods and Cowley and of Greiner et al. providing the focus respectively. It is stressed that, contrary to a very recent assertion by Nazario and Santiago, 4He is crucially different from BECs at the lowest temperatures.
The depletion of a quasi-two-dimensional (quasi-2D) dipolar Bose condensed gas in the presence of both contact and long-range 1/r interactions is investigated in the framework of Hartree–Fock–Bogoliubov (HFB) approximation. When the characteristic wavelength of a mode is much larger than the trap size, the dipole-dipole (DD) interaction can be treated as a contact interaction and in the low momentum limit the long-range nature of the 1/r interaction has the dominant contribution and leads to the nonlinear (nonphononic) dispersion relation. We will show that quantum depletion is temperature independent and is determined by the contact, DD and longrange 1/r coupling constants (ɛdd = gd/g and C). The the quantum depletion is affected by long-range 1/r interaction and at large momentum limits the momentum dependence of quantum depletion unaffected by 1/r interaction.