Roton excitations in Bose–Einstein condensates and a fluid–solid transition

Abstract

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 4 He 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, 4 He is crucially different from BECs at the lowest temperatures.It has been shown in the recent literature that the emergence of a roton dip in the dispersion relation of elementary excitations in a gaseous Bose-Einstein condensate (BEC) can be driven by interatomic correlations due to long-range interactions between dipoles, either permanent [1] or induced by irradiation with a far-off-resonance laser [2]. This feature in the excitation spectrum of a BEC may in turn lead to a quantum phase transition into a spatially modulated ground state [3,4]. Nazario and Santiago [5] have more recently proposed that roton excitations in a BEC may be signatures of proximity to a Mott insulating phase. Here their study is first related to previous theoretical conclusions drawn by Minguzzi et al. [3]. These authors drew on the work of O'Dell et al.[2] and interpreted the BEC structure factor S(k, I ) driven by laser intensity I as heralding a fluid-solid transition at a critical height of its main peak.

Microscopic model of cuprate superconductivity

“…b) We had proposed a charge 2 circular density wave in the fullerides, and the possibility that a roton-like entity could be generated by a transverse interaction of two charge density waves (or vibrations/phonons in a molecular case), especially if the system were in proximity to some type of charge ordering, seemed to support our contention that the fullerides and cuprates might have a similar superconducting mechanism. Others [13,18,19,20,21] have also suggested that a "magnetic roton" formation, similar to helium, the fractional Quantum Hall Effect, and other systems [22], might explain the correlation of the neutron and Raman scattering since the former detects a triplet in the spin resonance while the latter operates in the charge channel (Fig 2). c T How exactly this information relates to a superconducting pairing mechanism or any additional mechanistic features of HTSC was not initial apparent to us.…”

“…We examine a liquid material with uniform density, but modulated by a lattice, to understand the density excitation spectrum where the average velocity is zero, following others [18,19,25,26]. The Fourier expansions of the density and velocity operators are…”

“…Following others [18,19,25,26] and using the RPA [27], we can write a ground state wave function with density correlations as…”