Are Quasiparticles and Phonons Identical in Bose–Einstein Condensates?

Abstract

We study an interacting spinless Bose-Einstein condensate to clarify theoretically whether the spectra of its quasiparticles (one-particle excitations) and collective modes (two-particle excitations) are identical, as concluded by Gavoret and Nozières [Ann. Phys. 28, 349 (1964)]. We derive analytic expressions for their first and second moments so as to extend the Bijl-Feynman formula for the peak of the collective-mode spectrum to its width (inverse lifetime) and also to the one-particle channel. The obtained formulas indicate that the width of the collective-mode spectrum manifestly vanishes in the long-wavelength limit, whereas that of the quasiparticle spectrum apparently remains finite. We also evaluate the peaks and widths of the two spectra numerically for a model interaction potential in terms of the Jastrow wave function optimized by a variational method. It is thereby found that the width of the quasiparticle spectrum increases towards a constant as the wavenumber decreases. This marked difference in the spectral widths implies that the two spectra are distinct. In particular, the lifetime of the quasiparticles remains finite even in the long-wavelength limit.

3/2-Body Correlations and Coherence in Bose–Einstein Condensates

“…Thus, the result here also supports (i ′ ), as does our previous study. 15 The finite lifetime of non-condensed particles may be regarded as a crucial element for realizing and sustaining temporal coherence in the condensate. This paper is organized as follows.…”

Strong connection between single-particle and density excitations in Bose-Einstein condensates

“…The ultracold atomic gases may also serve as an ideal potential platform for directly addressing the strong connection between the single-particle excitation and the density excitation in BECs. On the other hand, several theories have been proposed that cast doubt on the paradigm about the BEC [25][26][27][28][29][30][31]: the correspondence between the single-particle excitation and the collective excitation in the low-energy and low-momentum region.…”

A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions

“…Moreover, our finitetemperature analysis in terms of discrete Matsubara frequencies, where the frequency renormalization factor B becomes irrelevant, indicates clearly that the Bogoliubov dispersion should be absent at least at finite temperatures for d ≤ 4. Moreover, the argument on the persistence of the linear dispersion by Nepomnyashchi ȋ and Nepomnyashchi ȋ39,40 is implicitly based on the Gavoret-Nozières result 6 that the one-and two-particle Green's functions share a common pole, whose validity we have been questioning; 43,44 see also the second paragraph below on this point. Instead, we here argue that no branch with a linear dispersion exists in the one-particle channel at T > 0 for d ≤ 4.…”

“…2,3 Indeed, it was shown that, when applied to Bose-Einstein condensates, the two distinct proofs are relevant to the poles of one-and two-particle Green's functions, 43 respectively, which are not necessarily identical. 44 The work by Watanabe and Murayama 16 on Goldstone's theorem (II) predicts a single Nambu-Goldstone mode in the two-particle channel with a linear dispersion relation ∝ k for k → 0. On the other hand, the present study relevant to the one-particle channel predicts no modes with a linear dispersion below d c = 4 (d c = 3) at finite temperatures (zero temperature).…”