Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate

Abstract

Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems, and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, socalled Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for weak impurity-boson interaction, if the transferred momentum/energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak coupling results. Using this, we show that the Landau effective interaction in general is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering, or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. Finally, we show how the Landau effective interaction leads to a sizeable shift of the quasiparticle energy with increasing impurity concentration, which should be detectable with present day experimental techniques.

Induced p -Wave Pairing in Bose-Fermi Mixtures

“…Since the Fock selfenergy, Eq. (9) includes all dominant second order diagrams for a fermion interacting with a BEC [30,42], our theory recovers the exact second order result [33]…”

“…As explained in Ref. [42], the Fock diagram in Fig. 1 with the induced interaction given by (6), is identical to the second order self-energy of a fermion in a BEC.…”

Critical slowdown of non-equilibrium polaron dynamics

“…For example it suggest that a associated with the emission of a phonon with momentum k by an impurity moving with different indicated momenta p. The energy difference is shown as a function of the phonon momentum components parallel ( || k ) and perpendicular (k ) to the impurity momentum. The black dots indicate the minimum of DE p k , which defines the frequency ω p for p>p c according to equations (29) and (30). As discussed in the text, the polaron formation time, t f , is related to the slope of DE p k , around k=0, which vanishes for p=p c (red surface) and causes t f to diverge.…”

“…Experiments on imbalanced Fermi gases [8][9][10][11][12] provide an ideal quantum simulation platform for the Fermi polaron [13][14][15]. At the same time, the possibility to realize so-called Bose polarons in atomic Bose-Einstein condensates (BECs) [16,17] has raised further questions and ushered in new theoretical investigations [18][19][20][21][22][23][24][25][26][27][28][29][30], expanding our understanding of quantum impurity physics. The properties of the Bose polaron is arguably closer to the generic solid-state polaron, since the surrounding BEC has a linear low energy dispersion in analogy with acoustic phonons in a solid.…”

Analyzing a Bose polaron across resonant interactions

“…Our new analysis paves the way for several intriguing new research directions, including experimental studies of the interactions between polarons [29,33] and the formation of bipolarons [51], explorations of temperature effects and associated new quasiparticle states [49], as well as investigations of non-equilibrium effects and the formation dynamics of the polaron [27,[52][53][54].…”