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, so-called 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 a 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 scheme, 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 sizable shift of the quasiparticle energy with an increasing impurity concentration, which should be detectable with present-day experimental techniques.
- Received 19 December 2017
- Revised 28 February 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031042
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Because of the intricate laws of quantum mechanics, it is often prohibitively complex to accurately describe systems consisting of a large number of interacting particles. To make the problem more manageable, physicists often describe complicated quantum systems in terms of particlelike objects called quasiparticles, a theory first put forward by Lev Landau. In Landau’s theory, the interaction between quasiparticles plays a crucial role, leading to important effects such as superconductivity. Unfortunately, these interactions are difficult to experimentally probe using conventional systems. Here, we show that a system consisting of impurity atoms in a Bose-Einstein condensate (BEC) can probe the quasiparticle interaction systematically and in regimes never realized before.
When interactions between the atoms are weak, we derive rigorous results for the Landau effective interaction, including the fact that it is very strong when two quasiparticles resonantly exchange sound modes in the BEC. We then calculate the effective interaction for arbitrary interaction strengths and show that, in general, it is large because of the compressibility of a BEC. In particular, the interaction becomes very large when the quasiparticles move at the speed of sound or when the boson impurity scattering is close to its maximum value. Finally, we discuss how our results can be explored using present-day experimental technology.
Our results show how cold atomic gases can be used to explore and extend Landau’s theory of quasiparticles, an important goal, given that the theory forms a powerful platform for our description of many-body systems across a wide range of energy scales.
