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arXiv:2501.16657 · Physical Review A

Induced interactions and bipolarons in spin-orbit-coupled Bose-Einstein condensates

Zhe Yang, Shan–Shan Ding, Qizhong Zhu

Published Apr 11, 2025• 1 citation
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Abstract

Impurities immersed in a Bose-Einstein condensate (BEC) can interact indirectly through the exchange of Bogoliubov excitations. These impurities, which form dressed quasiparticles known as Bose polarons due to their interaction with the BEC, can pair up to form a bound state called a bipolaron, via an induced interaction. Previous studies on induced interactions have focused primarily on cases with an isotropic excitation spectrum. In this work, we investigate the properties of induced interactions and bipolarons mediated by anisotropic Bogoliubov excitations using field theory. Taking a BEC with spin-orbit coupling as an example, we show that the induced interaction becomes anisotropic. Notably, a double-minima feature appears in the induced interaction in momentum space due to the exchange of roton excitations. Additionally, we calculate the binding energy and wave functions of these bipolarons induced by anisotropic interactions. Unlike previously studied bipolarons formed through the exchange of isotropic phonon excitations, we identify an alternative type of bipolaron whose wave functions feature a double-peak structure under strong impurity-boson interactions. Our work extends the theory of induced interactions from isotropic to anisotropic systems, and it reveals the novel features in both the induced interactions and bipolarons arising from BEC with an unconventional excitation spectrum.

DOI
10.1103/physreva.111.043306

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Impurities immersed in a Bose-Einstein condensate (BEC) can interact indirectly through the exchange of Bogoliubov excitations. These impurities, which form dressed quasiparticles known as Bose polarons due to their interaction with the BEC, can pair up to form a bound state called a bipolaron, via an induced interaction. Previous studies on induced interactions have focused primarily on cases with an isotropic excitation spectrum. In this work, we investigate the properties of induced interactions and bipolarons mediated by anisotropic Bogoliubov excitations using field theory. Taking a BEC with spin-orbit coupling as an example, we show that the induced interaction becomes anisotropic. Notably, a double-minima feature appears in the induced interaction in momentum space due to the exchange of roton excitations. Additionally, we calculate the binding energy and wave functions of these bipolarons induced by anisotropic interactions. Unlike previously studied bipolarons formed through the exchange of isotropic phonon excitations, we identify an alternative type of bipolaron whose wave functions feature a double-peak structure under strong impurity-boson interactions. Our work extends the theory of induced interactions from isotropic to anisotropic systems, and it reveals the novel features in both the induced interactions and bipolarons arising from BEC with an unconventional excitation spectrum.
Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schrödinger equation describing this for an arbitrarily strong impurity-boson interaction. We furthermore compare with quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments, and we describe a procedure to probe their properties.
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.
We predict the existence of a roton-induced Bose polaron for an impurity immersed in a three-dimensional Bose-Einstein condensate with Raman-laser-induced spin-orbit coupling, where the condensate is in a finite-momentum plane-wave state with an intriguing roton minimum in its excitation spectrum. This novel polaron is formed by dressing the impurity with roton excitations, instead of phonon excitations as in a conventional (i.e., phonon-induced) Bose polaron, and acquires a significant center-of-mass momentum and highly anisotropic effective mass. We find that the roton-induced polaron evolves from a phonon-induced polaron, as the interaction between impurity and atoms increases across a Feshbach resonance. The evolution is not smooth, and a first-order phase transition from a phonon- to roton-induced polaron is observed at a critical interaction strength.
When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and represents a quasiparticle with a large dispersion and a negative effective mass near zero momentum. We discuss possible experimental implementation of the conditions for the formation of such repulsively bound bipolarons.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
We study the effects of quasiparticle interactions in a quasi-two-dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly nontrivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, low-energy phonons experience no damping, and higher-energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. When the dipoles are tilted off the axis of symmetry, the damping rates acquire an anisotropic character. Surprisingly, this anisotropy does not simply track the anisotropy of the dipolar interactions, rather, the mechanisms for damping are qualitatively modified in the anisotropic case. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and nonequilibrium dynamics in these systems. Further, our results are relevant for other 2D superfluids with roton excitations, including spin-orbit-coupled Bose gases, magnon condensates, and 4He^{4}\mathrm{He}4He films.