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arXiv:1902.08333 · Physical Review Letters

Roton-Induced Bose Polaron in the Presence of Synthetic Spin-Orbit Coupling

Jia Wang, Xia-Ji Liu, Hui Hu

Published Nov 19, 2019• 14 citations
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Abstract

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.

DOI
10.1103/physrevlett.123.213401

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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.
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.
We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling (SOC) coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spin-selected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass (c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.
We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of 23Na^{23}\mathrm{Na}23Na could be a candidate for observing the stripe condensate with high contrast fringes.
Roton-type excitations usually emerge from strong correlations or long-range interactions, as in superfluid helium or dipolar ultracold atoms. However, in a weakly short-range interacting quantum gas, the recently synthesized spin-orbit (SO) coupling can lead to various unconventional phases of superfluidity and give rise to an excitation spectrum of roton-maxon character. Using Bragg spectroscopy, we study a SO-coupled Bose-Einstein condensate of ^{87}Rb atoms and show that the excitation spectrum in a "magnetized" phase clearly possesses a two-branch and roton-maxon structure. As Raman coupling strength Ω is decreased, a roton-mode softening is observed, as a precursor of the phase transition to a stripe phase that spontaneously breaks spatially translational symmetry. The measured roton gaps agree well with theoretical calculations. Furthermore, we determine sound velocities both in the magnetized and in the nonmagnetized phases, and a phonon-mode softening is observed around the phase transition in between. The validity of the f-sum rule is examined.
We use a class of variational wave functions to study the properties of an impurity in a Bose-Einstein condensate, i.e., the Bose polaron. The impurity interacts with the condensate through a contact interaction, which can be tuned by a Feshbach resonance. We find a stable attractive polaron branch that evolves continuously across the resonance to a tight-binding diatomic molecule deep in the positive scattering length side. A repulsive polaron branch with finite lifetime is also observed and it becomes unstable as the interaction strength increases. The effective mass of the attractive polaron also changes smoothly across the resonance connecting the two well-understood limits deep on both sides.
We use a nonperturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fr\"ohlich Hamiltonian with renormalized parameters is possible. Its strong-coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. Already for weaker interactions, before the polaron mass diverges, we predict a transition to a regime where states exist below the polaron energy and the attractive polaron is no longer the ground state. On the repulsive side of the Feshbach resonance we recover the repulsive polaron, which has a finite lifetime because it can decay into low-lying molecular states. We show for the entire range of couplings that the polaron energy has logarithmic corrections in comparison with predictions by the mean-field approach. We demonstrate that they are a consequence of the polaronic mass renormalization which is due to quantum fluctuations of correlated phonons in the polaron cloud.