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Physical Review A

Dissipative-interaction-induced polaron-molecule transition in three-dimensional Fermi polarons

Lijun Yang

Published Jun 3, 2024• 2 citations
Publisher

Abstract

The non-Hermitian interaction in many-body systems may lead to novel phenomena. We study an impurity immersed in three-dimensional ideal Fermi gases, with a complex-valued contact interaction between the fermions and impurity that arise from two-body dissipation. Generalizing the unified variational approach to the non-Hermitian case, we study the effects of the dissipative attraction on the polaronic and molecular states of the impurity for different mass ratios. We find that the dissipation attraction can induce polaron-molecule transition despite the transition being absent in the Hermitian case, which is demonstrated to be a first-order phase transition between different total momenta. In addition, we show that the non-Hermitian attraction leads to significant decay of the polaronic and molecular states; however, increasing the mass ratio between the impurity and majority fermions will help suppress the decay. Our results illustrate the applicability of the unified variational approach in non-Hermitian Fermi polaron systems and the method may be extended to include higher-order particle-hole excitations and to study other types of bound states.

DOI
10.1103/physreva.109.063305

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The non-Hermitian interaction in many-body systems may lead to novel phenomena. We study an impurity immersed in three-dimensional ideal Fermi gases, with a complex-valued contact interaction between the fermions and impurity that arise from two-body dissipation. Generalizing the unified variational approach to the non-Hermitian case, we study the effects of the dissipative attraction on the polaronic and molecular states of the impurity for different mass ratios. We find that the dissipation attraction can induce polaron-molecule transition despite the transition being absent in the Hermitian case, which is demonstrated to be a first-order phase transition between different total momenta. In addition, we show that the non-Hermitian attraction leads to significant decay of the polaronic and molecular states; however, increasing the mass ratio between the impurity and majority fermions will help suppress the decay. Our results illustrate the applicability of the unified variational approach in non-Hermitian Fermi polaron systems and the method may be extended to include higher-order particle-hole excitations and to study other types of bound states.
We study the polaron problem of an impurity immersed in a dissipative spin-orbit coupled Fermi gas via a non-self-consistent T -matrix method. We first propose an experimental scheme to realize a spin-orbit coupled Fermi bath with dissipation, and show that such a system can be described by a non-Hermitian Hamiltonian that contains an imaginary spin-flip term and an imaginary constant shift term. We find that the non-Hermiticity will change the single-particle dispersion of the bath gas, and modify the properties of attractive and repulsive polarons such as energy, quasi-particle residue, effective mass, and decay rate. We also investigate the Thouless criteria corresponding to the instability of the polaron-molecule transition, which suggests a molecule state is more facilitated with stronger bath dissipation. Finally, we consider the case with finite impurity density and calculate the interaction between polarons. Our result extends the study of polaron physics to non-Hermitian systems and may be realized in future experiments.
We revisit the polaron-molecule transition in three-dimensional (3D) fermion systems using the well-established variational approach. The molecule is found to be intrinsically unstable against lowest-order particle-hole excitations, and it can only approximate the ground state of impurity systems with a finite total momentum in the strong-coupling regime. The polaron-molecule transition can therefore be reinterpreted as a first-order transition between single impurity systems with different total momenta. Within a certain interaction window near their transition, both states appear as local minima in the dispersion curve, indicating they can coexist in a realistic system. We have further confirmed the polaron-molecule coexistence in the presence of a finite impurity concentration and at low temperature, which directly leads to a smooth polaron-molecule transition as observed in recent experiments of 3D ultracold Fermi gases. Our results have provided an unambiguous physical picture for the competition and conversion between a polaron and molecule, and also shed light on Fermi polaron properties in low dimensions.
We address the problem of a single impurity atom moving in a two-dimensional (2D) layer immersed in a 3D Fermi gas. Using a variational approach, we show that in this mixed-dimensional (MD) system, there is a transition between polaron and molecule ground states, similar to the case of pure 3D. Moreover, we find that the attractive polaron energy in MD is higher than that in 3D, while molecular energy in MD is lower than that in 3D, which leads to a shift of the critical interaction strength of transition. Further analysis shows that the energy difference between 3D and MD systems is attributed to the increment of the effective mass of the impurity, which is induced by the spatial constraint on the impurity.
It has been commonly believed that a polaron-to-molecule transition occurs in three-dimensional (3D) and 2D Fermi polaron systems as the attraction between the single impurity and majority fermions gets stronger. The conclusion has been drawn from the separate treatment of polaron and molecule states and thus deserves a close reexamination. In this work, we explore the physics of polarons and molecules by utilizing a unified variational Ansatz with up to two particle-hole (ph) excitations (V-2ph). We confirm the existence of a first-order transition in 3D and 2D Fermi polarons, and we show that the nature of such a transition lies in an energy competition between systems with different momenta, $\mathbf{Q}=\mathbit{0}$ and ∣Q∣=kF|\mathbf{Q}|={k}_{F}∣Q∣=kF​; here Q\mathbf{Q}Q is defined as the momentum of a Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum kF{k}_{F}kF​). The literally proposed molecule Ansatz is identified as an asymptotic limit of the ∣Q∣=kF|\mathbf{Q}|={k}_{F}∣Q∣=kF​ state in a strong-coupling regime, which implies a huge SO(3)\text{SO}(3)SO(3) (for 3D) or SO(2)\text{SO}(2)SO(2) (for 2D) ground-state degeneracy in this regime. The recognition of such degeneracy is crucially important for evaluating the molecule occupation in realistic systems with finite impurity density and at finite temperature. To compare with recent experiment of 3D Fermi polarons, we have calculated various physical quantities under the V-2ph framework, and we obtained results that are in good agreement with experimental data in the weak-coupling and near-resonance regime. Further, to check the validity of our conclusion in 2D, we have adopted a different variational method based on the Gaussian sample of high-order ph excitations (V-Gph), and we found the same conclusion on the nature of the polaron-molecule transition therein. For a 1D system, the V-2ph method predicts no sharp transition, and the ground state is always at the $\mathbf{Q}=\mathbit{0}$ sector, consistent with the exact Bethe-Ansatz solution. The presence/absence of a polaron-molecule transition is analyzed to be closely related to the interplay effect of Pauli-blocking and ph excitations in different dimensions.
We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.
Abstract Polaron, a typical quasi-particle that describes a single impurity dressed with surrounding environment, serves as an ideal platform for bridging few- and many-body physics. In particular, different few-body correlations can compete with each other and lead to many intriguing phenomena. In this work, we review the recent progresses made in understanding few-body correlation effects in attractive Fermi polarons of ultracold gases. By adopting a unified variational ansatz that incorporates different few-body correlations in a single framework, we will discuss their competing effects in Fermi polarons when the impurity and majority fermions have the same or different masses. For the equal-mass case, we review the nature of polaron-molecule transition that is driven by two-body correlations, and especially highlight the finite momentum character and huge degeneracy of molecule states. For the mass-imbalanced case, we focus on the smooth crossover between polaron and various dressed clusters that originate from high-order correlations. These competing few-body correlations reviewed in Fermi polarons suggest a variety of exotic new phases in the corresponding many-body system of Fermi-Fermi mixtures.