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 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.
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; here Q is defined as the momentum of a Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum kF). The literally proposed molecule Ansatz is identified as an asymptotic limit of the ∣Q∣=kF state in a strong-coupling regime, which implies a huge SO(3) (for 3D) or 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.
Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short-ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoretically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact parameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition.
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.
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.
The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.
We develop a non-Gaussian variational approach that enables us to study both equilibrium and far-from-equilibrium physics of the two-dimensional Fermi polaron. This method provides an unbiased analysis of the polaron-to-molecule phase transition without relying on truncations in the total number of particle-hole excitations. Our results—which include the ground-state energy and quasiparticle residue—are in qualitative agreement with the known Monte Carlo calculations. The main advantage of the non-Gaussian states compared to conventional numerical methods is that they enable us to explore long-time polaron evolution and, in particular, study various spectral properties accessible to both solid-state and ultracold atom experiments. We design two types of radiofrequency spectroscopies to measure polaronic and molecular spectral functions. Depending on the parameter regime, we find that these spectral functions and fermionic density profiles near the impurity either display long-lived oscillations between the repulsive and attractive polaron branches or exhibit fast relaxational dynamics to the molecular state.