The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.
The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.
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 metastability associated with the first-order transition from the normal to the superfluid phase is investigated in the phase diagram of two-component polarized Fermi gases. We begin by detailing the dominant decay processes of single quasiparticles, determining the momentum thresholds of each process and calculating their rates. This understanding is then applied to a Fermi sea of polarons, and we predict a region of metastability for the normal partially polarized phase. We propose experiments to observe the threshold of the metastable region, the interaction strength at which the quasiparticle ground state changes character, and the decay rate of polarons.
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.
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.
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.
We study polaron excitations induced by an impurity interacting with a two-dimensional p+ip Fermi superfluid. As the Fermi-Fermi pairing interaction is tuned, the background Fermi superfluid undergoes a topological phase transition. We show that such a transition is accompanied by a discontinuity in the second derivative of the polaron energy, regardless of the impurity-fermion interaction. We also identify a polaron to trimer crossover when the Fermi superfluid is in the strongly interacting, thus topologically trivial, regime. However, the trimer state is metastable against the molecular state where the impurity binds a Bogoliubov quasiparticle from the Fermi superfluid. By comparing the polaron to molecule transition in our system with that of an impurity in a noninteracting Fermi sea, we find that pairing interactions in the background Fermi superfluid effectively facilitate the impurity-fermion binding. Our results suggest the possibility of using the impurity as a probe for detecting topological phase transitions in the background; they also reveal interesting competitions between various many-body states in the system.