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.
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 system with 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 certain interaction window near their transition, both states appear as local minima i…
Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clea…
We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. Our results indicate that the physics of realistic mixed polaron models is much richer than that of simplified models. We then show that ultracold molecules trapped in optical lattices can be used to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with e…
A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirot…
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 analys…
The problem of a single down spin particle interacting with a Fermi sea of up spin particles is of current interest in the field of cold atoms. The Hubbard model, appropriate to atoms in an optical lattice potential, is considered in parallel with a gas model. As the strength of an attractive short-range interaction is increased there is a crossover from "polaron" behaviour, in which the Fermi sea is weakly perturbed, to "molecule" behaviour in which the down spin particle is bound to a single up spin particle. It is shown that this is a smooth crossover, not a sharp transition as claimed by m…
Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bond molecule. Thus it is seen that the system undergos a cross-over from a mean field polaron-like nature into a mixture of excess fermion…
We study the impurity problem in a gas of $^{173}$Yb atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state $^1S_0$ interact with those in the long-lived excited $^3P_0$ state with magnetically tunable interactions. We consider an impurity atom with a given hyperfine spin in the $^3P_0$ state interacting with a single-component Fermi sea of atoms in the ground $^1S_0$ manifold. Close to the orbital Feshbach resonance, the impurity can induce collective particle-hole excitations out of the Fermi sea, which can be reg…
We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority atom in an ultracold gas, exciton in a solid) by attraction strong enough to form a molecule/trion. We introduce a diagrammatic scheme which allows treating a finite mass impurity while reproducing the Fermi edge singularity in the immobile limit. For large binding energies the spectrum is characterized by a semi-coherent repulsive polaron and an incoherent molecule-hole continuum, which is the lowest-energy feature in the single-particle spectrum. The previously predicted attractive polaron seems not to exist for stro…
In this work, we explore the polaron and molecule physics by utilizing a unified variational ansatz with up to two particle-hole(p-h) excitations(V-2ph). We confirm the existence of a first-order transition in 3D and 2D Fermi polarons, and show that the nature of such transition lies in an energy competition between systems with different momenta ${\mathbf Q}=0$ and $|{\mathbf Q}|=k_F$, here ${\mathbf Q}$ is defined as the momentum of Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum $k_F$). The literally proposed molecule ansatz is identified as an a…
We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\downarrow$ impurities attractively interacting with a sea of $\uparrow$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\uparrow$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperat…
We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological su…
In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions, the so-called Fermi polaron problem. On one side, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides quantitatively reliable insight into the phase diagram of strongly interacting population imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to study itinerant ferromagnetism, a long standing problem in quantum mechanics.
A light impurity in a Fermi sea undergoes a transition from a polaron to a molecule for increasing interaction. We develop a new method to compute the spectral functions of the polaron and molecule in a unified framework based on the functional renormalization group with full self-energy feedback. We discuss the energy spectra and decay widths of the attractive and repulsive polaron branches as well as the molecular bound state and confirm the scaling of the excited state decay rate near the transition. The quasi-particle weight of the polaron shifts from the attractive to the repulsive branch…
We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of part…
We address the problem of a single "spin-down" impurity atom interacting attractively with a spin-up Fermi gas in two dimensions (2D). We consider the case where the mass of the impurity is greater than or equal to the mass of a spin-up fermion. Using a variational approach, we resolve the questions raised by previous studies and we show that there is, in fact, a transition between polaron and molecule (dimer) ground states in 2D. For the molecule state, we use a variational wave function with a single particle-hole excitation on the Fermi sea and we find that its energy matches that of the ex…
We consider the ground state of a single "spin-down" impurity atom interacting attractively with a "spin-up" atomic Fermi gas. By constructing variational wave functions for polarons, molecules and trimers, we perform a detailed study of the transitions between each of these dressed bound states as a function of mass ratio $r=m_\uparrow/m_\downarrow$ and interaction strength. We find that the presence of a Fermi sea enhances the stability of the $p$-wave trimer, which can be viewed as a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) molecule that has bound an additional majority atom. For sufficientl…
The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground state ener…
We study the impurity problem in a Fermi gas of $^{173}$Yb atoms near an orbital Feshbach resonance, where a single moving particle in the $^3P_0$ state interacting with two background Fermi seas of particles in different nuclear states of the ground $^1S_0$ manifold. By employing wave function ansatzs for molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. We find that in comparison to the case of only one Fermi sea is populated, the presence of an additional Fermi sea acts as an energy shift between the two…
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, effec…
We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction st…
It has long been expected that quantum degenerate gases of molecules would open access to a wide range of phenomena in molecular and quantum sciences. However, the very complexity that makes ultracold molecules so enticing has made reaching degeneracy an outstanding experimental challenge over the past decade. We now report the production of a Fermi degenerate gas of ultracold polar molecules of potassium--rubidium (KRb). Through coherent adiabatic association in a deeply degenerate mixture of a rubidium Bose-Einstein condensate and a potassium Fermi gas, we produce molecules at temperatures b…
We investigate the properties a mobile ion immersed in a Bose-Einstein condensate (BEC) using different theoretical approaches. A coherent state variational ansatz predicts that the ion spectral function exhibits several branches in addition to polaronic quasiparticle states, and we employ a diagrammatic analysis of the ion-atom scattering in the BEC to identify them as arising from the binding of an increasing number of bosons to the ion. We develop a simplified model describing the formation of these molecular ions showing that their spectral weight scales with the number of bound atoms. The…
We report on the preparation of a quantum degenerate mixture of $^{23}$Na$^{40}$K molecules and $^{40}$K atoms. A deeply degenerate atomic mixture of $^{23}$Na and $^{40}$K atoms with a large number ratio ($N_F/N_B\approx 6$) is prepared by the mode-matching loading of atoms from a cloverleaf-type magnetic trap into a large-volume horizontal optical dipole trap and evaporative cooling in a large-volume three-beam optical dipole trap. About $3.0\times10^4$ $^{23}$Na$^{40}$K ground-state molecules are created through magneto-association followed by stimulated adiabatic Raman passage. The 2D dens…
The heavy Fermi polaron I: the Lithium-Cesium experiment
Physikalisches Institut, Universität Heidelberg（海德堡大学物理研究所）；Department of Physics and Research Center OPTIMAS, RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工大学物理系与OPTIMAS研究中心）
We consider the impurity problem in an orbital Feshbach resonance (OFR), with a single excited clock state $|e\uparrow\rangle$ atom immersed in a Fermi sea of electronic ground state $|g\downarrow\rangle$. We calculate the polaron effective mass and quasi-particle residue, as well as the polaron to molecule transition. By including one particle-hole excitation in the molecular state, we find significant correction to the transition point. This transition point moves toward the BCS side for increasing particle densities, which suggests that the corresponding many-body physics is similar to a na…
Quantum degenerate molecules represent a new paradigm for fundamental studies and practical applications. Association of already quantum degenerate atoms into molecules provides a crucial shortcut around the difficulty of cooling molecules to ultracold temperatures. Whereas association can be induced with either laser or magnetic fields, photoassociation requires impractical laser intensity to overcome poor overlap between the atom pair and molecular wavefunctions, and experiments are currently restricted to magnetoassociation. Here we model realistic production of a quantum degenerate gas of …
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 polar…
We discuss the interaction of a quantum impurity with a one-dimensional degenerate Bose gas forming a Bose-polaron. In three spatial dimensions the quasiparticle is typically well described by the extended Fröhlich model, in full analogy with the solid-state counterpart. This description, which assumes an undepleted condensate, fails however in 1D, where the backaction of the impurity on the condensate leads to a self-bound mean-field polaron for arbitrarily weak impurity-boson interactions. We present a model that takes into account this backaction and describes the impurity-condensate intera…
We report spectroscopic observation of Rydberg polarons in an atomic Bose gas. Polarons are created by excitation of Rydberg atoms as impurities in a strontium Bose-Einstein condensate. They are distinguished from previously studied polarons by macroscopic occupation of bound molecular states that arise from scattering of the weakly bound Rydberg electron from ground-state atoms. The absence of a $p$-wave resonance in the low-energy electron-atom scattering in Sr introduces a universal behavior in the Rydberg spectral lineshape and in scaling of the spectral width (narrowing) with the Rydberg …
We discuss properties of a single impurity atom immersed in the spin-$1/2$ dilute Fermi gas with equal populations of two species in the deep Bose-Einstein condensate (BEC) phase. In this limit, when an almost undepleted BEC of the tightly bound molecules of spin-up and spin-down fermions is formed, we calculate the parameters of an impurity spectrum. It is justified that the leading-order contribution to the impurity energy, while being determined by the two- and three-body scattering processes, is dominated by the former ones.
We show that s-wave scattering resonances induced by dipolar interactions in a polar molecular gas have a universal large and positive effective range, which is very different from Feshbach resonances realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequence in many-body physics. At high temperature regime, a positive effective range gives rise to stronger repulsive interaction energy for positive scattering length, and weaker attractive interaction energy for negative scattering length. While at low-temperatures, we …
The interplay between measurement and quantum correlations in many-body systems can lead to novel types of collective phenomena which are not accessible in isolated systems. In this work, we merge the Zeno-paradigm of quantum measurement theory with the concept of polarons in condensed-matter physics. The resulting quantum-Zeno Fermi-polaron is a quasi-particle which emerges for lossy impurities interacting with a quantum-degenerate bath of fermions. For loss rates of the order of the impurity-fermion binding energy the quasi-particle is short lived. However, we show that in the strongly dissi…
We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson\textquoteright s orthogonality catastrophe that occurs in a non-interacting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity…
We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state i…
We investigate thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using a self-consistent framework of strong-coupling diagrammatic approaches, both of the ejection and reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp tran…
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 s…
Institute for Quantum Optics and Quantum Information (IQOQI)（量子光学与量子信息研究所）；University of Innsbruck（因斯布鲁克大学）；International School for Advanced Studies (SISSA)（高级研究国际学校）；Monash University（莫纳什大学）；Aarhus University（奥胡斯大学）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
We consider the dynamics of a quantum impurity after a sudden interaction quench into a one-dimensional degenerate Bose gas. We use the Keldysh path integral formalism to derive a truncated Wigner like approach that takes the back action of the impurity onto the condensate into account already on the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us not only to calculate the real space trajectory of the impurity but also the absorption spectrum. We find that quantum corrections and thermal effects play a crucial role for th…
Efficient variational approach to the Fermi polaron problem in two dimensions, both in and out of equilibrium
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；ETH Zurich（苏黎世联邦理工学院）；Harvard University（哈佛大学）
The study of polaron of an open quantum system plays an important role in both verifying the effectiveness of approximate many-body theory and predicting novel quantum phenomenone in open quantum systems. In a pioneering work, Piazza et al have proposed a Fermi-polaron scheme with a lossy impurity [54], which exhibits a novel long-lived attractive polaron branch in the quantum Zeno limit. However, we would also run into a counterpart problem that an impurity scatters with an open quantum bath exciting polarons, which is what we focus in on. In this work, we conclude the molecular state under t…
Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron -- a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon -- a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accura…
Based on the recently developed interaction renormalization for the one-dimensional $p$-wave interaction, we study the problem of a single impurity immersed in a highly polarized Fermi sea. They interact through a narrow $p$-wave Feshbach resonance, so the effective range $r_{0}$ naturally appears in the system. We use the variational approach limited to single-particle-hole excitations on top of the unperturbed Fermi sea. The polaron exhibits two branches of solutions, namely, the attractive and repulsive branches, with varying scattering length across the resonance. We calculate the energy s…
We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes …
We present the essential experimental steps of our all-optical approach to prepare a double-degenerate Fermi-Fermi mixture of 6Li and 40K atoms, which then serves as a starting point for molecule formation. We first describe the optimized trap loading procedures, the internal-state preparation of the sample, and the combined evaporative and sympathetic cooling process. We then discuss the preparation of the sample near an interspecies Feshbach resonance, and we demonstrate the formation of heteronuclear molecules by a magnetic field ramp across the resonance.
Long-Range Fermi-Polaron Blockade in Monolayer MoSe$_2$
Purdue University（普渡大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Columbia University（哥伦比亚大学）；National Institute for Materials Science（国立材料研究所）
We use a non-perturbative 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 Fröhlich 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. …
