We unravel the polaronic properties of impurities immersed in a correlated trapped one-dimensional (1D) Bose-Bose mixture. This setup allows for the impurities to couple either attractively or repulsively to a specific host, thus offering a highly flexible platform for steering the emergent polaronic properties. Specifically, the polaronic residue peak and strength of induced interactions can be controlled by varying the coupling of the impurities to the individual bosonic components. In particular, it is possible to maintain the quasiparticle character for larger interaction strengths as compared to the case of impurities immersed in a single bosonic species. We explicate a hierarchy of the polaron binding energies in terms of the impurity-medium interactions, thereby elucidating the identification of the polaronic resonances in recent experimental radiofrequency schemes. For strong attractive impurity-medium couplings bipolaron formation is captured. Our findings pave the way for continuously changing the quasiparticle character, under the impact of trap effects, while exposing the role of correlations in triple mixture settings.
We apply the diagrammatic Monte Carlo approach to three-dimensional Fermi-polaron systems with mass-imbalance, where an impurity interacts resonantly with a noninteracting Fermi sea whose atoms have a different mass. This method allows to go beyond frequently used variational techniques by stochastically summing all relevant impurity Feynman diagrams up to a maximum expansion order limited by the sign problem. Polaron energy and quasiparticle residue can be accurately determined over a broad range of impurity masses. Furthermore, the spectral function of an imbalanced polaron demonstrates the …
Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.
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…
Polarons can serve as an ideal platform to identify few-body correlations in tackling complex many-body problems. In this work, we reveal various crystalline few-body correlations smoothly emergent from the mass-imbalanced Fermi polarons in two dimensions. A unified variational approach up to three particle-hole excitations allows us to extract the dominant dimer, trimer or tetramer correlation in a single framework. When the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron is found to undergo a smooth crossover, instead of a sharp transition, from the polaronic …
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…
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 study theoretically the collective mode spectrum of a strongly imbalanced two-component unitary Fermi gas in a cigar-shaped trap, where the minority species forms a gas of polarons. We describe the collective breathing mode of the gas in terms of the Fermi liquid kinetic equation taking collisions into account using the method of moments. Our results for the frequency and damping of the longitudinal in-phase breathing mode are in good quantitative agreement with an experiment by Nascimbène et al. [Phys. Rev. Lett. 103, 170402 (2009)] and interpolate between a hydrodynamic and a collisionles…
We study a highly imbalanced Fermi gas in a one-dimensional optical lattice from the polaronic point of view. The time-evolving block decimationg algorithm is used to calculate the ground state and dynamics of the system. We find qualitatively similar polaronic behaviour as in the recent experiment by Schirotzek et al. \cite{Schirotzek2009a} where radio-frequency spectroscopy was used to observe polarons in three-dimensional space. In the weakly interacting limit our exact results are in excellent agreement with a polaron ansatz, and in the strongly interacting limit the results match with an …
The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that in the strongly imbalanced regime the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi liquid state in this regime is unstable to p-wave superfluidity, in accordance with the result…
Recently Mora and Chevy [Phys. Rev. Lett. 104, 230402 (2010), arXiv:1003.0213v2], in studying the energy of an atomic Fermi gas consisting of a majority species, 1, and a minority species, 2, showed that, due to interatomic interactions, the energy density E of the gas has a contribution of the form E^(2)= f n_2^2 /2, where n_i is the density of species i. They attribute this term to a `modification of the single polaron properties due to Pauli blocking'. In this Comment, we demonstrate that E^(2) may equivalently be understood in terms of the familiar interaction between minority atoms induce…
The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly-interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime.
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.
We propose a new protocol to examine many-polaron properties in a cold atom experiment. Initially, polaronic clouds are prepared around the opposite edges of a majority gas cloud. After time evolution, the collision of two clouds exhibits various polaronic effects. To see how {\it collective} properties of many polarons with mediated interactions appear in the case in which the impurity and majority gases are composed of mass-balanced fermions with different spin components, we perform a nonlinear hydrodynamic simulation for collisional dynamics of two Fermi polaronic clouds. We found that the…
We present measurements of spin transport in ultracold gases of fermionic lithium-6 in a mixture of two spin states at a Feshbach resonance. In particular, we study the spin dipole mode, where the two spin components are displaced from each other against a harmonic restoring force. We prepare a highly-imbalanced, or polaronic, spin mixture with a spin dipole excitation and observe strong, unitarity limited damping of the spin dipole mode. In gases with small spin imbalance, below the Pauli limit for superfluidity, we observe strongly damped spin flow despite the presence of a superfluid core.
The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well-known case is an impurity coupled to a bosonic bath, for example lattice vibrations. Here the impurity together with its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-Tc superconductors as well as in colossal-magnetoresistance in manganites. For impurities in a fermionic bath, the attention so far has been mostly on heavy or immobile impurities which exhibit Anderson's orthogonal…
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose-Fermi and Fermi-Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron …
We investigate the properties of a strongly interacting imbalanced mixture of bosonic $^{41}$K impurities immersed in a Fermi sea of ultracold $^6$Li atoms. This enables us to explore the Fermi polaron scenario for large impurity concentrations including the case where they form a Bose-Einstein condensate. The system is characterized by means of radio-frequency injection spectroscopy and interspecies interactions are widely tunable by means of a well-characterized Feshbach resonance. We find that the energy of the Fermi polarons formed in the thermal fraction of the impurity cloud remains rath…
We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density $x=n\ds /n\us$ is usually considered as a gas of non interacting polarons. This allows to calculate, in the expansion of the total energy of the system in powers of $x$, the terms proportional to $x$ (corresponding to the binding energy of the polaron) and to $x^{5/3}$ (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically d…
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, whe…
We study by diagrammatic methods a mixture of single-component bosons and fermions, with boson-fermion coupling tuned by a Fano-Feshbach resonance. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. Such quantum critical point depends very weakly on the population imbalance and for vanishing boson densities coincides with that found for the polaron-molecule transition in a strongly imbalanced Fermi gas, thus bridging two quite distinct physical systems.
We study pairing formation and the appearance of induced spin-triplet p-wave superfluidity in dilute three-dimensional imbalanced Fermi gases in the presence of a uniform non-Abelian gauge field. This gauge field generates a synthetic Rashba-type spin-orbit interaction which has remarkable consequences in the induced p-wave pairing gaps. Without the synthetic gauge field, the p-wave pairing occurs in one of the components due to the induced (second-order) interaction via an exchange of density fluctuations in the other component. We show that this p-wave superfluid gap induced by density fluct…
We have created a triply quantum degenerate mixture of bosonic $^{41}$K and two fermionic species $^{40}$K and $^6$Li. The boson is shown to be an efficient coolant for the two fermions, spurring hopes for the observation of fermionic superfluids with imbalanced masses. We observe multiple heteronuclear Feshbach resonances, in particular a wide s-wave resonance for the combination $^{41}$K-$^{40}$K, opening up studies of strongly interacting {\it isotopic} Bose-Fermi mixtures. For large imbalance, we enter the polaronic regime of dressed impurities immersed in a bosonic or fermionic bath.
Mixing two kinds of particles that repel each other usually results in either a homogeneous mixture when the repulsion is weak, or a complete phase separation of the two kinds when their repulsion is too strong. It is shown however that there is an intermediate regime where the two kinds can coexist in their ground state as a bubble immersed in a gas of one kind. Such a situation is obtained by adding heavy repulsive impurities into a Bose-Einstein condensate. Above a certain strength of the mutual repulsion, a stable bubble of impurities and bosons can be formed, resulting from the equilibriu…
Bose-Fermion pair correlations in a mixture are considered at zero temperature in the T-matrix approximation. Special attention is paid to the Luttinger theorem. In a strict RPA variant of the Nozieres-Schmitt-Rink approach, it is shown that this theorem is respected also in the homogeneous infinite matter case. We calculate the corresponding occupation numbers of fermions and bosons and the condensate depletion. We also show that in the limit of very small boson density, our results are in good agreement with the results found in the literature for the Fermi polaron in strongly imbalanced Fer…
We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture $^{87}$Rb $-^{40}$K for different values of the density imbalance. We then analyse the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of …
We investigate numerically the problem of few (one, two) noninteracting spin$-1/2$ fermions in a shallow harmonic trap coupled via contact repulsive interactions to a uniform one-dimensional bath of lattice bosons, described by the Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract the binding energy and the effective mass of quasiparticles, including dressed impurities (polarons) and their two-body bound states (bipolarons), emerging from the effective non-local Casimir interaction between the impurities. We show that the mixture exhibits rathe…
We explore the dynamical transport of an impurity between different embedding majority species which are spatially separated in a double well. The transfer and storage of the impurity is triggered by dynamically changing the interaction strengths between the impurity and the two majority species. We find a simple but efficient protocol consisting of linear ramps of majority-impurity interactions at designated times to pin or unpin the impurity. Our study of this highly imbalanced few-body triple mixture is conducted with the multi-layer multi-configuration time-dependent Hartree method for ato…
