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arXiv:1412.5280 · Physical Review Letters

Polaronic Atom-Trimer Continuity in Three-Component Fermi Gases

Yusuke Nishida

Published Mar 20, 2015• 60 citations
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Abstract

Recently it has been proposed that three-component Fermi gases may exhibit a new type of crossover physics in which an unpaired Fermi sea of atoms smoothly evolves into that of trimers in addition to the ordinary BCS-BEC crossover of condensed pairs. Here we study its corresponding polaron problem in which a single impurity atom of one component interacts with condensed pairs of the other two components with equal populations. By developing a variational approach in the vicinity of a narrow Feshbach resonance, we show that the impurity atom smoothly changes its character from atom to trimer with increasing the attraction and eventually there is a sharp transition to dimer. The emergent polaronic atom-trimer continuity can be probed in ultracold atoms experiments by measuring the impurity spectral function. Our novel crossover wave function properly incorporating the polaronic atom-trimer continuity will provide a useful basis to further investigate the phase diagram of three-component Fermi gases in more general situations.

DOI
10.1103/physrevlett.114.115302

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Recently it has been proposed that three-component Fermi gases may exhibit a new type of crossover physics in which an unpaired Fermi sea of atoms smoothly evolves into that of trimers in addition to the ordinary BCS-BEC crossover of condensed pairs. Here we study its corresponding polaron problem in which a single impurity atom of one component interacts with condensed pairs of the other two components with equal populations. By developing a variational approach in the vicinity of a narrow Feshbach resonance, we show that the impurity atom smoothly changes its character from atom to trimer with increasing the attraction and eventually there is a sharp transition to dimer. The emergent polaronic atom-trimer continuity can be probed in ultracold atoms experiments by measuring the impurity spectral function. Our novel crossover wave function properly incorporating the polaronic atom-trimer continuity will provide a useful basis to further investigate the phase diagram of three-component Fermi gases in more general situations.
A three-component Fermi gas near a broad Feshbach resonance does not have a universal ground state due to the Thomas collapse, while it does near a narrow Feshbach resonance. We explore its universal phase diagram in the plane of the inverse scattering length 1/ak(F) and the resonance range R(*)k(F). For a large R(*)k(F), there exists a Lifshitz transition between superfluids with and without an unpaired Fermi surface as a function of 1/ak(F). With decreasing R(*)k(F), the Fermi surface coexisting with the superfluid can change smoothly from that of atoms to trimers ("atom-trimer continuity"), corresponding to the quark-hadron continuity in a dense nuclear matter. Eventually, there appears a finite window in 1/ak(F) where the superfluid is completely depleted by the trimer Fermi gas, which gives rise to a pair of quantum critical points. The boundaries of these three quantum phases are determined in regions where controlled analyses are possible and are also evaluated based on a mean-field plus trimer model.
The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.
We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid, by using a many-body TTT-matrix approach that excludes Efimov trimer bound states. Termed the BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $\mathrm{\ensuremath{\Delta}}$, we find that the repulsive polaron branch becomes less well defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2\mathrm{\ensuremath{\Delta}}$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue, and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.
We study a type of Fermi polaron induced by an impurity interacting with an ultracold Fermi superfluid. Due to the three-component nature of the system, the polaron can become trimerlike with a nonuniversal energy spectrum. We identify multiple avoided crossings between impurity- and trimerlike solutions in both the attractive and the repulsive polaron spectra. In particular, the widths of avoided crossings gradually increase as the Fermi superfluid undergoes a crossover from the BCS side towards the Bose-Einstein condensate side, which suggests instabilities towards three-body losses. Such losses can be reduced for interaction potentials with small effective ranges. We also demonstrate, using the second-order perturbation theory, that the mean-field evaluation of the fermion-impurity interaction energy is inadequate even for small fermion-impurity scattering lengths, due to the essential effects of Fermi superfluid and short-range physics in such a system. Our results are practically useful for cold-atom experiments on mixtures.
The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments and in particular we exemplify the modifications of the medium either in the presence of Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.
We investigate the Fermi-polaron system with one mobile impurity immersed atop a two-component interacting fermion bath in one- and two-dimensional square lattices, where the impurity atom interacts with only one species (the spin-up component) of the background. The ground state with a given total momentum can be approximated by an extended Gaussian state, which is constructed from the combination of Gaussian states and a non-Gaussian polaronic transformation (Lee-Low-Pines transformation). In the few-body limit, the variational energies of two- and three-body systems show good agreement with exact results, which indicates the validity of the non-Gaussian variational method. We then move on to the many-body limit, i.e., the polaron problem with an interacting background. We choose two representative fillings of the background fermions, $\ensuremath{\rho}=1/4,1/2$, and obtain the corresponding ground states. Our results show that the system will undergo a smooth crossover from a Fermi-polaron to a Bose-polaron system as the interaction between background fermions increases. We further analyze the double occupancy and momentum distribution of the background fermions and find that the impurity will not significantly affect the background pairing.