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Physical Review A

Crossover from Fermi to Bose polarons in one- and two-dimensional interacting Fermi gases

Yue-Ran Shi, Ruijin Liu, Wei Zhang

Published Jul 25, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.013324

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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, \ensuremathρ=1/4,1/2\ensuremath{\rho}=1/4,1/2\ensuremathρ=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.
We study the Fermi polaron problem of one mobile spin-up impurity immersed atop the bath consisting of spin-down fermions in one- and two-dimensional square lattices. We solve this problem by applying a variational approach with non-Gaussian states after separating the impurity and the background via the Lee-Low-Pines transformation. The ground state with a fixed total momentum can be obtained via imaginary-time evolution. For the one-dimensional case, the variational ground-state energy is compared with exact Bethe ansatz solutions and numerical density matrix renormalization-group results with excellent agreement. In two-dimensional lattices, we focus on the dilute limit, and find a polaron-molecule evolution consistent with previous results obtained by variational and quantum Monte Carlo methods for models in continuum space. Compared to previous works, our method provides the lowest ground-state energy in the entire parameter region considered, and has an apparent advantage as it does not need to assume a priori any specific form of the variational wave function.
Abstract We study the polaron problem of an impurity immersed in the background of a Fermi sea confined in one-dimensional or two-dimensional isotropic traps. By changing the trapping potential from loose to tight, a dimensional crossover from anisotropically trapped three-dimensional to quasi-two-dimensional (quasi-2D) or quasi-one-dimensional (quasi-1D) configurations is investigated by calculating the ground-state energy in a wide range of interaction strength. We adopt a low-dimensional effective Hamiltonian in the form of a two-channel model, where the excited levels in the confined directions are described phenomenologically by a dressed molecule, and use the variational approach up to one pair of particle-hole fluctuations to calculate the energies of polaron and molecule states. We map out the phase diagrams for both quasi-1D and quasi-2D configurations and different mass ratios, and conclude that the polaron phase is preferable with tighter confinement and lighter impurity mass in lower dimensions. We also find that owing to the significant population of excited levels by strong interaction, a strictly low-dimensional system with all particles residing in the ground state of the trap can never work when study polaron-molecule transition, even in the tightly confined limit. This discrepancy has been observed in an experiment of quasi-2D gases of 40 K atoms and is well explained by our calculation.
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.
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.