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Modern Physics Letters B

Polarons and molecules in a mixed-dimensional Fermi gas

Baihua Gong, Xinhui Zhang

Published May 25, 2021• 0 citations
Publisher

Abstract

We address the problem of a single impurity atom moving in a two-dimensional (2D) layer immersed in a 3D Fermi gas. Using a variational approach, we show that in this mixed-dimensional (MD) system, there is a transition between polaron and molecule ground states, similar to the case of pure 3D. Moreover, we find that the attractive polaron energy in MD is higher than that in 3D, while molecular energy in MD is lower than that in 3D, which leads to a shift of the critical interaction strength of transition. Further analysis shows that the energy difference between 3D and MD systems is attributed to the increment of the effective mass of the impurity, which is induced by the spatial constraint on the impurity.

DOI
10.1142/s0217984921503541

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We address the problem of a single impurity atom moving in a two-dimensional (2D) layer immersed in a 3D Fermi gas. Using a variational approach, we show that in this mixed-dimensional (MD) system, there is a transition between polaron and molecule ground states, similar to the case of pure 3D. Moreover, we find that the attractive polaron energy in MD is higher than that in 3D, while molecular energy in MD is lower than that in 3D, which leads to a shift of the critical interaction strength of transition. Further analysis shows that the energy difference between 3D and MD systems is attributed to the increment of the effective mass of the impurity, which is induced by the spatial constraint on the impurity.
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 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 exact solution in the limit of infinite impurity mass. Thus, we expect the variational approach to provide a reliable tool for investigating 2D systems.
The non-Hermitian interaction in many-body systems may lead to novel phenomena. We study an impurity immersed in three-dimensional ideal Fermi gases, with a complex-valued contact interaction between the fermions and impurity that arise from two-body dissipation. Generalizing the unified variational approach to the non-Hermitian case, we study the effects of the dissipative attraction on the polaronic and molecular states of the impurity for different mass ratios. We find that the dissipation attraction can induce polaron-molecule transition despite the transition being absent in the Hermitian case, which is demonstrated to be a first-order phase transition between different total momenta. In addition, we show that the non-Hermitian attraction leads to significant decay of the polaronic and molecular states; however, increasing the mass ratio between the impurity and majority fermions will help suppress the decay. Our results illustrate the applicability of the unified variational approach in non-Hermitian Fermi polaron systems and the method may be extended to include higher-order particle-hole excitations and to study other types of bound states.
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|\mathbf{Q}|={k}_{F}∣Q∣=kF​; here Q\mathbf{Q}Q is defined as the momentum of a Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum kF{k}_{F}kF​). The literally proposed molecule Ansatz is identified as an asymptotic limit of the ∣Q∣=kF|\mathbf{Q}|={k}_{F}∣Q∣=kF​ state in a strong-coupling regime, which implies a huge SO(3)\text{SO}(3)SO(3) (for 3D) or SO(2)\text{SO}(2)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.
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.
A new generation of cold atom experiments trapping atomic mixtures in species-selective optical potentials opens up the intriguing possibility to create systems in which different atoms live in different spatial dimensions. Inspired by this, we investigate a mixed-dimensional Bose polaron consisting of an impurity particle moving in a two-dimensional (2D) layer immersed in a 3D Bose-Einstein condensate (BEC), using a theory that includes the mixed-dimensional vacuum scattering between the impurity and the bosons exactly. We show that similarly to the pure 3D case, this system exhibits a well-defined polaron state for attractive boson-impurity interaction that evolves smoothly into a mixed-dimensional dimer for strong attraction, as well as a well-defined polaron state for weak repulsive interaction, which becomes overdamped for strong interaction. We furthermore find that the properties of the polaron depend only weakly on the gas parameter of the BEC as long as the Bogoliubov theory remains a valid description for the BEC. This indicates that higher-order correlations between the impurity and the bosons are suppressed by the mixed-dimensional geometry in comparison to a pure 3D system, which led us to speculate that the mixed-dimensional polaron has universal properties in the unitarity limit of the impurity-boson interaction.