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arXiv:2202.05363 · Physical Review A

Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: Formalism and applications

Jia Wang, Xia-Ji Liu, Hui Hu

Published Apr 26, 2022• 32 citations
arXivHTMLPDF

Abstract

We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson's orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wave function. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the subgap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.

DOI
10.1103/physreva.105.043320

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We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson's orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wave function. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the subgap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.
Abstract In this brief review, we report some new development in the functional determinant approach (FDA), an exact numerical method, in the studies of a heavy quantum impurity immersed in Fermi gases and manipulated with radio-frequency pulses. FDA has been successfully applied to investigate the universal dynamical responses of a heavy impurity in an ultracold ideal Fermi gas in both the time and frequency domain, which allows the exploration of the renowned Anderson’s orthogonality catastrophe (OC). In such a system, OC is induced by the multiple particle-hole excitations of the Fermi sea, which is beyond a simple perturbation picture and manifests itself as the absence of quasiparticles named polarons. More recently, two new directions for studying heavy impurity with FDA have been developed. One is to extend FDA to a strongly correlated background superfluid background, a Bardeen–Cooper–Schrieffer (BCS) superfluid. In this system, Anderson’s orthogonality catastrophe is prohibited due to the suppression of multiple particle-hole excitations by the superfluid gap, which leads to the existence of genuine polaron. The other direction is to generalize the FDA to the case of multiple RF pulses scheme, which extends the well-established 1D Ramsey spectroscopy in ultracold atoms into multidimensional, in the same spirit as the well-known multidimensional nuclear magnetic resonance and optical multidimensional coherent spectroscopy. Multidimensional Ramsey spectroscopy allows us to investigate correlations between spectral peaks of an impurity-medium system that is not accessible in the conventional one-dimensional spectrum.
We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using the 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's orthogonality catastrophe that occurs in a noninteracting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum, and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the subgap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a nonmagnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.
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.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
Locally probing pairing in fermionic superfluids, ranging from micro- to macroscopic scales, has been a long-standing challenge. Here, we investigate a new approach that uses Rydberg impurities as a spectroscopic sensor of the surrounding strongly correlated state of ultracold paired fermions. The extended wave function of the Rydberg electron induces a finite-range potential that can bind atoms from the BCS medium, forming molecular states. As a consequence, the optical absorption spectrum of the impurity encodes key many-body properties. Using the functional determinant approach, we provide a direct measure of the superfluid gap through frequency shifts of dimer and trimer peaks. The spectra also reveal whether the Cooper pairs are broken or trapped intact. For static Rydberg atoms, we relate this signature of pairing to the suppression of the orthogonality catastrophe due to the superconducting gap resulting in the formation of well-defined polaron quasiparticles. Our Letter establishes Rydberg atom spectroscopy as a powerful local probe of strongly correlated matter.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T = 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. We also consider the highly polarized gas and the competition between a polaronic and a molecular picture.