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arXiv:1912.12832 · Physical Review A

Collisional dynamics of polaronic clouds immersed in a Fermi sea

Hiroyuki Tajima, Junichi Takahashi, Eiji Nakano, Kei Iida

Published Nov 9, 2020• 9 citations
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Abstract

We propose a 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 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 dynamics is governed by the impurity Fermi pressure, polaron energy, and multipolaron correlations. In particular, shock waves occur in such a way as to reflect the many-body properties of polarons through the first sound of minority clouds. Our idea is applicable to other systems such as Bose polarons as well as mass-imbalanced mixtures.

DOI
10.1103/physreva.102.051302

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We propose a 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 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 dynamics is governed by the impurity Fermi pressure, polaron energy, and multipolaron correlations. In particular, shock waves occur in such a way as to reflect the many-body properties of polarons through the first sound of minority clouds. Our idea is applicable to other systems such as Bose polarons as well as mass-imbalanced mixtures.
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 $x={n}_{\ensuremath{\downarrow}}/{n}_{\ensuremath{\uparrow}}$ is usually considered as a gas of noninteracting polarons. This allows us to calculate, in the expansion of the total energy of the system in powers of xxx, the terms proportional to xxx (corresponding to the binding energy of the polaron) and to x5/3{x}^{5/3}x5/3 (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to x2{x}^{2}x2 and x7/3{x}^{7/3}x7/3. We find three such terms. The first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the nonzero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte Carlo results. The possible origins of this discrepancy are discussed.
An extremely polarized mixture of an ultracold Fermi gas is expected to reduce to a Fermi polaron system, which consists of a single impurity immersed in the Fermi sea of majority atoms. By developing a many-body T-matrix theory, we investigate spectral properties of the polarized mixture in experimentally relevant regimes in which the system of finite impurity concentration at nonzero temperature is concerned. We explicitly demonstrate presence of polaron physics in the polarized limit and discuss effects of many polarons in an intermediate regime in a selfconsistent manner. By analyzing the spectral function at finite impurity concentration, we extract the attractive and repulsive polaron energies. We find that a renormalization of majority atoms via an interaction with minority atoms is of significance to depict the many-polaron regime.
We investigate the low-lying compression modes of a unitary Fermi gas with imbalanced spin populations. For low polarization, the strong coupling between the two spin components leads to a hydrodynamic behavior of the cloud. For large population imbalance we observe a decoupling of the oscillations of the two spin components, giving access to the effective mass of the Fermi polaron, a quasiparticle composed of an impurity dressed by particle-hole pair excitations in a surrounding Fermi sea. We find m*/m = 1.17(10), in agreement with the most recent theoretical predictions.
This study develops an experimental method of deducing the profile of interaction induced between impurities in a trapped gas of ultracold Fermi or Bose atoms, which are often referred to as Fermi or Bose polarons. In this method, we consider a two-body Fermi or Bose polaron collision experiment in which impurities and atoms interact only weakly. Numerical simulations of the quantum dynamics reveal the possibility to obtain information regarding the nonlocal-induced interaction between two polarons from a measured profile of the polaron wave packet at several snapshots. This is because the potential of the induced interaction is well balanced by the quantum potential whenever the WKB approximation for the relevant Schr\"odinger equation is applicable.
An extremely polarized mixture of an ultracold Fermi gas is expected to reduce to a Fermi polaron system, which consists of a single impurity immersed in the Fermi sea of majority atoms. By developing a many-body T -matrix theory, we investigate spectral properties of the polarized mixture in experimentally relevant regimes in which the system of finite impurity concentration at nonzero temperature is concerned. We explicitly demonstrate presence of polaron physics in the polarized limit and discuss effects of many polarons in an intermediate regime in a selfconsistent manner. By analyzing the spectral function at finite impurity concentration, we extract the attractive and repulsive polaron energies. We find that a renormalization of majority atoms via an interaction with minority atoms and a thermal depletion of the impurity chemical potential are of significance to depict the many-polaron regime.