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arXiv:2101.02941 · Physical Review C

Fermi polaron in low-density spin-polarized neutron matter

Isaac Vidaña

Published May 17, 2021• 11 citations
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Abstract

I study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, I analyze its energy (${E}_{\ensuremath{\downarrow}}$), effective mass (${m}_{\ensuremath{\downarrow}}^{*}$), and quasiparticle residue (${Z}_{\ensuremath{\downarrow}}$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner-Hartree-Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at ${\mathrm{N}}^{3}\mathrm{LO}$ with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the ${}^{1}{S}_{0}$ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. It is shown that for Fermi momenta between $\ensuremath{\approx}0.25$ and $\ensuremath{\approx}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ the energy, effective mass, and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $\ensuremath{-}0.604\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.635\phantom{\rule{0.16em}{0ex}}{E}_{F}$, $1.300\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.085\phantom{\rule{0.16em}{0ex}}m$, and $0.741<{Z}_{\ensuremath{\downarrow}}<0.836$ in the case of the chiral interaction, and $\ensuremath{-}0.621\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.643\phantom{\rule{0.16em}{0ex}}{E}_{F}$, $1.310\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.089\phantom{\rule{0.16em}{0ex}}m$, and $0.739<{Z}_{\ensuremath{\downarrow}}<0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25\ensuremath{\lesssim}{k}_{F}\ensuremath{\lesssim}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.

DOI
10.1103/physrevc.103.l052801

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I study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, I analyze its energy (E\ensuremath↓{E}_{\ensuremath{\downarrow}}E\ensuremath↓​), effective mass (m\ensuremath↓∗{m}_{\ensuremath{\downarrow}}^{*}m\ensuremath↓∗​), and quasiparticle residue (Z\ensuremath↓{Z}_{\ensuremath{\downarrow}}Z\ensuremath↓​). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner-Hartree-Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N3LO{\mathrm{N}}^{3}\mathrm{LO}N3LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the 1S0{}^{1}{S}_{0}1S0​ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. It is shown that for Fermi momenta between \ensuremath≈0.25\ensuremath{\approx}0.25\ensuremath≈0.25 and \ensuremath≈0.45fm\ensuremath−1\ensuremath{\approx}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}\ensuremath≈0.45fm\ensuremath−1 the energy, effective mass, and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges \ensuremath−0.604EF<E\ensuremath↓<\ensuremath−0.635EF\ensuremath{-}0.604\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.635\phantom{\rule{0.16em}{0ex}}{E}_{F}\ensuremath−0.604EF​<E\ensuremath↓​<\ensuremath−0.635EF​, 1.300m<m\ensuremath↓∗<1.085m1.300\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.085\phantom{\rule{0.16em}{0ex}}m1.300m<m\ensuremath↓∗​<1.085m, and 0.741<Z\ensuremath↓<0.8360.741<{Z}_{\ensuremath{\downarrow}}<0.8360.741<Z\ensuremath↓​<0.836 in the case of the chiral interaction, and \ensuremath−0.621EF<E\ensuremath↓<\ensuremath−0.643EF\ensuremath{-}0.621\phantom{\rule{0.16em}{0ex}}{E}_{F}<{E}_{\ensuremath{\downarrow}}<\ensuremath{-}0.643\phantom{\rule{0.16em}{0ex}}{E}_{F}\ensuremath−0.621EF​<E\ensuremath↓​<\ensuremath−0.643EF​, 1.310m<m\ensuremath↓∗<1.089m1.310\phantom{\rule{0.16em}{0ex}}m<{m}_{\ensuremath{\downarrow}}^{*}<1.089\phantom{\rule{0.16em}{0ex}}m1.310m<m\ensuremath↓∗​<1.089m, and 0.739<Z\ensuremath↓<0.8320.739<{Z}_{\ensuremath{\downarrow}}<0.8320.739<Z\ensuremath↓​<0.832 when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range 0.25\ensuremath≲kF\ensuremath≲0.45fm\ensuremath−10.25\ensuremath{\lesssim}{k}_{F}\ensuremath{\lesssim}0.45\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}0.25\ensuremath≲kF​\ensuremath≲0.45fm\ensuremath−1 exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.
We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.
We investigate the highly polarized limit of a two-dimensional Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer, or even larger clusters. Similarly to three dimensions, we find that the Fermi sea favors the trimer state so that it exists for ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario that corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.
Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at T=0T=0T=0, and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting quasiparticle model. The contact parameter is estimated by fitting the pair distribution function of atoms in different spin states.
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 impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole excitation, the drag parameter, and the medium-density modification around the impurity. These quantities are shown to exhibit spatial anisotropies in such a way as to reflect the momentum anisotropy of the background dipolar Fermi gas. We also give numerical results for the polaron properties at the unitarity limit of the impurity-fermion interaction in the case in which the impurity and fermion masses are equal. It has been found that the transverse effective mass and the transverse momentum drag parameter of the polaron both tend to decrease by $\ensuremath{\sim}10%$ when the DDI strength is raised from 0 up to around its critical value, while the longitudinal ones exhibit a very weak dependence on the DDI.
We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant ppp-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the ppp-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Moreover, two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of 1S0^{1}S_{0}1S0​ neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result is useful for understanding many-body physics in astrophysical environments as well as the formation of multinucleon clusters in neutron-halo nuclei.