Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases

Massignan, Pietro; Zaccanti, Matteo; Bruun, Georg M.

doi:10.1088/0034-4885/77/3/034401

Cited by 422 publications

(565 citation statements)

References 179 publications

(452 reference statements)

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“…Pertinently, rf spectroscopy can directly probe the spectral properties of quantum impurities [12,15,16,47,48], and has prompted theoretical investigations of impurity spectral functions [34,35,49,50].…”

Section: Introductionmentioning

confidence: 99%

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Shashi¹,

Grusdt²,

Abanin³

et al. 2014

Phys. Rev. A

104

182

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Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a δ-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.

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Section: Introductionmentioning

confidence: 99%

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Shashi¹,

Grusdt²,

Abanin³

et al. 2014

Phys. Rev. A

104

182

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“…These theoretical values are consistent with experimental extractions of η = −0.58(5) [25] and −0.64(7) [26] from ultracold atoms across a Feshbach resonance. The Fermi polaron continues to be an exciting area of research [27,28], with recent studies of the polaron in two dimensions [29,30] and of the P-wave polaron [31].Here, we generalize the polaron to strongly interacting neutrons, where the effective range r e = 2.7 fm is important, and k F r e ∼ 1 is not small, as is relevant for nuclei. We calculate the polaron energy using an effective field theory (EFT) for large a and large r e , and from chiral EFT interactions that include contributions beyond the effective range.…”

mentioning

confidence: 98%

Neutron polaron as a constraint on nuclear density functionals

et al. 2014

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We study the energy of an impurity (polaron) that interacts strongly in a sea of fermions when the effective range of the impurity-fermion interaction becomes important, thereby mapping the Fermi polaron of condensed matter physics and ultracold atoms to strongly interacting neutrons. We present Quantum Monte Carlo results for this neutron polaron, and compare these with effective field theory calculations that also include contributions beyond the effective range. We show that stateof-the-art nuclear density functionals vary substantially and generally underestimate the neutron polaron energy. Our results thus provide constraints for adjusting the time-odd components of nuclear density functionals to better characterize polarized systems. Energy-density functionals are the only method available to study heavy nuclei and to globally describe the chart of nuclides [1,2]. Due to the need for a precise description of low-energy observables, parameters of these functionals are generally fit to properties of nuclei, including masses and radii. This empirical construction can therefore also benefit from additional input to constrain their properties in exotic, i.e., neutron-rich or spin-polarized systems. Examples of such pseudo-data include calculations of neutron matter [3-9] and neutron drops [10]. This approach has been successfully used to shape new functionals (see, e.g., Refs. [11-16]). In this work, we study the neutron polaron and use its energy as a constraint on nuclear density functionals.The polaron was first introduced in condensed matter physics, and has recently been investigated in strongly interacting ultracold Fermi gases [17] -a system that has many similarities with the physics of low-density neutron matter (see, e.g., Refs. [3,4]). The Fermi polaron is an impurity interacting in a Fermi sea, realized in ultracold atoms and neutron matter as a spin-down fermion in a sea of N ↑ spin-up fermions. The polaron energy E pol = E N ↑ +1 − E N ↑ is defined as the energy difference between the system with the polaron added and the N ↑ (noninteracting) Fermi system. In the thermodynamic limit, this is equivalent to the spin-down chemical potential in the limit of high polarization, and therefore constrains the phase diagram of strongly interacting Fermi systems as a function of spin imbalance [18][19][20][21][22].For attractive interactions, E pol < 0 measures the polaron binding energy in the Fermi sea. In the unitary limit, where the S-wave scattering length |a| → ∞, the polaron energy is universal at low densities and scales as E pol = ηE F where E F = k 2 F /2m is the Fermi energy (with Fermi momentum k F ) and η < 0 is a universal number [18]. Neutrons, whose scattering length is large (a = −18.5 fm), have low-density properties close to the unitary limit. At unitarity, the polaron energy admits a variational bound that sums one-particle-one-hole excitations, η ≤ −0.6066 [18], which is remarkably close to a full manybody treatment [23], η = −0.6158, and agrees with Quantum Monte Carlo (QMC) calculation...

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“…However, in general, the BA equations in Eq. (7,8) can not be solved analytically. We have to resort to numerical method.…”

Section: B Strong Couplingmentioning

confidence: 99%

Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas

Mao

Guan

2016

Phys. Rev. A

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Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clear distinction between the polaron and molecule is conceived by the probability distribution, single particle reduced density matrix and density-density correlations, which are calculated directly from the Bethe ansatz wave function. Such a polaron-molecule crossover presents a universal nature of an impurity immersed into a fermionic medium with an attraction in one dimension.

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Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases

Cited by 422 publications

References 179 publications

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Neutron polaron as a constraint on nuclear density functionals

Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas

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