Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

Zyl, Brandon P. van; Zaremba, E.; Towers, J.

doi:10.1103/physreva.90.043621

Cited by 8 publications

(8 citation statements)

References 34 publications

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“…The structure of the full force of the magnetic dipole-dipole interaction obtained in Ref. [105] corresponds to the exchange part of the exchange electric dipole interaction derived in our paper for purely two dimensional dipolar fermions (see formula (53) below). Let us also note that quantum hydrodynamic derivation of the force of magnetic dipole-dipole interaction (the spin-spin interaction) for three dimensional systems of particles with the exchange spin-spin interaction was presented in Ref.…”

Section: Introductionmentioning

confidence: 60%

“…Collective excitations of a harmonically trapped, twodimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime was considered in Ref. [105], where authors applied the Thomas-Fermi von Weizsäcker energy functional for the neutral atoms with the magnetic moments. They obtained the force field F of the magnetic dipole-dipole interaction proportional to ∇n 2D due to different definition of the force F).…”

Section: Introductionmentioning

confidence: 99%

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Destabilization effect of exchange dipole-dipole interaction on the spectrum of electric dipolar ultracold Fermi gas

Andreev¹

2014

Preprint

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The self-consistent field approach for the electric dipolar ultracold spin-1/2 fermions is discussed. Contribution of the exchange part of the electric dipole interaction is found. Hence we obtain a model of dipolar fermions beyond the self-consistent field approximation. It is shown that the exchange interaction of electric dipolar fermions depends on the spin-polarisation of the system. For instance the electric dipole exchange interaction equals to zero for spin-unpolarised systems, namely all low laying quantum states occupied by two-particles with opposite spins. In opposite limit of the full spin polarisation of the degenerate fermions, then we have one particle in each quantum states, the exchange interaction has maximum value, which is comparable with the self-consistent field part of the dipole-dipole interaction. The self-consistent part of the electric dipole-dipole interaction gives a positive contribution into the spectrum of collective excitations, while the exchange part of the dipole-dipole interaction leads to a negative term in the spectrum. At angles between the equilibrium polarisation and the direction of wave propagation close to π/2 the full dipolar part of the spectrum becomes negative. At the electric dipole moment of fermions of order of several Debay the dipolar part is large enough to exceed the Fermi pressure, that reveals in an instability. We also consider spectrum of the quasi two-dimensional cloud of fermions in the trap. We consider the regime of purely two dimensional structure of dipolar fermions with the exchange dipole-dipole interaction in the three dimensional space and calculate the spectrum in this regime. We assume that the equilibrium polarisation is perpendicular to the two dimensional structure. Major picture of the spectrum behavior in low dimensional regimes is similar to the three-dimensional one. Since the two-dimensional perturbations propagate perpendicular to the equilibrium polarisation we find that the dipolar part of the spectrum is negative in these regimes.

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Destabilization effect of exchange dipole-dipole interaction on the spectrum of electric dipolar ultracold Fermi gas

Andreev¹

2014

Preprint

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“…Fermions are studied by a set of different hydrodynamic models. For instance, there is the Thomas-Fermivon Weizsäcker hydrodynamic theory [16,17] applied for examination of a zero-temperature, spin-polarized, harmonically trapped, dipolar Fermi gas.…”

Section: Hydrodynamic Minimal Coupling Model In Third Order By the In...mentioning

confidence: 99%

“…The application of simple hydrodynamic model for description of collective motion of fermions goes back to the first half of the XX century (Bloch's hydrodynamic theory) [14]. The last decades show application of simple hydrodynamic model [15] along with the development of new modifications [16,17].…”

Section: Introductionmentioning

confidence: 99%

Extended hydrodynamics of the degenerate partially spin polarized fermions with the short-range interaction up to the third order by the interaction radius approximation

Andreev¹

2020

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A possibility of the hydrodynamic description of ultracold fermions via the microscopic derivation of the model is described. Differently truncated hydrodynamic models are derived and compared. All models are based on the microscopic many-particle Schrödinger equation. Minimal coupling model based on the continuity and Euler equations are considered. The extended hydrodynamic model including the independent dynamics of the momentum flux (the pressure evolution) is derived. Influence of the spin polarization is described. The short-range interaction is considered in the isotropic limit. The interaction is considered up to the third order by the interaction radius. Therefore, the single fluid model of spin-1/2 fermions and the two fluid model of spin-1/2 fermions are under consideration in this paper. Spectra of bulk collective excitations are derived and compared in terms of different models.

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“…Recently, also the radial quadrupole mode was studied in detail in both the CL and the HD regime [62]. Moreover, numerical studies focusing on a two-dimensional system in the HD regime were performed [63]. The next natural step is the investigation of what happens, when the system undergoes a crossover from one regime to the other.…”

Section: Introductionmentioning

confidence: 99%

Low-lying excitation modes of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

2017

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By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.

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Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime

Cited by 8 publications

References 34 publications

Destabilization effect of exchange dipole-dipole interaction on the spectrum of electric dipolar ultracold Fermi gas

Destabilization effect of exchange dipole-dipole interaction on the spectrum of electric dipolar ultracold Fermi gas

Extended hydrodynamics of the degenerate partially spin polarized fermions with the short-range interaction up to the third order by the interaction radius approximation

Low-lying excitation modes of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

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