Collective excitations of degenerate Fermi gases in anisotropic parabolic traps

Csordás, András; Graham, R.

doi:10.1103/physreva.63.013606

Cited by 10 publications

(8 citation statements)

References 24 publications

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“…[47], where a deeper analysis, initially devised for BECs [48], is carried out. It is shown there that, despite the lack of an obvious spatial symmetry, the wave equation for the hydrodynamic modes is separable in elliptical coordinates.…”

Section: Low-lying Excitationsmentioning

confidence: 99%

Dipolar Fermi gases in anisotropic traps

Lima

Pelster

2010

Phys. Rev. A

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The quest for quantum degenerate Fermi gases interacting through the anisotropic and long-range dipole-dipole interaction is an exciting and fast developing branch within the cold-atoms research program. Recent experimental progress in trapping, cooling, and controlling polar molecules with large electric dipole moments has, therefore, motivated much theoretical effort. In a recent letter, we have briefly discussed the application of a variational time-dependent Hartree-Fock approach to study theoretically both the static and the dynamic properties of such a system in a cylindersymmetric harmonic trap. We focused on the hydrodynamic regime, where collisions assure the equilibrium locally. Here, we present a detailed theory, extended to encompass the general case of a harmonic trap geometry without any symmetry. After deriving the equations of motion for the gas, we explore their static solutions to investigate key properties like the aspect ratios in both real and momentum space as well as the stability diagram. We find that, despite the lack of symmetry of the trap, the momentum distribution remains cylinder symmetric. The equations of motion are then used to study the low-lying hydrodynamic excitations, where, apart from the quadrupole and monopole modes, also the radial quadrupole mode is investigated. Furthermore, we study the timeof-flight dynamics as it represents an important diagnostic tool for quantum gases. We find that the real-space aspect ratios are inverted during the expansion, while the one in momentum space becomes asymptotically unity. In addition, anisotropic features of the dipole-dipole interaction are discussed in detail. These results could be particularly useful for future investigations of strongly dipolar heteronuclear polar molecules deep in the quantum degenerate regime.

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Section: Low-lying Excitationsmentioning

confidence: 99%

Dipolar Fermi gases in anisotropic traps

Lima

Pelster

2010

Phys. Rev. A

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“…Evolution of scalar pressure is considered in context of quantum gases in Ref. [26], the spectrum of small amplitude collective excitations of degenerate fermions in parabolic traps is described there. Nonuniform scalar pressure contribution in the spectrum of collective modes in finite temperature bosons is discussed in Ref.…”

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confidence: 99%

On the interaction constant measurement of polarized fermions via sound wave spectra obtained from hydrodynamics with the pressure evolution equation

Andreev

2019

Preprint

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Usually, hydrodynamic equations are restricted by the continuity and Euler equations. However, the account of the higher moments of the distribution function gives better description of the kinetic properties. Therefore, the pressure tensor evolution equation (PTEE) is derived for spin polarized degenerate fermions. Moreover, it is found that the pressure tensor enters the interaction term generalizing the p-wave interaction in the Euler equation. Hence, the PTEE allows to give a more accurate description of the interaction in Euler equation. Next, the interaction is calculated for the PTEE. The developed model is applied to the small amplitude bulk collective excitations in homogeneous and trapped fermions in order to suggest the methods of experimental measurement of the interaction constant of polarized fermions. It is demonstrated that the anisotropy in the momentum space revealing in the difference of the pressures in the anisotropy direction and the perpendicular directions leads to a method of detection of the interaction constant.

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“…On the one hand, a hydrodynamic approach derived from the balance equations for the moments of the Wigner distribution function permitted to compute the sound mode spectrum of one [18] and two [19] hyperfine fermion species. Such an approach, which can be generalized for anisotropically trapped systems [20] and was applied as well to predict the characteristics of scissor modes in a superfluid Fermi gas [21], conceals the hypothesis of underlying local equilibrium of the oscillating gas, i.e., the validity of the Fermi gas equation of state. On the other hand, since collision rates in a very cold and strongly dilute gas are small for moderate numbers of confined particles [19,22], one may expect that a zero sound regime shows up at low excitation energies and temperatures in these systems; in fact, collective energies of a single-species fermion gas were estimated within a sum-rule approach [23] for the lowest multipolarities.…”

Section: Introductionmentioning

confidence: 99%

Zero-sound density oscillations in Fermi-Bose mixtures

Capuzzi

Hernández

2001

Phys. Rev. A

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Within a mean field plus Random-Phase Approximation formalism, we investigate the collective excitations of a three component Fermi-Bose mixture of K atoms, magnetically trapped and subjected to repulsive s-wave interactions. We analyze both the single-particle excitation and the density oscillation spectra created by external multipolar fields, for varying fermion concentrations. The formalism and the numerical output are consistent with the Generalized Kohn Theorem for the whole multispecies system. The calculations give rise to fragmented density excitation spectra of the fermion sample and illustrate the role of the mutual interaction in the observed deviations of the bosonic spectra with respect to Stringari's rule.

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Collective excitations of degenerate Fermi gases in anisotropic parabolic traps

Cited by 10 publications

References 24 publications

Dipolar Fermi gases in anisotropic traps

Dipolar Fermi gases in anisotropic traps

On the interaction constant measurement of polarized fermions via sound wave spectra obtained from hydrodynamics with the pressure evolution equation

Zero-sound density oscillations in Fermi-Bose mixtures

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