arXiv:0711.0182 · Physical Review A

Generic features of the spectrum of trapped polarized fermions

Erich J. Mueller

Published Oct 1, 2008• 6 citations

Abstract

We show that bimodal radio frequency spectra universally arise at intermediate temperatures in models of strongly interacting trapped Fermi gases. The bimodality is independent of superfluidity or pseudogap physics, depending only on the functional form of the equation of state---which is constrained by dimensional analysis at low temperatures and the virial expansion at high temperatures. In addition to these model independent results, we present a simple calculation of the radio frequency line shape of a highly polarized Fermi gas which uses energetic considerations to include final state interactions. While this model only qualitatively captures the line shapes observed in the experiments, it provides a conceptually clean and powerful technique for estimating the energy scales and how they vary with experimental parameters.

DOI: 10.1103/physreva.78.045601

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arXiv:0711.0182 · Physical Review A

Generic features of the spectrum of trapped polarized fermions

Erich J. Mueller

Published Oct 1, 2008• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.78.045601

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{T}_{c}

. We discuss a series of scenarios for the experimentally observed zero-temperature pseudogap phase and show how present and future RF experiments may help in its elucidation. We conclude that the experiments of Zwierlein and co-workers at the lowest

T

may well reflect ground-state properties, but take issue with their claim that the pairing gap survives up to temperatures of the order of the degeneracy temperature

{T}_{F}

at unitarity.

0.08{ϵ}_{F}<T<0.8{ϵ}_{F}

using auxiliary field Monte Carlo technique in which continuum auxiliary fields with a density-dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap--pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at

T=0

, the effective mass has to be ${m}^{\ensuremath{\ast}}\ensuremath{\sim}1.43m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.

Using a second-order quantum virial expansion, we theoretically study the high-temperature thermodynamics of spin-polarized Fermi gases with

p

-wave interaction confined in two-dimensional harmonic traps. The second virial coefficient is calculated based on the energy spectrum of two harmonically trapped fermions. We find that the two-body spectrum can correctly be evaluated only when the

p

-wave effective range is properly considered, which is referred to as the well-known Wigner's bound. According to the quantum virial expansion, the high-temperature thermodynamics of the system is then discussed based on the two-body solutions. In addition, we investigate the high-temperature behavior of

p

-wave contacts in harmonic traps within the quantum virial expansion, which characterize a set of universal relations of strongly interacting spin-polarized Fermi gases. Our results can provide an accurate benchmark at high temperature for future numerical simulations as well as high-precision thermodynamic measurements of harmonically trapped spin-polarized Fermi gases in two dimensions.

We present two exact results for singular features in the radio frequency intensity

I(ω)

for ultracold Fermi gases. First, in the absence of final state interactions,

I(ω)

has a universal high frequency tail $ Cω^{-3/2}$ for \emph{all} many-body states, where

C

is Tan's contact. Second, in a \emph{normal} Fermi liquid at T=0,

I(ω)

has a jump discontinuity of

Z/(1 - m/m^{*})

, where

Z

is the quasiparticle weight and

m^*/m

the mass renormalization. We then describe various approximations for

I(ω)

in polarized normal gases. We show why an approximation that is exact in the $n_\dn=0$ limit, fails qualitatively for $n_{\dn} > 0$: there is no universal tail and sum rules are violated. The simple ladder approximation is qualitatively correct for very small $n_{\dn}$, but not quantitatively.