Finite temperature effects in light scattering off Cooper-paired Fermi atoms

Bimalendu Deb

Published Nov 21, 2012• 0 citations

Abstract

Abstract. We study stimulated light scattering off a superfluid Fermi gas of atoms at finite temperature. We derive response function that takes into account vertex correction due to final state interactions; and analyze finite temperature effects on collective and quasiparticle excitations of a uniform superfluid Fermi gas. Light polarization is shown to play an important role in excitations. Our results suggest that it is possible to excite Bogoliubov-Anderson phonon at a large scattering length by light scattering. PACS numbers: 03.75.Ss,74.20.-z,32.80.LgFinite temperature effects in light scattering off Cooper-paired Fermi atoms 2 1.

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OpenAlex

Abstract

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2Δ

where

Δ

is the superfluid gap energy. Furthermore, polarization-selective light scattering allows for unequal energy and momentum transfer to the two partner atoms of a Cooper-pair. In the regime of low energy (

<< 2Δ

) and low momentum (

<2Δ/(\hbar v_F)

v_F

being the Fermi velocity) transfer, a small difference in momentum transfers to the two spin-components may be useful in exciting Bogoliubov-Anderson phonon mode. We present detailed results on the dynamic structure factor (DSF) deduced from the response function making use of generalized fluctuation-dissipation theorem. Model calculations using local density approximation for trapped superfluid Fermi gas shows that when the energy transfer is less than

2Δ_0

, where

Δ_0

refers to the gap at the trap center, DSF as a function of energy transfer has reduced gradient compared to that of normal Fermi gas.

{T}_{c}

in the collisionless regime. The spectra of collective modes are calculated within the Gaussian pair fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a nonperturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of

{T}_{c}

, we find analytically a weakly damped collective mode whose velocity vanishes with a critical exponent of

1/2

, and whose quality factor diverges logarithmically with ${T}_{c}\ensuremath{-}T$, thereby clarifying an existing debate in the literature [Andrianov and Popov, Theor. Math. Phys. 28, 829 (1976); Ohashi and Takada, J. Phys. Soc. Jpn. 66, 2437 (1997)]. A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.

We present detailed measurements of the frequency and damping of three different collective modes in an ultracold trapped Fermi gas of

^{6}\mathrm{Li}

atoms with resonantly tuned interactions. The measurements are carried out over a wide range of temperatures. We focus on the unitarity limit, where the scattering length is much greater than all other relevant length scales. The results are compared to theoretical calculations that take into account Pauli blocking and pair correlations in the normal state above the critical temperature for superfluidity. We show that these two effects nearly compensate each other and the behavior of the gas is close to that of a classical gas.