Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

Abstract

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended T -matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility χ t (r, T ) in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of χ t (r, T ). Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a uniform Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from χ t (r, T ), to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.

Spin Susceptibility Above the Superfluid Onset in Ultracold Fermi Gases

“…However, we are able to describe this reduction over the whole temperature range using the mean-field model. Consistent with previous results [29] and theory [36,37], we find the susceptibility at the onset of superfluidity to be about 33 ± 3 % of the non-interacting trap-averaged value when (k F a) −1 = 0. Extrapolating our model to the lowest temperatures the ratio with a uniform non-interacting gas would be 38 ± 1%, slightly less than the value of approximately 50% for a model calibrated to data extrapolated from spin-imbalanced samples at low temperature [27].…”

“…This model agrees well with our data throughout the phase diagram (a different mean field parameter is used for each value of the interaction strength). Our data are also consistent with calculations [37] based on a pairing fluctuation scenario throughout the whole temperature region. In this sense, small pairing fluctuations cannot be ruled out, but the mean-field model is still a largely adequate description near unitarity in the normal state [27].…”

“…Similarly, we characterize the interaction strength as (k t F a) −1 , where k t F = (2mk B T t F ) 1/2 . The solid curves are calculated with our mean-field model and take into account the experimental density profiles, which leads to slight non-monotonic behavior for trap-averaged susceptibility [37]. This model agrees well with our data throughout the phase diagram (a different mean field parameter is used for each value of the interaction strength).…”

Many Fermi polarons at nonzero temperature

“…However, such an approximation does not contain an interaction between impurities, which is inevitable to discuss the finite impurity concentration case. To overcome the drawback of the non-selfconsistent approximation, we adopt an extended T-matrix approximation (ETMA) [53][54][55][56][57], which contains the interaction between impurities (see figure 1) and therefore meets the purpose of the paper. In this formalism, as diagrammatically shown in figure 1(a), the self-energy Σ σ (p, iω n ) is given by…”

“…This result indicates the importance of effects of a harmonic trap potential to see the mass renormalization effects from the y-dependence of polaron energies. Since the harmonic trap enhance the finite temperature effects due to the inhomogeneous density profile [57], it may also be related to the suppression of effects of polaron-polaron interaction in the experiment. , where we set an offset (=2.5ε F ) on the attractive polaron energy.…”