Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas

Abstract

We investigate magnetic properties and effects of pairing fluctuations in the BCS (BardeenCooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas.Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T -matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended T -matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6 Li Fermi gas done by Sanner and co-workers. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature T c , as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below T c in the BCS-BEC crossover regime of cold Fermi gases.

Heteropairing and component-dependent pseudogap phenomena in an ultracold Fermi gas with different species with different masses

“…[42], we overcame this difficulty by employing an extended T -matrix approximation (ETMA) [77,78], which involves higher order pairing fluctuations beyond the TMA.…”

Spin Susceptibility and Effects of Inhomogeneous Strong Pairing Fluctuations in a Trapped Ultracold Fermi Gas

“…Theoretically, the possibility of the so-called spin-gap phenomenon has been discussed in the crossover region near the superfluid phase transition temperature T c 17,18,19,20,21 , where the spin susceptibility is anomalously suppressed by preformed spin-singlet Cooper pairs. Since preformed Cooper pairs also cause the pseudogap phenomenon 22,23,24,25,26 (where the single-particle density of states exhibits a gap-like structure even in the normal state), the spin-gap phenomenon and pseudogap phenomenon are deeply related to each other in the cold Fermi gas system.…”

“…Since preformed Cooper pairs also cause the pseudogap phenomenon 22,23,24,25,26 (where the single-particle density of states exhibits a gap-like structure even in the normal state), the spin-gap phenomenon and pseudogap phenomenon are deeply related to each other in the cold Fermi gas system. So far, the spin susceptibility has theoretically been discussed in a uniform Fermi gas 18,19,20,21 , although a real ultracold Fermi gas is always prepared in a trap potential. In this paper, thus, taking this realistic situation into account, we study how spatially inhomogeneous pairing fluctuations affect the spin-gap phenomenon in a trapped unitary Fermi gas.…”

“…In this paper, thus, taking this realistic situation into account, we study how spatially inhomogeneous pairing fluctuations affect the spin-gap phenomenon in a trapped unitary Fermi gas. For this purpose, we employ the extended T -matrix approximation (ETMA) developed in the uniform system 18,21 , to include effects of a harmonic trap within the local density approximation (LDA) 23,26 . In a uniform Fermi gas, it has been shown that ETMA correctly describes the BCS-BEC crossover behavior of the spin susceptibility 18,21 , which makes us expect that this strong-coupling theory is also valid for the trapped case.…”

“…For this purpose, we employ the extended T -matrix approximation (ETMA) developed in the uniform system 18,21 , to include effects of a harmonic trap within the local density approximation (LDA) 23,26 . In a uniform Fermi gas, it has been shown that ETMA correctly describes the BCS-BEC crossover behavior of the spin susceptibility 18,21 , which makes us expect that this strong-coupling theory is also valid for the trapped case. We briefly note that the ordinary T -matrix approximation 22,25,27 , as well as the strong-coupling theory developed by Nozières and Schmitt-Rink 6,7 , are known to unphysically give negative spin susceptibility in the BCS-BEC crossover region, although these theories have successfully explained various many-body phenomena in the BCS-BEC crossover region.…”