Collective modes in a two-band superfluid of ultracold alkaline-earth-metal atoms close to an orbital Feshbach resonance

Abstract

We discuss the collective modes in an alkaline-earth Fermi gas close to an orbital Feshbach resonance. Unlike the usual Feshbach resonance, the orbital Feshbach resonance in alkaline-earth atoms realizes a two-band superfluid system where the fermionic nature of both the open and the closed channel has to be taken into account. We show that apart from the usual Anderson-Bogoliubov mode which corresponds to the oscillation of total density, there also appears the long-sought Leggett mode corresponding to the oscillation of relative density between the two channels. The existence of the phonon and the Leggett modes and their evolution are discussed in detail. We show how these collective modes are reflected in the density response of the system. [5][6][7], is that there are two clock states, the electronic s-and p-states, both of which have zero electronic angular momentum J = 0. As a result, there is no hyperfine coupling between the electronic and nuclear spins. The inter-atomic interactions which depend (primarily) on the electronic configurations thus become independent of nuclear spins. This realizes the so-called SU (N ) symmetries, where N is the number of nuclear spin components [8][9][10][11][12][13][14][15]. The OFR relies on the atoms residing on both the s and p-states which possess slight different Landé g-factors [16,17], thus allowing tuning by external magnetic field.

Leggett collective excitations in a two-band Fermi superfluid at finite temperatures

“…Because γ>0, the stable background solution for the gaps is the in-phase solution: Δ 2 /Δ 1 >0. For T=0, the obtained Leggett mode frequencies precisely match the results of [14].…”

“…Here, the treatment is performed for nonzero temperatures. Remarkably, although the starting fermionic model action of our work [18] is different from that of [14], they lead to the same effective bosonic actions.…”

“…First, we consider the Fermi superfluid in the BEC regime, which is typical for Fermi gases realized using OFR. The Leggett collective modes for a Fermi gas with OFR are studied at T=0 in [13,14]. Here, the treatment is performed for nonzero temperatures.…”

“…OFR has been later successfully realized in a condensed 173 Yb gas [9,10]. This stimulated theoretical efforts to describe the two-band superfluid states [11,12] and Leggett modes [13,14]. BCS-BEC crossover in a two-band atomic superfluid has been studied at the mean-field level and with fluctuations pointing to unique features of the two-component condensate in recent works [15,16].…”

“…The Leggett mode frequencies in cold Fermi gases with OFR were first calculated in [13] at zero temperature, solving the Gaussian pair fluctuation (GPF) propagator for undamped modes. The work [14] reprersents an alternative method exploiting the density-density response function. In the recent work [17], the massive Leggett mode and gapless phonon mode of the two-band Fermi superfluid are studied for the Sarma phase.…”