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arXiv:1112.1282 · Physical Review A

Highly polarized Fermi gases across a narrow Feshbach resonance

Ran Qi, Hui Zhai

Published Apr 13, 2012• 20 citations
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Abstract

We address the phase of a highly polarized Fermi gases across a narrow Feshbach resonance starting from the problem of a single down-spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron-to-pairing transition will take place on the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For the pairing phase, we find the critical strength of the repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with $s$-wave BCS superfluidity at large Zeeman fields, which is a remarkable property absent in conventional BCS superconductors (or fermion-pair superfluids).

DOI
10.1103/physreva.85.041603

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We address the phase of a highly polarized Fermi gases across a narrow Feshbach resonance starting from the problem of a single down-spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron-to-pairing transition will take place on the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For the pairing phase, we find the critical strength of the repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with sss-wave BCS superfluidity at large Zeeman fields, which is a remarkable property absent in conventional BCS superconductors (or fermion-pair superfluids).
We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.
We study the phase diagram of the dilute two-component Fermi gas at zero temperature as a function of the polarization and coupling strength. We map out the detailed phase separations between superfluid and normal states near the Feshbach resonance. We show that there are three different coexistence of superfluid and normal phases corresponding to phase separated states between: (I) the partially polarized superfluid and the fully polarized normal phases, (II) the unpolarized superfluid and the fully polarized normal phases and (III) the unpolarized superfluid and the partially polarized normal phases from strong-coupling BEC side to weak-coupling BCS side. For pairing between two species, we found this phase separation regime gets wider and moves toward the BEC side for the majority species are heavier but shifts to BCS side and becomes narrow if they are lighter.
Based on the recently developed interaction renormalization for the one-dimensional ppp-wave interaction, we study the problem of a single impurity immersed in a highly polarized Fermi sea. They interact through a narrow ppp-wave Feshbach resonance, so the effective range r0{r}_{0}r0​ naturally appears in the system. We use the variational approach limited to single-particle--hole excitations on top of the unperturbed Fermi sea. The polaron exhibits two branches of solutions, namely, the attractive and repulsive branches, with varying scattering length across the resonance. We calculate the energy spectrum, residue, and effective mass for each of the branches. We compare the polaronic energy with the energy of the dressed molecule and find that the molecular state is energetically favored when increasing the interaction strength. The critical interaction strength for the polaron-to-molecule transition will shift to the BCS side of the ppp-wave resonance as the effective range increases.
The pairing of fermionic particles is an essential ingredient of superconductivity and of the superfluidity of 3He. While such phenomena are accurately described by BCS theory in the limit of weak pairing strength, a complete understanding remains elusive when pairing strength is increased, such as in high temperature superconductors. We create ultracold gases of trapped fermionic 6Li atoms, through which we directly observe fermionic pairing. In our system, there are no impurities whatsoever, and parameters such as the number and temperature of the trapped atoms are precisely and independently controlled. In addition, a Feshbach resonance enables the continuous tuning of interaction strength and sign between the paired atoms. This control allows us to observe the smooth crossover of a molecular Bose Einstein condensate (MBEC) to a superfluid of weakly interacting Cooper pairs. With these tools, we have performed several fundamental measurements of pairing in fermionic systems.\nWe use optical molecular spectroscopy to precisely measure the closed-channel contribution to the many body state of paired 6Li atoms within a broad Feshbach resonance. The magnitude of this contribution is small, and supports the concept of universality for the description of broad Feshbach resonances. Moreover, the dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover, and for the first time, into the weakly interacting BCS regime.\nWe also prepare a polarized Fermi gas with unequal numbers of two spin states of 6Li atoms. The real-space densities of the polarized, strongly-interacting, two-component Fermi gas reveal two low temperature regimes. At the lowest temperatures, the gas separates into a phase with a uniformly paired superfluid core surrounded by a shell of normal, unpaired atoms. This phase separation is accompanied by a spatial deformation of the core. At higher temperatures, the uniformly paired core persists, though it does not deform. This temperature dependence is consistent with a tri-critical point in the phase diagram. These measurements of pairing in a polarized Fermi gas are relevant to predictions of exotic phases of quark matter and magnetized superconductors.
We propose to realize a strongly interacting Fermi superfluid near a narrow Feshbach resonance using the recently discovered ``orbital Feshbach resonance.'' The orbital Feshbach resonance is a type of magnetic field tunable scattering resonance theoretically predicted and experimentally observed recently in the alkaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb atom. We first show that the orbital Feshbach resonance is a narrow resonance in energy, while it is hundreds Gauss wide in terms of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore, this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We further show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alikaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal 40K^{40}\mathrm{K}40K and 6Li^{6}\mathrm{Li}6Li systems.
We investigate the highly polarized limit of a two-dimensional Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer, or even larger clusters. Similarly to three dimensions, we find that the Fermi sea favors the trimer state so that it exists for ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario that corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.