Superfluid shells for trapped fermions with mass and population imbalance G.-D. Lin, W. Yi*, and L.-M. Duan FOCUS center and MCTP, Department of Physics, University of Michigan, Ann Arbor, Michigan We map out the phase diagram of strongly interacting fermions in a potential trap with mass and population imbalance between the two components. As a unique feature distinctively different from the equal-mass case, we show that the superfluid here forms a shell structure which is not simply connected in space. Different types of normal states occupy the trap regions inside and outside this superfluid shell. We calculate the atomic density profiles, which provide an experimental signature for the superfluid shell structure. Introduction The recent experimental advance in superfluidity in polarized ultracold Fermi gases has raised strong interest in studying the phase configuration of this system. The experiments have suggested a phase separation picture with a superfluid core surrounded by a shell of normal gas. This picture has been confirmed also by a number of theoretical calculations of the atomic density profiles in the trap. As Feshbach resonances between different atomic species with unequal masses have been reported, the next step is to consider the properties of a strongly interacting Fermi gas with both mass and population imbalance between the two components. There have been a few recent theoretical works in this direction, with focus on the properties of a homogeneous gas. Atomic Number Distributions in a TrapZero-Temperature Phase Diagrams Model Hamiltonian A strongly interacting Fermi gas near a wide Feshbach resonance can be well described by the following single-channel Hamiltonian: where U is the atom-atom interaction rate, ε k σ = k 2 /(2 m σ ) (σ=↑,↓) with m σ denotes the mass of species-σ, and μ σ is the chemical potential associated with its population. We define μ=(μ ↑ +μ ↓ )/2 and h=(μ ↑ -μ ↓ )/2 for convenience in later discussion. Under the mean-field approximation, one can obtain the thermodynamical potential: where Here we use the local density approximation to account for the trapping potential. One can solve for Δ, the superfluid order parameter (T=0) or the total gap (finite T), by minimizing Ω. The number constraints are where u k 2 =[E k +(ε kr -μ r )]/(2E k ), v k 2 =[E k -(ε kr -μ r )]/(2E k ), and f(x)=1/(1+e x/T ), subject to N=  (n ↑ +n ↓ )d 3 r and p=  (n ↑ -n ↓ )d 3 r/N. m r is the reduced mass mass mismatch parameter quasi-particle dispersion relation local chemical potential SF: Superfluid state (balanced population) NMx: Normal mixture with x as majority NPx: Normal fully polarized gas of species x BP1: Breached pairing phase of type 1 (only one zero in the dispersion relation) Thermo-potential Ω as a function of Δ. Upper curves correspond to more eccentric locations away from the center of the trap. Double-to-single Well Transition ( 6 Li ↓ - 40 K ↑, α=0.74 p=0.2, T=0, On resonance ) Fermi-Surface Mismatch and Shell Structure One can understand the shell structure introduced by unequal masses by first considering the two Fermi surfaces in k-space formed by the NON-interacting atoms of two species. The radius of the Fermi surface at a certain location then can be found to be k F σ (r)=[2m σ (μ σ -r 2 )] 1/2 (in a standard unit), which decreases faster for massive atoms as r increases. When the interaction is turned on, pairing is preferred only if the two k F -surfaces are sufficiently close. Otherwise, the local phase remains normal. This picture should be qualitatively valid even if the atoms strongly interact. The solid (dashed) curves are for 40 K ( 6 Li) atoms, respectively. The insets in (a) and (b) show the amplified tails of the profiles. The other parameters are (a) T=0, resonance, and p=0.2, (b) T=0.1T F, resonance, and p=0.2, (c) T=0, k F a s −1 =−1 (BCS side), p=−0.4, and (d) T=0, k F a s −1 =0.2 (BEC side), p=0.3. [1] W. Yi and L.-M. Duan, Phys. Rev. A 73, (R) (2006); 74, (2006). [2] M. Iskin and C.A.R. Sá de Melo, Phys. Rev. Lett. 97, (2006); e-print cond-mat/ [3] S.-T Wu, C.-H. Pao, S.-K. Yip, Phys. Rev. B 74, (2006). _______________ * Current Address: Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, A-6020, Innsbruck, Austria