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 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 finitemomentum 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 singlespecies Fermi-sea, is a stable ground state.Recent experimental realizations of paired superfluidity in trapped fermionic atoms interacting via a Feshbach resonance (FR) [1,2] have opened a new chapter of many-body atomic physics. Almost exclusively, the focus has been on equal mixtures of two hyperfine states exhibiting pseudo-spin singlet superfluidity that can be tuned from the momentum-pairing BCS regime of strongly overlapping Cooper pairs (for large positive detuning) to the coordinate-space pairing Bose-Einstein condensate (BEC) regime of dilute molecules (for negative detuning) [3].In contrast, s-wave pairing for unequal numbers of atoms in the two pairing hyperfine states has received virtually no experimental attention and only some recent theoretical activity [4,5,6,7,8,9]. Associating the two pairing hyperfine states with up (↑) and down (↓) pseudo-spin σ, the density difference δn = n ↑ − n ↓ is isomorphic to "magnetization" m ≡ δn and the corresponding chemical potential difference δµ = µ ↑ − µ ↓ to a purely Zeeman field h ≡ δµ/2. This subject dates back to the work of Fulde and Ferrell (FF) [10] and Larkin and Ovchinnikov (LO) [11] who proposed that, in the presence of a Zeeman field, an s-wave BCS superconductor is unstable to magnetized pairing at a finite momentum Q ≈ k F↑ − k F↓ with k Fσ the Fermi wavevector of fermion σ. This FFLO state, which remains elusive in condensed matter systems where it is obscured by orbital and disorder effects, spontaneously breaks rotational and translational symmetry and emerges as a compromise between competing singlet pairing and Pauli paramagnetism.Thus atomic fermion gases (where the above deleterious effects are absent), tuned near an s-wave FR, are promising ideal systems for a realization of the FFLO and related finite-magnetization paired states, that can be studied throughout the full BCS-BEC crossover.In this Letter, we map out the detuning-magnetization phase diagram (Fig

We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by ↑, ↓) of fermionic atoms when the numbers N ↑ and N ↓ of the two species are unequal , i.e., the system is "polarized". We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population difference ∆N ≡ N ↑ − N ↓ . Our findings are summarized by a "polarization" (∆N ) versus Feshbach-resonance detuning (δ) zero-temperature phase diagram, which exhibits regions of phase separation, a periodic FFLO superfluid, a polarized normal Fermi gas and a polarized molecular superfluid consisting of a molecular condensate and a fully polarized Fermi gas. We describe numerous experimental signatures of such phases and the transitions between them, in particular focusing on their spatial structure in the inhomogeneous environment of an atomic trap.

We show that the emergent relativistic symmetry of electrons in graphene near its quantum critical point (QCP) implies a crucial importance of the Coulomb interaction. We derive scaling laws, valid near the QCP, that dictate the nontrivial magnetic and charge response of interacting graphene. Our analysis yields numerous predictions for how the Coulomb interaction will be manifested in experimental observables such as the diamagnetic response and electronic compressibility.

We present an overview of recent developments in species-imbalanced ("polarized") Feshbach-resonant Fermi gases. We summarize the current status of thermodynamics of these systems in terms of a phase diagram as a function of the Feshbach resonance detuning, polarization and temperature. We review instabilities of the swave superfluidity across the BEC-BCS crossover to phase separation, FFLO states, polarized molecular superfluidity and the normal state, driven by the species imbalance. We discuss different models and approximations of this system and compare their predictions to current experiments.

We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin-1/2 fermion flavors with Sp(2N ) symmetry. For N → ∞ this problem is exactly solved by the BCS-BEC mean-field theory, with corrections small in the parameter 1/N . The large-N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in proximity to) unitarity, including the energy, the pairing gap, and the upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of N = 1, among other quantities, we predict in the unitarity regime, the energy of the gas to be ξ = 0.28 times that for the non-interacting gas and the pairing gap to be 0.52 times the Fermi energy.

We study vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential. We show that, in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an anisotropic superflow whose profile strongly depends on the distance to the trap axis. One consequence of this superflow anisotropy is vortex precession about the trap axis in the absence of an imposed rotation. In the complementary regime of a finite prescribed rotation, we compute the minimum-energy vortex density, showing that in the rapidrotation limit it is extremely uniform, despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density ρs(r). The weak radially-dependent contribution (∝ ∇ 2 ln ρs(r)) to the vortex distribution, that vanishes with the number of vortices Nv as 1 Nv , arises from the interplay between vortex quantum discretness (namely their inability to faithfully support the imposed rigid-body rotation) and the inhomogeneous superfluid density. This leads to an enhancement of the vortex density at the center of a typical concave trap, a prediction that is in quantitative agreement with recent experiments. One striking consequence of the inhomogeneous vortex distribution is an azimuthally-directed, radially-shearing superflow.

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In the cuprate superconductor YBa2Cu3O6+x, hole doping in the CuO2 layers is controlled by both oxygen content and the degree of oxygen ordering. At the composition YBa2Cu3O6.35, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from 0 to 20 K. Here we exploit this to study the c-axis penetration depth as a function of temperature and doping. The temperature dependence shows the d-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering with the nodal quasiparticles. The only apparent doping dependence is a smooth decline of superfluid density as T(c) decreases.