We present a theory of a degenerate atomic Fermi gas, interacting through a narrow Feshbach resonance, whose position and therefore strength can be tuned experimentally, as demonstrated recently in ultracold trapped atomic gases. The distinguishing feature of the theory is that its accuracy is controlled by a dimensionless parameter proportional to the ratio of the width of the resonance to Fermi energy. The theory is therefore quantitatively accurate for a narrow Feshbach resonance. In the case of a narrow s-wave resonance, our analysis leads to a quantitative description of the crossover between a weakly paired BCS superconductor of overlapping Cooper pairs and a strongly paired molecular Bose-Einstein condensate of diatomic molecules. In the case of pairing via a p-wave resonance, that we show is always narrow for a sufficiently low density, we predict a detuning-temperature phase diagram, that in the course of a BCS-BEC crossover can exhibit a host of thermodynamically distinct phases separated by quantum and classical phase transitions. For an intermediate strength of the dipolar anisotropy, the system exhibits a p x + ip y paired superfluidity that undergoes a topological phase transition between a weakly coupled gapless ground state at large positive detuning and a strongly paired fully gapped molecular superfluid for a negative detuning. In two dimensions the former state is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian vortex excitations familiar from fractional quantum Hall systems.

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 D-dimensional polymerized membranes embedded in d dimensions using a selfconsistent screening approximation. It is exact for large d to order 1/d, for any d to order ǫ = 4 − D and for d = D. For flat physical membranes (D = 2, d = 3) it predicts a roughness exponent ζ = 0.590. For phantom membranes at the crumpling transition the size exponent is ν = 0.732. It yields identical lower critical dimension for the flat phase and crumpling transition D lc (d) = 2d d+1 (D lc = √ 2 for codimension 1). For physical membranes with random quenched curvature ζ = 0.775 in the new T = 0 flat phase in good agreement with simulations.

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 study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm2, the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

We study a periodic medium driven over a random or periodic substrate, characterizing the nonequilibrium phases which occur by dynamic order parameters and their correlations. Starting with a microscopic lattice Hamiltonian, we perform a careful coarse-graining procedure to derive continuum hydrodynamic equations of motion in the laboratory frame. This procedure induces nonequilibrium effects (e.g. convective terms, KPZ nonlinearities, and non-conservative forces) which cannot be derived by a naive Galileian boost. Rather than attempting a general analysis of these equations of motion, we argue that in the random case instabilities will always destroy the LRO of the lattice. We suggest that the only periodicity that can survive in the driven state is that of a transverse smectic, with ordering wavevector perpendicular to the direction of motion. This conjecture is supported by an analysis of the linearized equations of motion showing that the induced nonequilibrium component of the force leads to displacements parallel to the mean velocity that diverge with the system size. In two dimensions, this divergence is extremely strong and can drive a melting of the crystal along the direction of motion. The resulting driven smectic phase should also occur in three dimensions at intermediate driving. It consists of a periodic array of flowing liquid channels, with transverse displacements and density ("permeation mode") as hydrodynamic variables. We study the hydrodynamics of the driven smectic within the dynamic functional renormalization group in two and three dimensions. The finite temperature behavior is much less glassy than in equilibrium, owing to a disorder-driven effective "heating" (allowed by the absence of the fluctuation-dissipation theorem). This, in conjunction with the permeation mode, leads to a fundamentally analytic transverse response for T > 0.