Cold Fermionic Atoms Research Articles

Novel realization of non-Abelian anyons in s-wave superfluids of cold fermionic atoms

We propose a novel realization of non-Abelian anyons using an s-wave superfluid of ultra cold fermionic atoms via the s-wave Feshbach resonance. With a large Zeeman field and an effective Rashba spin–orbit coupling generated by laser fields, a topological phase with non-Abelian anyons is obtained in the s-wave superfluid. We also point out that the non-Abelian anyon can be realized by twisting a phase of the Rashba spin–orbit interaction.

Crystallization of trions in SU(3) cold-atom gases trapped in optical lattices

Cold Fermionic atoms with three different hyperfine states confined in optical lattices show pronounced Atomic Density Waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal of strongly bound trions. We show that the crystalline phase is incompressible and robust against SU(3) symmetry breaking interaction. We also show that it is generic in the presence of the trap due to its incompressible characteristics. A simulation of the time evolution of the fermionic gas after the trapping potential is switch off shows that the formation of the trionic crystal is marked by a freezing of the dynamics in the lattice.

Non-Abelian Topological Order ins-Wave Superfluids of Ultracold Fermionic Atoms

It is proposed that in s-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach to the realization of quantum computation based on the manipulation of non-Abelian anyons via an s-wave Feshbach resonance.

Competition between Anderson Localization and Antiferromagnetism in Correlated Lattice Fermion Systems with Disorder

The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.

Raman coupling and cooper pairing in cold atomic Fermi gases

We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hainan coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.

Spin–charge separation and electron pairing instabilities in Hubbard nanoclusters

Electron charge and spin pairing instabilities in various cluster geometries for attractive and repulsive electrons are studied exactly under variation of interaction strength, electron doping and temperature. The exact diagonalization, level crossing degeneracies, spin–charge separation and separate condensation of paired electron charge and opposite spins yield intriguing insights into the origin of magnetism, ferroelectricity and superconductivity seen in inhomogeneous bulk nanomaterials and various phenomena in cold fermionic atoms in optical lattices. Phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases found recently in high- T c cuprates, manganites and multiferroic nanomaterials probed by scanning tunneling microscopy. Separate condensation of electron charge and spin degrees at various crossover temperatures offers a new route for superconductivity, different from the BCS scenario. The calculated phase diagrams resemble a number of inhomogeneous paired phases, superconductivity, ferromagnetism and ferroelectricity found in Nb and Co nanoparticles. The phase separation and electron pairing, monitored by electron doping and magnetic field surprisingly resemble incoherent electron pairing in the family of doped high- T c cuprates, ruthenocuprates, iron pnictides and spontaneous ferroelectricity in multiferroic materials.

Cold Fermionic Atoms in Two-Dimensional Traps: Pairing versus Hund’s Rule

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

Odd-frequency pairing in a binary mixture of bosonic and fermionic cold atoms

We study fermionic superfluidity in a boson-single-species-fermion cold-atom mixture. We argue that apart from the standard $p$-wave fermion pairing mediated by the phonon field of the boson gas, the system also exhibits $s$-wave pairing with the anomalous correlator being an odd function of time or frequency. We show that such a superfluid phase can have a much higher transition temperature than the $p$-wave and may exist for sufficiently strong couplings between fermions and bosons. These conditions for odd-frequency pairing are favorable close to the value of the coupling at which the mixture phase separates. We evaluate the critical temperatures for this system and discuss the experimental realization of this superfluid in ultracold atomic gases.

Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap

We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle excitations are gapped and the phase diagram is separated into two regions: one where the two-particle excitation gap is zero, and one where it is finite. In the first region, the two-body pairing fluctuations (BCS) compete with the density ones. In the other one, a molecular superfluid (MS) phase, in which bound-states of four particles form, competes with the density fluctuations. The properties of the transition line between these two regions is studied through the behavior of the entanglement entropy. The physical features of the various phases, comprising leading correlations, Friedel oscillations, and excitation spectra, are presented. To make the connection with experiments, the effect of a harmonic trap is taken into account. In particular, we emphasize the conditions under which the appealing MS phase can be realized, and how the phases could be probed by using the density profiles and the associated structure factor. Lastly, the consequences on the flux quantization of the different nature of the pairing in the BCS and MS phases are studied in a situation where the condensate is in a ring geometry.

Magnetism of cold fermionic atoms on thepband of an optical lattice

We carry out \textit{ab initio} study of ground state phase diagram of spin-1/2 cold fermionic atoms within two-fold degenerate $p$-band of an anisotropic optical lattice. Using the Gutzwiller variational approach, we show that a robust ferromagnetic phase exists for a vast range of band fillings and interacting strengths. The ground state crosses over from spin density wave state to spin-1 Neel state at half filling. Additional harmonic trap will induce spatial separation of varies phases. We also discuss several relevant observable consequences and detection methods. Experimental test of the results reported here may shed some light on the long-standing issue of itinerant ferromagnetism.

Pseudogap and the superconducting energy in hole-doped high-temperature superconductors

The pseudogap measured by different techniques in the high-temperature superconductors is interpreted as a two-particle screened Zhang-Rice singlet type state. The so-called (neutron) resonance energy measures the energy lowering of the superconducting state relative to the normal one and should be called the superconducting energy or the order parameter. The superconductivity in the high-temperature superconductors is in the crossover regime between a Bose-Einstein condensate and a BCS state, similar in physics to the situation for the fermionic cold atoms. The superconducting transition temperature is given as the product of the pseudogap energy $({E}_{\text{pg}})$ and the carrier density, leading to its parabolic dependence on the doping. The formation of the Zhang-Rice singlet and the accompanying creation of the pseudogap are instrumental for the occurrence of the high-temperature superconductivity, as also for the large magnetoresistance in the manganites. The lowest ionization state in transition-metal compounds therefore constitutes a promising tool for the engineering of materials.

DMRG studies for 1-D random Hubbard chain close to the half-filling

We numerically study the repulsive Hubbard model with random potential by using the density-matrix renormalization group method. When a few holes are doped to the half-filling, i.e., in slightly doped Mott insulator, we clearly find that “Mott plateaus” and “hole localized valleys” well-separately form in strong on-site repulsive U / t and strong randomness. These nano-scale structures are non-trivial ones created due to strong correlation incorporating randomness. We suggest that these structures qualitatively capture phenomena seen in heavily under-doped high- T c superconductors, while cold atomic Fermi gases loaded on an optical lattice can experimentally confirm the structures under a well-controllable manner.

Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms

We study a simple model of N-component fermions with contact interactions which describes fermionic atoms with N=2F+1 hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound-states made of N fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an SU(N) symmetry between the hyperfine states.

Competing orders in one-dimensional half-integer fermionic cold atoms: A conformal field theory approach

The physical properties of arbitrary half-integer spins F = N − 1 / 2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F ⩾ 3 / 2 : A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2 N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z N parafermionic degrees of freedom. The quantum phase transition for F = 3 / 2 , 5 / 2 is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for F ⩾ 7 / 2 , the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.

Ratio of shear viscosity to entropy density for trapped fermions in the unitarity limit

We extract the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature $\ensuremath{\eta}/s$ is roughly equal to 1/2 in units of $\ensuremath{\hbar}/{k}_{B}$. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound $1/(4\ensuremath{\pi})$ than any other known liquid.

Magnetic and superfluid phases of confined fermions in two-dimensional optical lattices

We examine antiferromagnetic and $d$-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases, antiferromagnetism induces superfluidity by charge redistributions. We furthermore demonstrate how these shell structures can be detected as distinct antibunching dips and pairing peaks in the density-density correlation function probed in expansion experiments.

Pairing and Density-Wave Phases in Boson-Fermion Mixtures at Fixed Filling

We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two isospin states and the bosons have Bose-Einstein condensed. Number density fluctuations of the condensate form delocalized bosonic modes which couple to the fermionic atoms similarly to the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site. We find that tuning of the lattice parameters and interaction strengths drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity, or a charge density-wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.

Mott insulating phases and quantum phase transitions of interacting spin-32fermionic cold atoms in optical lattices at half filling

We study various Mott insulating phases of interacting spin-$\frac{3}{2}$ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.

Temperature-dependent errors in nuclear lattice simulations

We study the temperature dependence of discretization errors in nuclear lattice simulations. We find that for systems with strong attractive interactions the predominant error arises from the breaking of Galilean invariance. We propose a local ``well-tempered'' lattice action which eliminates much of this error. The well-tempered action can be readily implemented in lattice simulations for nuclear systems as well as cold atomic Fermi systems.

Confinement versus deconfinement of Cooper pairs in one-dimensional spin-3∕2fermionic cold atoms

The phase diagram of spin-$3∕2$ fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.