Superfluid-insulator transition of strongly interacting fermi gases in optical lattices

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height Vo/ER between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.     

Anomaly driven signatures of new invisible physics at the Large Hadron Collider

Many extensions of the Standard Model (SM) predict new neutral vector bosons at energies accessible by the Large Hadron Collider (LHC). We study an extension of the SM with new chiral fermions subject to non-trivial anomaly cancellations. If the new fermions have SM charges, but are too heavy to be created at LHC, and the SM fermions are not charged under the extra gauge field, one would expect that this new sector remains completely invisible at LHC. We show, however, that a non-trivial anomaly cancellation between the new heavy fermions may give rise to observable effects in the gauge boson sector that can be seen at the LHC and distinguished from backgrounds.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Scalar Resonance at 750 GeV as Composite of Heavy Vector-Like Fermions

We study a model of scalars which includes both the SM Higgs and a scalar singlet as composites of heavy vector-like fermions. The vector-like fermions are bounded by the super-strong four-fermion interactions. The scalar singlet decays to SM vector bosons through loop of heavy vector-like fermions. We show that the surprisingly large production cross section of di-photon events at 750 GeV resonance and the odd decay properties can all be explained. This model serves as a good model for both SM Higgs and a scalar resonance at 750 GeV.     

Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement

We develop a multichannel scattering theory for atom-atom collisions in quasi-1D geometries. We apply our general framework to the low energy scattering of two spin-polarized fermions and show that tightly confined fermions have infinitely strong interactions at a particular value of the 3D, free-space p-wave scattering volume. Moreover, we describe a mapping of this strongly interacting system of two quasi-1D fermions to a weakly interacting system of two 1D bosons.     

Nonlinear dynamics of fermions during preheating

We study the role of dynamical fermions during preheating after inflation. We compute the nonequilibrium dynamics of Dirac fermions coupled to a scalar (inflaton) field at next-to-next-to-leading order in a coupling expansion of the 2PI effective action. Besides the well-known parametric production of bosons and fermions and their back-reaction on the background inflaton field, this includes direct interactions between produced particles, which have been neglected in previous studies. We present preliminary numerical results in 3+1 dimensions which indicates that, for intermediate Yukawa couplings, the latter can dramatically affect the usual picture of preheating.     

Negative-energy spinors and the Fock space of lattice fermions at finite chemical potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial “energy” in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.     

Shortcut to a Fermi-degenerate gas of molecules via cooperative association

We theoretically examine the creation of a Fermi-degenerate gas of molecules by considering a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of a degenerate gas atoms into a macroscopic number of diatomic molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and a rapid adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.     

Superfluid-insulator transitions of the fermi gas with near-unitary interactions in a periodic potential

We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period a_{L}, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V=V_{c}. We compute the universal ratio V_{c}ma_{L};{2}/variant Planck's over 2pi;{2} at N=infinity in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.     

Majorana fermions in equilibrium and in driven cold-atom quantum wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.     

Capacities of quantum channels for massive bosons and fermions

We consider the capacity of classical information transfer for noiseless quantum channels carrying a finite average number of massive bosons and fermions. The maximum capacity is attained by transferring the Fock states generated from the grand-canonical ensemble. Interestingly, the channel capacity for a Bose gas indicates the onset of Bose-Einstein condensation, by changing its qualitative behavior at the criticality, while for a channel carrying weakly attractive fermions, it exhibits the signatures of Bardeen-Cooper-Schrieffer transition. We also show that, for noninteracting particles, fermions are better carriers of information than bosons.     

Signal for an extra-dimensional model of flavor at the Large Hadron Collider

In Randall-Sundrum models with gauge bosons and fermions in the extra-dimensional bulk, it is possible to build models of flavor by localizing the fermions in the extra dimension. Since the Higgs boson must be localized at or close to the TeV scale fixed point, heavier fermions must be localized close to this brane. The first Kaluza-Klein excitations of the gauge bosons are also TeV-localized, so they have stronger couplings to heavier fermions leading to tree-level flavor-violating couplings. We investigate the potential of the Large Hadron Collider to observe flavor violation in single top production at very high invariant masses, in addition to the observation of the corresponding t-t[over] resonance. We conclude that the Large Hadron Collider will be able to observe tree-level flavor violation in single top production, probing Kaluza-Klein masses at least as large as 2 TeV, as well as a very interesting region of the parameters.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

Anomalous currents in dense matter under a magnetic field

We consider fermionic dense matter under a magnetic field, where fermions couple minimally to gauge fields, and calculate anomalous currents at one loop. We find anomalous currents are spontaneously generated along the magnetic field but fermions only in the lowest Landau level contribute to anomalous currents. We then show that there are no more corrections to the anomalous currents from two or higher loops.     

BCS–BEC crossover in one-dimensional integrable model

The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.     

On the thermodynamics of an ideal fermi gas on the lattice at finite density

We study the ideal gas of fermions on a lattice at finite density for both naive and Wilson fermions. Comparing the thermodynamical quantities thus calculated with the known results in the continuum theory, we are led to propose a modification of the naive form of the lattice action, which is same for both the naive and the Wilson fermions. The thermodynamical quantities, calculated by using this form, are shown to have the correct continuum limit.     

Fermions on colliding branes

We study the behaviour of five-dimensional fermions localized on branes, which we describe by domain walls, when two parallel branes collide in a five-dimensional Minkowski background spacetime. We find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants unless the fermions exist on both branes.     

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.     

Trimer liquids and crystals of polar molecules in coupled wires

We investigate pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. Combining analytical and numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons and fermions. We show that these exotic quantum phases are robust against conditions of confinement of the molecular gas to harmonic finite-size potentials.