Population imbalanced fermions in harmonically trapped optical lattices

The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de Gennes formalism to analyze the ground state phases of population imbalanced fermion mixtures in harmonically trapped two-dimensional optical lattices. In the low density limit the superfluid order parameter modulates in the radial direction towards the trap edges to accommodate the unpaired fermions that are pushed away from the trap center with a single peak in their density. However in the high density limit while the order parameter modulates in the radial direction towards the trap center for low imbalance, it also modulates towards the trap edges with increasing imbalance until the superfluid to normal phase transition occurs beyond a critical imbalance. This leads to a single peak in the density of unpaired fermions for low and high imbalance but leads to double peaks for intermediate imbalance.Comment: 4 pages with 4 figures, accepted to appear in PR

Fermi condensates for dynamic imaging of electro-magnetic fields

Ultracold gases provide micrometer size atomic samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors \cite{Wildermuth2005a} in atom chip \cite{Folman2002a,Fortagh2007a} experiments. As such, they offer a combination of resolution and sensitivity presently unattainable by other methods \cite{Wildermuth2006a}. Here we propose that condensates of Fermionic atoms can be used for non-invasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations of the gas by the field create both collective excitations and quasiparticles. Excitation of quasiparticles requires the frequency of the perturbation to exceed the energy gap. Thus, by tuning the gap, the frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable for instance by RF-spectroscopy. We analyse the proposed method by calculating the density-density susceptibility, i.e. the dynamic structure factor, of the gas. We discuss the sensitivity and spatial resolution of the method which may, with advanced techniques for quasiparticle observation \cite{Schirotzek2008a}, be in the half a micron scale.Comment: 10 pages, 4 figure

Pair formation and collapse in imbalanced Fermion populations with unequal masses

We present an exact Quantum Monte Carlo study of the effect of unequal masses on pair formation in Fermionic systems with population imbalance loaded into optical lattices. We have considered three forms of the attractive interaction and find in all cases that the system is unstable and collapses as the mass difference increases and that the ground state becomes an inhomogeneous collapsed state. We also address the question of canonical vs grand canonical ensemble and its role, if any, in stabilizing certain phases

Noise correlations of the ultra-cold Fermi gas in an optical lattice

In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and BP (breach pair) state, are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at non-zero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results also to the computation of correlation signals in a one-dimensional lattice. We find that the density noise correlations reveal important information about the structure of the underlying order parameter as well as about the quasiparticle dispersions.Comment: 25 pages, 11 figures. Some figures are updated and text has been modifie

Finite temperature phase diagram of a polarized Fermi gas in an optical lattice

We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair (BP), and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.Comment: Journal versio

Unconventional superconducting phases in a correlated two-dimensional Fermi gas of nonstandard quasiparticles: a simple model

We discuss a detailed phase diagram and other microscopic characteristics on the applied magnetic field - temperature (H_a-T) plane for a simple model of correlated fluid represented by a two-dimensional (2D) gas of heavy quasiparticles with masses dependent on the spin direction and the effective field generated by the electron correlations. The consecutive transitions between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases are either continuous or discontinuous, depending on the values of H_a and T. In the latter case, weak metamagnetic transitions occur at the BCS-FFLO boundary. We single out two different FFLO phases, as well as a reentrant behaviour of one of them at high fields. The results are compared with those for ordinary Landau quasiparticles in order to demonstrate the robustness of the FFLO states against the BCS state for the case with spin-dependent masses (SDM). We believe that the mechanism of FFLO stabilization by SDM is generic: other high-field low-temperature (HFLT) superconducting phases benefit from SDM as well.Comment: 10 pages, 4 figure

Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD

We determine masses and decay constants of heavy-heavy and heavy-charm pseudoscalar mesons as a function of heavy quark mass using a fully relativistic formalism known as Highly Improved Staggered Quarks for the heavy quark. We are able to cover the region from the charm quark mass to the bottom quark mass using MILC ensembles with lattice spacing values from 0.15 fm down to 0.044 fm. We obtain f_{B_c} = 0.427(6) GeV; m_{B_c} = 6.285(10) GeV and f_{\eta_b} = 0.667(6) GeV. Our value for f_{\eta_b} is within a few percent of f_{\Upsilon} confirming that spin effects are surprisingly small for heavyonium decay constants. Our value for f_{B_c} is significantly lower than potential model values being used to estimate production rates at the LHC. We discuss the changing physical heavy-quark mass dependence of decay constants from heavy-heavy through heavy-charm to heavy-strange mesons. A comparison between the three different systems confirms that the B_c system behaves in some ways more like a heavy-light system than a heavy-heavy one. Finally we summarise current results on decay constants of gold-plated mesons.Comment: 16 pages, 12 figure

Precision tests of the J/{\psi} from full lattice QCD: mass, leptonic width and radiative decay rate to {\eta}_c

We calculate the J/{\psi} mass, leptonic width and radiative decay rate to \gamma \eta_c from lattice QCD including u, d and s quarks in the sea for the first time. We use the Highly Improved Staggered Quark formalism and nonperturbatively normalised vector currents for the leptonic and radiative decay rates. Our results are: M_{J/\psi} -M_{\eta_c} = 116.5(3.2) MeV; \Gamma(J/{\psi} to e^+e^-) = 5.48(16) keV; \Gamma(J/{\psi} to \gamma \eta_c) = 2.49(19) keV. The first two are in good agreement with experiment, with \Gamma(J/{\psi} to e^+e^-) providing a test of a decay matrix element in QCD, independent of CKM uncertainties, to 2%. At the same time results for the time moments of the correlation function can be compared to values from the charm contribution to \Gamma(e^+e^- to hadrons), giving a 1.5% test of QCD. Our results show that an improved experimental error would enable a similarly strong test from \Gamma(J/{\psi} to \gamma \eta_c).Comment: 20 pages, 16 figures. Added some text plus a figure and two tables comparing the time moments of the charmonium vector correlator to results extracted from experiment for the charm contribution to e^+e^- -> hadrons. This allows a 1.5% test of QCD. Further minor amendments to the text. Version accepted for publication by Physical Review

Magnetic phases of one-dimensional lattices with 2 to 4 fermions per site

We study the spectral and magnetic properties of one-dimensional lattices filled with 2 to 4 fermions (with spin 1/2) per lattice site. We use a generalized Hubbard model that takes account all interactions on a lattice site, and solve the many-particle problem by exact diagonalization. We find an intriguing magnetic phase diagram which includes ferromagnetism, spin-one Heisenberg antiferromagnetism, and orbital antiferromagnetism.Comment: 8 pages, 6 figure

Direct determination of the strange and light quark condensates from full lattice QCD

We determine the strange quark condensate from lattice QCD for the first time and compare its value to that of the light quark and chiral condensates. The results come from a direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution, derived here, to convert the non-normal-ordered mψ̅ ψ to the MS̅ scheme at a fixed scale. This is then a well-defined physical “nonperturbative” condensate that can be used in the operator product expansion of current-current correlators. The perturbative subtraction is calculated through O(αs) and estimates of higher order terms are included through fitting results at multiple lattice spacing values. The gluon field configurations used are “second generation” ensembles from the MILC collaboration that include 2+1+1 flavors of sea quarks implemented with the highly improved staggered quark action and including u/d sea quarks down to physical masses. Our results are ⟨s̅ s⟩MS̅ (2  GeV)=-(290(15)  MeV)3, ⟨l̅ l⟩MS̅ (2  GeV)=-(283(2)  MeV)3, where l is a light quark with mass equal to the average of the u and d quarks. The strange to light quark condensate ratio is 1.08(16). The light quark condensate is significantly larger than the chiral condensate in line with expectations from chiral analyses. We discuss the implications of these results for other calculations