Noise Correlations in one-dimensional systems of ultra-cold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using Bosonization, we study such noise correlations in generic one dimensional systems of ultra cold fermions. Specifically, we show how pairing as well as spin and charge density wave correlations may be identified and extracted from the time of flight images. These incipient orders manifest themselves as power law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.Comment: 5 pages, 3 figures. Added discussion on the visibility of noise correlation features for realistic condition

A Z2_2 spin-orbital liquid state in the square lattice Kugel-Khomskii model

We argue for the existence of a liquid ground state in a class of square lattice models of orbitally degenerate insulators. Starting with the SU(4) symmetric Kugel-Khomskii model, we utilize a Majorana Fermion representation of spin-orbital operators to access novel phases. Variational wavefunctions of candidate liquid phases are thus obtained, whose properties are evaluated using Variational Monte Carlo. These states are disordered, and are found to have excellent energetics and ground state overlap ($>40$) when compared with exact diagonalization on 16 site clusters. We conclude that these are spin-orbital liquid ground states with emergent nodal fermions and Z$_2$ gauge fields. Connections to spin 3/2 cold atom systems and properties in the absence of SU(4) symmetry are briefly discussed.Comment: 9 pages, 4 figures, 3 tables, published versio

Dynamic projection on Feshbach molecules: a probe of pairing and phase fluctuations

We describe and justify a simple model for the dynamics associated with rapid sweeps across a Feshbach resonance, from the atomic to the molecular side, in an ultra cold Fermi system. The model allows us to relate the observed molecule momentum distribution, including its dependence on the sweep rate, to equilibrium properties of the initial state. For initial state near resonance, we find that phase fluctuations sharply reduce the observed condensate fraction. Moreover, for very fast sweeps and low temperatures, we predict a surprising nonmonotonic dependence of the molecule condensate fraction on detuning, that is a direct signature of quantum phase fluctuations. The dependence of the total molecule number on sweep rate is found to be a sensitive probe of pairing in the initial state, whether condensed or not. Hence it can be utilized to establish the presence of a phase fluctuation induced `psuedogap' phase in these systems.Comment: Added reference