We determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

%B Physical Review A %V 94 %P 023607 %8 2016/08/05 %G eng %U http://arxiv.org/abs/1602.00979 %N 2 %R http://dx.doi.org/10.1103/PhysRevA.94.023607 %0 Journal Article %J Physical Review A %D 2015 %T Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas %A Marlon Nuske %A Eite Tiesinga %A L. Mathey %X We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional non-resonant two-body losses make a lower initial resonance energy with non-linear dependence on temperature preferable. %B Physical Review A %V 91 %P 043626 %8 2015/04/20 %G eng %U http://arxiv.org/abs/1412.8473v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.91.043626 %0 Journal Article %J Physical Review A %D 2011 %T Detecting paired and counterflow superfluidity via dipole oscillations %A Anzi Hu %A L. Mathey %A Eite Tiesinga %A Ippei Danshita %A Carl J. Williams %A Charles W. Clark %X We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. %B Physical Review A %V 84 %8 2011/10/27 %G eng %U http://arxiv.org/abs/1103.3513v3 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.84.041609 %0 Journal Article %J Physical Review A %D 2010 %T Noise correlations of one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Carl J. Williams %A Charles W. Clark %X We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. %B Physical Review A %V 81 %8 2010/6/2 %G eng %U http://arxiv.org/abs/1002.4918v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.063602 %0 Journal Article %J Physical Review A %D 2009 %T Collisional cooling of ultra-cold atom ensembles using Feshbach resonances %A L. Mathey %A Eite Tiesinga %A Paul S. Julienne %A Charles W. Clark %X We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. %B Physical Review A %V 80 %8 2009/9/8 %G eng %U http://arxiv.org/abs/0903.2568v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.80.030702 %0 Journal Article %J Physical Review A %D 2009 %T Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Ippei Danshita %A Eite Tiesinga %A Carl J. Williams %A Charles W. Clark %X We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. %B Physical Review A %V 80 %8 2009/8/24 %G eng %U http://arxiv.org/abs/0906.2150v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.80.023619