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.

1 aNuske, Marlon1 aMathey, L.1 aTiesinga, Eite uhttp://arxiv.org/abs/1602.0097901328nas a2200157 4500008004100000245008400041210006900125260001500194300001100209490000700220520085400227100001801081700001901099700001501118856003701133 2015 eng d00aOptimization of collisional Feshbach cooling of an ultracold nondegenerate gas0 aOptimization of collisional Feshbach cooling of an ultracold non c2015/04/20 a0436260 v913 a 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. 1 aNuske, Marlon1 aTiesinga, Eite1 aMathey, L. uhttp://arxiv.org/abs/1412.8473v101241nas a2200181 4500008004100000245007500041210006900116260001500185490000700200520070200207100001300909700001500922700001900937700002000956700002300976700002300999856003701022 2011 eng d00aDetecting paired and counterflow superfluidity via dipole oscillations0 aDetecting paired and counterflow superfluidity via dipole oscill c2011/10/270 v843 a 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. 1 aHu, Anzi1 aMathey, L.1 aTiesinga, Eite1 aDanshita, Ippei1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/1103.3513v301378nas a2200157 4500008004100000245007600041210006900117260001300186490000700199520090300206100001301109700001501122700002301137700002301160856003701183 2010 eng d00aNoise correlations of one-dimensional Bose mixtures in optical lattices0 aNoise correlations of onedimensional Bose mixtures in optical la c2010/6/20 v813 a 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. 1 aHu, Anzi1 aMathey, L.1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/1002.4918v201137nas a2200157 4500008004100000245008200041210006900123260001300192490000700205520065000212100001500862700001900877700002300896700002300919856003700942 2009 eng d00aCollisional cooling of ultra-cold atom ensembles using Feshbach resonances 0 aCollisional cooling of ultracold atom ensembles using Feshbach r c2009/9/80 v803 a 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. 1 aMathey, L.1 aTiesinga, Eite1 aJulienne, Paul, S.1 aClark, Charles, W. uhttp://arxiv.org/abs/0903.2568v101819nas a2200181 4500008004100000245009700041210006900138260001400207490000700221520125900228100001301487700001501500700002001515700001901535700002301554700002301577856003701600 2009 eng d00aCounterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices 0 aCounterflow and paired superfluidity in onedimensional Bose mixt c2009/8/240 v803 a 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. 1 aHu, Anzi1 aMathey, L.1 aDanshita, Ippei1 aTiesinga, Eite1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/0906.2150v1