We study the quantum dynamics of a number of model systems as their coupling constants are changed rapidly across a quantum critical point. The primary motivation is provided by the recent experiments of Greiner et al. (Nature 415, 39 (2002)) who studied the response of a Mott insulator of ultracold atoms in an optical lattice to a strong potential gradient. In a previous work (cond-mat/0205169), it had been argued that the resonant response observed at a critical potential gradient could be understood by proximity to an Ising quantum critical point describing the onset of density wave order. Here we obtain numerical results on the evolution of the density wave order as the potential gradient is scanned across the quantum critical point. This is supplemented by studies of the integrable quantum Ising spin chain in a transverse field, where we obtain exact results for the evolution of the Ising order correlations under a time-dependent transverse field. We also study the evolution of transverse superfluid order in the three dimensional case. In all cases, the order parameter is best enhanced in the vicinity of the quantum critical point.Comment: 10 pages, 6 figure
Spin-orbit coupling is an important ingredient in many recently discovered phenomena such as the spin-Hall effect and topological insulators. Of particular interest is topological superconductivity, with its potential application in topological quantum computation. The absence of disorder in ultra-cold atomic systems makes them ideal for quantum computation applications, however, the spin-orbit (SO) coupling schemes proposed thus far are experimentally impractical owing to large spontaneous emission rates in the alkali fermions. In this paper, we develop a scheme to generate Rashba SO coupling with a low spontaneous emission extension to a recent experiment. We show that this scheme generates a Fermi surface spin texture for 40 K atoms, which is observable in timeof-flight measurements. The chiral spin texture, together with conventional s-wave interactions leads to topological superconductivity and non-Abelian Majorana quasiparticles.
We describe the properties of a mixture of fermionic and bosonic atoms, as they are tuned across a Feshbach resonance associated with a fermionic molecular state. Provided the number of fermionic atoms exceeds the number of bosonic atoms, we argue that there is a critical detuning at which the Bose-Einstein condensate (BEC) is completely depleted. The phases on either side of this quantum phase transition can also be distinguished by the distinct Luttinger constraints on their Fermi surfaces. In both phases, the total volume enclosed by all Fermi surfaces is constrained by the total number of fermions. However, in the phase without the BEC, which has two Fermi surfaces, there is a second Luttinger constraint: the volume enclosed by one of the Fermi surfaces is constrained by the total number of bosons, so that the volumes enclosed by the two Fermi surfaces are separately conserved. The phase with the BEC may have one or two Fermi surfaces, but only their total volume is conserved. We obtain the phase diagram as a function of atomic parameters and temperature, and describe critical fluctuations in the vicinity of all transitions. We make quantitative predictions valid for the case of a narrow Feshbach resonance, but we expect the qualitative features we describe to be more generally applicable. As an aside, we point out intriguing connections between the BEC depletion transition and the transition to the fractionalized Fermi liquid in Kondo lattice models.
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