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Cambridge, United Kingdom

Cooper N.R.,TCM Group | Dalibard J.,Kastler-Brossel Laboratory | Dalibard J.,College de France
Physical Review Letters | Year: 2013

We present a robust scheme by which fractional quantum Hall states of bosons can be achieved for ultracold atomic gases. We describe a new form of optical flux lattice, suitable for commonly used atomic species with ground state angular momentum Jg=1, for which the lowest energy band is topological and nearly dispersionless. Through exact diagonalization studies, we show that, even for moderate interactions, the many-body ground states consist of bosonic fractional quantum Hall states, including the Laughlin state and the Moore-Read (Pfaffian) state. These phases are shown to have energy gaps that are larger than temperature scales achievable in ultracold gases. © 2013 American Physical Society.

Caio M.D.,Kings College London | Cooper N.R.,TCM Group | Bhaseen M.J.,Kings College London
Physical Review Letters | Year: 2015

We explore the nonequilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and nontopological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample. © 2015 American Physical Society.

Scaffidi T.,Ecole Normale Superieure de Paris | Scaffidi T.,University of Oxford | Moller G.,TCM Group
Physical Review Letters | Year: 2012

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the ground state of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the ν=1/2 Laughlin state of bosons in the continuum fractional quantum Hall problem. © 2012 American Physical Society.

Price H.M.,TCM Group | Cooper N.R.,TCM Group
Physical Review Letters | Year: 2013

Topological energy bands have important geometrical properties described by the Berry curvature. We show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field. Using an operator approach, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of energy bands. © 2013 American Physical Society.

Beri B.,TCM Group | Cooper N.R.,TCM Group
Physical Review Letters | Year: 2011

We describe how optical dressing can be used to generate band structures for ultracold atoms with nontrivial Z2 topological order. Time-reversal symmetry is preserved by simple conditions on the optical fields. We first show how to construct optical lattices that give rise to Z2 topological insulators in two dimensions. We then describe a general method for the construction of three-dimensional Z2 topological insulators. A central feature of our approach is a new way to understand Z2 topological insulators starting from the nearly free electron limit. © 2011 American Physical Society.

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