Quantum state engineering in strongly correlated ultracold atomic gases

Exciting new prospects for atomic physics to help gaining insight into very complicated condensed matter systems and the physical effects which lead to important and intriguing phenomena like high Tc superconductivity and superfluidity have arisen recently. A cloud of very cold Rubidium atoms which all behave in exactly the same way due to their low temperatures (a so called atomic Bose-Einstein condensate) is loaded into an optical lattice. This lattice is created by three pairs of counter propagating laser beams which produce a periodic potential that traps atoms at each of its minima. An example of such a system is schown in the figure. When the depth of the lattice is increased the atoms get pushed closer together and the barrier height between the minima increases. It thus gets harder for the particles to hop from one site to the next and at the same time the repulsion between two atoms sitting in the same lattice site gets larger. In this situation the atoms become strongly correlated with each other and behave very similarly to condensed matter systems. However, the system of atoms is in many ways much easier to work with since the underlying physics is precisely known. Loss processes and impurities are much rarer than in genuine condensed matter systems and the control over the atoms by the external laser parameters is unprecedented. One can therefore experimentally realize Hamiltonian quantum dynamics with varying controllable parameters. Based on these properties we study the dynamics of atoms which can be trapped in two different internal hyperfine states (i.e. states which correspond to different stable configurations of the electron shell and the nucleus) in this research project. This will give significant insight into the transfer of entanglement and superposition states when the depth of the lattice is varied and we will suggest possible applications of the resulting quantum states for quantum computing, entanglement assisted metrology and condensed matter studies.
Then we will use a recent observation that an atom which is trapped in an excited motional state of a lattice can emit a phonon (which is a special kind of excitation) into a surrounding cloud of atoms to be de-excited back to its ground state just like it emits photons to go from excited electronic states to its ground state. This mechanism will be combined with blocking due to the repulsion between the atoms to yield an experimentally feasible scheme for creating arbitrary atomic patterns in optical lattices with very high accuracy. Since the emission of phonons is irreversible, loading can be repeated for improving the quality of the patterns. Variations of the loading methods will furthermore enable us to cool atomic patterns to their ground state and thus repair holes in patterns that emerged from loss processes where particles escape the lattice. The generation of virtually defect free atomic patterns is of paramount importance in quantum computing and for quantum simulators which always assume a perfect quantum register for performing calculations.
We will use analytical as well as numerical methods in our work. Strongly correlated systems are very difficult to describe on a classical computer due to their large number of degrees of freedom. However, we will utilize a new simulation method which emerged from theoretical entanglement studies in one dimensional strongly correlated systems with nearest neighbour interactions. They showed that for such arrangements the amount of entanglement is limited and using methods from quantum information theory one can thus efficiently simulate these setups on a classical computer. We will extend those algorithms to multi component systems, finite temperatures, and loss processes to be applicable to the setups explored in this project. Furthermore we will work on the difficult task of performing numerical simulations for two dimensional strongly correlated systems. There the amount of entanglement is not limited and thus new approaches will be necessary.

Investigators:  M. Rodriguez, S.R. Clark and D. Jaksch
  
Funded by:  EPSRC First Grant scheme; Grant No EP/C519833/1(P)
  
Start date:  2005-01-01
End date:  2007-02-28
  

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