The recent trapping of degenerate fermions in optical lattices suggests that such systems could be used as laboratory implementations of strongly correlated electrons.

The theory of such "quantum simulations" seeks to find both the recipes for the accurate experimental realisation of the models under consideration, together with the correct way of interpreting the experimental results.

One important observation we have made is that the thermodynamic limit in atom traps is singular. This implies that in order to use optical lattices as quantum simulations one needs not only finite-size scaling (involving varying the size of the trap) but also "finite curvature scaling" (involving systematic changes in the shape of the trap). Devising appropriate protocols is a subject of our current research.

Ultimately, we aim to make possible experiments on cold atom systems whose results can be directly compared to measurements of condensed matter systems carried out at ISIS and similar facilities.

**References:**For a non-technical overview of strong correlations, with particular emphasis on cold atoms as quantum simulations, see

- J. Quintanilla & C. Hooley,

The strong-correlations puzzle,

Physics World 22, 32-37 (June 2009) [pdf].

**Research articles:**

- S. T. Carr, J. Quintanilla & J. J. Betouras,
*Deconfinement and quantum liquid crystalline states of dipolar fermions in optical lattices,*

Int. J. Mod. Phys. B, in press (invited paper, proceedings of CMT32). arXiv:0903.0590 [cond-mat.str-el]. - J. Quintanilla, S. T. Carr & J. J. Betouras,
*Meta-nematic, smectic and crystalline phases of dipolar fermions in an optical lattice,*

Phys. Rev. A 79, 031601(R) (2009). - V. L. Campo, J. Quintanilla & C. Hooley,
*Critical behavior driven by the confining potential in optical lattices with ultra-cold fermions?,*

arXiv:0809.2186 [cond-mat.str-el]. - V. L. Campo, K. Capelle, J. Quintanilla & C. Hooley,
*Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling,*

Phys. Rev. Lett. 99, 240403 (2007). - C. Hooley, J. Quintanilla,

Finite-curvature scaling in optical lattice systems,

Physica B: Condensed Matter, 378-380, 1035-1036 (2006). - C. Hooley, J. Quintanilla,
*Single-atom density of states of an optical lattice,*

Phys. Rev. Lett. 93, 080404 (2004).

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