Andrew Daley's Research group at the University of Pittsburgh

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Understanding many phenomena we find in nature often relies on understanding the behaviour of the microscopic particles making up the things we want to describe. Examples of this range in scale from the behaviour of electrons in conductors, insulators and semiconductors to the properties of white dwarf stars. In many cases, this behaviour is described by quantum mechanics, and becomes very difficult to describe in a way where we can do calculations on a classical computer. In particular, for strongly interacting many-particle systems in quantum mechanics, this can require the storage of a number of parameters that grows exponentially with the size of the system. This has made modelling of complex materials such as high-temperature superconductors (where electrons can flow without resistance in materials at temperatures a little below room-temperature) very difficult, or in some cases essentially impossible.

A new way around this problem is to find a highly-controllable quantum system that we understand well on a microscopic level, and then use this system to model the properties of the system that we don't understand well. This can either be done by constructing a *quantum computer* to compute the properties of the other system (which is called * digital quantum simulation *) or by manipulating properties of the controllable system to that it directly resembles the system you would like to study (which is called *quantum emulation* or *analogue quantum simulation*).

**Quantum emulation with ultracold quantum gases**

A key example of a well-controlled quantum mechanical system that can be used as a quantum simulator is an ultracold quantum gas. Since 1995, where Bose-Einstein condensates were first realised in the laboratory (and for which the Nobel prize was awarded in 2001), many research groups around the world have been producing these systems, where gases of a few tens of millions of atoms or molecules are cooled to temperature around a few nanoKelvin above absolute zero. These systems are very well understood on a microscopic level, and are widely controllable via external laser and magnetic fields, which can be used to adjust the interatomic interactions and trapping for the atoms.

Over the last ten years a strong focus has been placed on using this level of control and microscopic understanding in atomic physics systems to study strongly correlated lattice and spin systems, as appear in modern solid state physics. By loading cold atoms into optical lattices, (which are formed via the AC-Stark shift from standing waves of laser light) it is possible to engineer microscopic many-body lattice models. There atoms are trapped at specific lattice sites, and the dynamics consist of atoms hopping from site to site, and interactions between atoms on the same site. Again, we have complete control of the hopping and interaction parameters via external laser and magnetic fields.

This has opened opportunities to use these systems as quantum emulators, implementing models describing the physics of interest, and exploring the many-body physics associated with them. There are two approaches for exploring physics in these systems:- To study these models in parameter regimes that are believed to contain important physics, but where there is no existing approach to rigorously solve the model mathematically (an example of this is the possible connection between the repulsive Fermi-Hubbard Model in 2D and high-temperature superconductivity of cuprates materials), or
- To see quantum gases as important physical systems in their own right, where new quantum phases and dynamical phenomena that have been studied theoretically can be explored in experiments

**Our research**

- Exploring phenomena that can be modelled and understood with quantum emulators, including situations where these systems can be applied to answer existing problems, and also where we explore fundamentally new physics
- Exploring and designing new techniques that could be used in experiments, e.g., to achieve lower temperatures or measure previously inaccessible quantities
- Working directly with experimental groups trying to implement these phenomena, modelling the experiments and making comparisons with experimental data
- Helping to set a roadmap for exploring fundamental physics in near-term and future experiments

**External links**

- Recent review of quantum simulation with atoms and ions: M. Müller, S. Diehl, G. Pupillo, and P. Zoller, arxiv:1203.6595 (2012)
- Reviews of quantum simulation in Nature Physics Insight, with
- General introduction and overview, J. Ignacio Cirac and Peter Zoller, Nature Physics
**8**, 264 (2012) - Ultracold gases, Immanuel Bloch, Jean Dalibard and Sylvain Nascimbčne, Nature Physics
**8**, 267 (2012) - Trapped Ions, R. Blatt and C. F. Roos, Nature Physics
**8**, 274 (2012) - Photonic systems, Alán Aspuru-Guzik and Philip Walther, Nature Physics
**8**, 285 (2012)

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