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Quantum Phase Transitions of Polaritons in Arrays of Coupled Micro-Cavities
M.J. Hartmann, F.G.S.L. Brandao and M.B. Plenio (Imperial College) have now proposed a quantum simulator in a new system, which allows for experimental access to properties of individual particles.
Quantum systems are much more complex than classical ones. One the one hand, they offer the possibility to perform computations that classical computers cannot perform, but, on the other hand, if they are large and composed of many particles, their description requires more data than a classical computer can handle. While special classes of quantum systems may be treated with numerical methods it is clear that there will be many quantum systems, for example those exhibiting long-range interactions, that cannot be simulated efficiently on a classical computer. For such systems we need a new approach. Quantum Simulators, systems that can emulate very complex quantum dynamics but are nonetheless well controllable in the laboratory, have thus become a topic of major scientific activity.
So far, experimental implementations of quantum simulators have either been limited by a short lifetime or by difficulties to address and measure single particles.
M.J. Hartmann, F.G.S.L. Brandao and M.B. Plenio (Imperial College) have now proposed a quantum simulator in a new system, which allows for experimental access to properties of individual particles (Nature Physics 2, (2006) available at http://dx.doi.org/10.1038/nphys462 and quant-ph/0606097 see also D.G. Angelakis, M.F. Santos and S. Bose quant-ph/0606159 for a subsequent related proposal). The approach makes use of arrays of micro-cavities, very small devices that can trap light for a long time. Atoms are trapped in each micro-cavity and interact with the light stored in it. Polaritons, superpositions of atomic excitations and photons form the particles of the effective model, i.e. the particles described by the simulated Hamiltonian. As the atomic excitation of the polaritons is stored in metastable atomic energy levels with a very long lifetime, the polaritons are very robust against spontaneous emission loss. In this setup an effective Bose Hubbard model with both, repulsive and attractive interactions can be created. The atoms in each cavity are driven by an external laser and, by adjusting the intensity of this laser, the effective system can undergo various quantum phase transitions including the transition between superfluid and Mott insulator regime.
The experimental realisation of such arrays of micro-cavities has seen some tremendous progress recently and the first arrays mounted on devices to trap the atoms in their vicinity have been realised. In view of these developments, an experimental realisation of a small scale demonstration of the proposed quantum simulator seems within reach.
Possible Implementation:
Figure: Toroidal microcavities are coupled via an optical fibre (green). Each cavity interacts with a cloud of atoms (orange) which are driven by external lasers (red). The sketch uses an SEM picture of a toroidal micro-cavity by T. Kippenberg
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