A new approach to quantum metamaterials proceeds along two paths. The first kind of structure is a set of nanowires containing quantum dots.

*Sketch of a quantum metamaterial made of an array of nanorods doped by quantum dots.*

Such a structure is interesting for several reasons: it is simple, it has many interesting properties (negative index, effective magnetism, all-dielectric cloaking), and it can be experimentally realized fairly easily. Furthermore, the quantum dots have a dipole with a controllable orientation. Each nanorod can be characterized by its scattering matrix, which relates the diffracted field to the incident field. For a wavelength that is sufficiently large compared to the diameter of the nanorod, the diffracted field can be characterized by an electric dipole and a magnetic dipole.

By pumping the dots, it is possible to switch this dipole on or off, opening or closing a conduction band. This kind of structure thus possesses a quantum reconfigurable band structure.

The second type of quantum metamaterial we are studying is made of artificial crystals of ultracold atoms, arranged periodically in optical traps, in what is called a Mott insulator state. Such artificial crystals have been realized in several laboratories, and exhibit a much larger periodicity than common crystals (of the order of a fraction of a micron). These quantum systems, whose extreme control and tunability allow their use as quantum clocks, show interesting interplays between the geometry of the lattice, the internal atomic structure, and the motional degrees of freedom of the atoms in their local trapping potential. In particular, we have shown that such structures may possess a full photonic band gap, as is the case for a four-level atomic structure arranged in a diamond lattice, or a two-level atomic structure in a cubic lattice. However, a four-level atomic structure in a cubic lattice does not possess any full photonic band gap. In fact, we have shown that the opening or closing of a band depends on the interplay between the lattice geometry and the internal quantum structure. That a collective property such as the photonic band depends on a quantum number shows the merit of the concept of quantum metamaterials in this context of cold atoms. Remarkably, such artificial crystals have recently been used to produce a 1D photonic-crystal lasing medium, where multiple Bragg reflections and the presence of a cold atom cloud simultaneously provide gain and feedback.

In summary, we have proposed new ways to make metamaterials enter the quantum world. Inserting artificial atoms (quantum dots) into periodic nanostructures or arranging real atoms (ultracold gases) into artificial periodic lattices can open new possibilities for collective light-matter behavior. In the future, we will study these new structures both experimentally (lattices of doped dielectric nanorods) and theoretically. By investigating several fundamental aspects linked to quantum fluctuations, we aim to reveal the existence of non-trivial collective phenomena resulting from hybridization of internal and global states

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