At low enough temperatures and at microscopic length scales the laws of quantum mechanics become apparent. The underlying superposition principle leads to interference phenomena for one degree of freedom and to the concept of entanglement for two and more. Entangled degrees of freedom are often correlated beyond their classically allowed correlation. These quantum correlations also appear in very large systems and are caused by strong interactions between the constituents. Strongly correlated forms of quantum matter became ubiquitous in condensed matter physics, with the discovery of heavy fermion materials, cuprates and other unconventional superconductors. Here the main players are electrons embedded in solid matter. But they also can be found in interacting quantum gases, where the main players are atoms. In the latter case the required temperatures for quantum correlations to appear are much lower. But in turn the length scales are larger and they can be embedded in well controlled potentials.

A fascinating possibility offered by present day technologies is to tailor matter in order to induce the emergence of new phenomena by controlling quantum correlations. One of the routes leading to spectacular advances is the configuration of nanomaterials like quantum dots or quantum wires on the basis of semiconducting substrates that allow, e.g., to manipulate the Kondo effect or Luttinger liquids affecting transport properties through such nanostructures. Another quite different route with at the moment unlimited potential is offered by quantum optics and atomic physics, when implemented to bring quantum gases into the strongly interacting regime. This can be achieved by optical lattices leading to Mott-insulators, or to two dimensional systems displaying Kosterlitz–Thouless behavior in bosonic gases, or by Feshbach resonances, leading to fermionic systems with unconventional superfluid states like the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) one.

In spite of the very different experimental realizations leading to the two routes mentioned above, they share a common goal, namely achieving a deep understanding of quantum correlations that will ultimately allow to control them and possibly realize new forms of matter. They also share the flexibility that allows to increase the complexity in quantum correlations by joining in a controlled manner well understood building units and/or by regulating their coupling to the environment.

It is under the common goal of understanding and controlling quantum correlations that we see the topics presented in this focus issue of New Journal of Physics, where both lines of development, that is on solid-state substrates or with quantum gases, give a timely view of the advances towards the above mentioned common goal.

Focus on Quantum Correlations in Tailored Matter Contents

Temperature changes when adiabatically ramping up an optical lattice
Lode Pollet, Corinna Kollath, Kris Van Houcke and Matthias Troyer

Numerical study of two-body correlation in a 1D lattice with perfect blockade
B Sun and F Robicheaux

Kinetic Monte Carlo modeling of dipole blockade in Rydberg excitation experiment
Amodsen Chotia, Matthieu Viteau, Thibault Vogt, Daniel Comparat and Pierre Pillet

Motion of Rydberg atoms induced by resonant dipole–dipole interactions
C Ates, A Eisfeld and J M Rost

Quantum coherence due to Bose–Einstein condensation of parametrically driven magnons
S O Demokritov, V E Demidov, O Dzyapko, G A Melkov and A N Slavin

Chaotic dynamics in spinor Bose–Einstein condensates
J Kronjäger, K Sengstock and K Bongs

Damped Bloch oscillations of Bose–Einstein condensates in disordered potential gradients
S Drenkelforth, G Kleine Büning, J Will, T Schulte, N Murray, W Ertmer, L Santos and J J Arlt

Rabi oscillations between ground and Rydberg states and van der Waals blockade in a mesoscopic frozen Rydberg gas
M Reetz-Lamour, J Deiglmayr, T Amthor and M Weidemüller

Excitations in two-component Bose gases
A Kleine, C Kollath, I P McCulloch, T Giamarchi and U Schollwöck

Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas
M Eckart, R Walser and W P Schleich

How to fix a broken symmetry: quantum dynamics of symmetry restoration in a ferromagnetic Bose–Einstein condensate
Bogdan Damski and Wojciech H Zurek

Landau levels of cold atoms in non-Abelian gauge fields
A Jacob, P Öhberg, G Juzeliunas and L Santos

Atomic four-wave mixing via condensate collisions
A Perrin, C M Savage, D Boiron, V Krachmalnicoff, C I Westbrook and K V Kheruntsyan

Semifluxons in superconductivity and cold atomic gases
R Walser, E Goldobin, O Crasser, D Koelle, R Kleiner and W P Schleich

Disorder-induced trapping versus Anderson localization in Bose–Einstein condensates expanding in disordered potentials
L Sanchez-Palencia, D Clément, P Lugan, P Bouyer and A Aspect

Critical tunneling currents in the regime of bilayer excitons
L Tiemann, W Dietsche, M Hauser and K von Klitzing

Quantum phases of trapped ions in an optical lattice
R Schmied, T Roscilde, V Murg, D Porras and J I Cirac

Generation and detection of a spin entanglement in nonequilibrium quantum dots
Stefan Legel, Jürgen König and Gerd Schön

Slow light in inhomogeneous and transverse fields
Leon Karpa and Martin Weitz

FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a non-uniform background potential
T K Koponen, T Paananen, J-P Martikainen, M R Bakhtiari and P Törmä

Geometry-dependent interplay of long- and short-range interactions in ultracold fermionic gases: models for condensed matter and astrophysics
B Deb, G Kurizki and I E Mazets

Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids
V Meden, S Andergassen, T Enss, H Schoeller and K Schönhammer

Luttinger hydrodynamics of confined one-dimensional Bose gases with dipolar interactions
R Citro, S De Palo, E Orignac, P Pedri and M-L Chiofalo

Towards deterministically controlled InGaAs/GaAs lateral quantum dot molecules
L Wang, A Rastelli, S Kiravittaya, P Atkinson, F Ding, C C Bof Bufon, C Hermannstädter, M Witzany, G J Beirne, P Michler and O G Schmidt

Effective parameters for weakly coupled Bose–Einstein condensates
S Giovanazzi, J Esteve and M K Oberthaler

Current statistics of correlated charge tunnelling through an impurity in a 1D wire
Alexander Herzog and Ulrich Weiss

Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap
Stephan A Schulz, Ulrich Poschinger, Frank Ziesel and Ferdinand Schmidt-Kaler

The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics
Z Hadzibabic, P Krüger, M Cheneau, S P Rath and J Dalibard

Dynamical protection of quantum computation from decoherence in laser-driven cold-ion and cold-atom systems
Goren Gordon and Gershon Kurizki

Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond
Ph Tamarat, N B Manson, J P Harrison, R L McMurtrie, A Nizovtsev, C Santori, R G Beausoleil, P Neumann, T Gaebel, F Jelezko, P Hemmer and J Wrachtrup

Superconductivity in the attractive Hubbard model: functional renormalization group analysis
R Gersch, C Honerkamp and W Metzner

Quantum stability of Mott-insulator states of ultracold atoms in optical resonators
Jonas Larson, Sonia Fernández-Vidal, Giovanna Morigi and Maciej Lewenstein