

Quantum phase transitionsSurprisingly, even at a temperature of absolute zero, quantum systems may allow for the reordering of matter and are capable of showing rapid changes of macroscopic properties. Such quantum phase transitions have been subject to intense investigation within the last decades and generally show very different properties compared to classical phase transitions. Classical phase transitions, e.g. the change of the state of aggregation or the reordering of the structure of a crystal, are driven by the competition between the internal energy and the entropy of the system. At low temperatures the system can minimize its energy by reaching an ordered state, whereas at high temperatures a loss of order allows it to maximize its entropy.
Quantum phase transitions, on the other hand, result from two competing terms in the systems’s Hamiltonian and they usually connect two groundstates of the system. A wellknown example is the BoseHubbard quantum phase transition from a superfluid to an insulating phase which has been observed a few years ago for weakly interacting bosonic gases [1].
Figure 1 sketches the two phases of a gas of weakly interacting bosons connected by a BoseHubbard transition. The properties of ultracold atoms (orange) can be controlled by the depth of an optical lattice (silver). For weak interactions the atoms are coherently spread over the whole lattice and form a superfluid (front). A deep lattice potential (back) is necessary to localize the atoms to individual lattice sites.
Pinning transitionIn Ref. [2] we show that, for sufficiently strong interactions in 1D geometry, an arbitrarily weak optical lattice is capable of inducing a quantum phase transition from a bosonic superfluid Luttinger liquid to an insulating state. In striking contrast to the weakly interacting case, the particles are instantly pinned when the weak lattice perturbation is introduced. In this regime, the standard BoseHubbard description of weaklyinteracting superfluids in periodic potentials fails and a quantumfield description based on the exactly solvable sineGordon model is applicable [3].
Figure 2 sketches the two phases of a gas of strongly interacting bosons connected by the Pinning transition. Particles with strong repulsive interaction "try to avoid" an overlap of their wave functions and form a strongly "ordered" TonksGirardeau gas (front). In this case, a small perturbation in form of a lattice potential is sufficient to "pin" the to individual lattice sites (back). The only requirement is the commensurability of the particle density, i.e. the average distance between the atoms matches the lattice spacing.
In Ref [2] both regimes of the Mottinsulator phase transition are studied. We observe the appearance of an energy gap in
the excitation spectrum and a change in the transport properties of the gas. The complete phase diagram of the Mott insulator transition is determined all the way from vanishing small lattice depth to the tight binding regime. As a result, we connect the physics of two important models of condensedmatter physics, the BoseHubbard model and the sineGordon
Teamtop, left to right Elmar Haller, Johann G. Danzl, Russell Hart, Manfred J. Mark bottom, left to right Guido Pupillo
Condensed Matter Theory, University of Bologna References[1a] Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms.
LinksPress release: german, english Photos for download: ultracold media photos
FundingThe experiments are supported by the STARTprize of the Bundesministerium für Wissenschaft und Forschung (BMWF) and the Austrian Science Fund (FWF), and by the project QuantumDegenerate Gases for Precision Measurements (QuDeGPM) of the European Science Foundation (ESF).


last change: 28072010 by EH 