The Pinning Quantum Phase Transition

Institut für Experimentalphysik,
University of Innsbruck, and
Austrian Academy of Sciences,
Innsbruck, Austria

Quantum phase transitions

Surprisingly, 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 ground-states of the system. A well-known example is the Bose-Hubbard quantum phase transition from a superfluid to an insulating phase which has been observed a few years ago for weakly interacting bosonic gases [1].


Bose-Hubbard transition

Fig.1 Sketch of the Bose-Hubbard quantum phase transition of weakly interacting bosons from a superfluid (front) to an insulator (back)


Figure 1 sketches the two phases of a gas of weakly interacting bosons connected by a Bose-Hubbard 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 transition

In 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 Bose-Hubbard description of weakly-interacting superfluids in periodic potentials fails and a quantum-field description based on the exactly solvable sine-Gordon model is applicable [3].


pinning transition

  Fig.2 Sketch of the Pinning transition of strongly interacting bosons from a Tonks-Girardeau gas (front) to an insulator (back).  


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" Tonks-Girardeau 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 Mott-insulator 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 condensed-matter physics, the Bose-Hubbard model and the sine-Gordon



top, left to right

Elmar Haller, Johann G. Danzl, Russell Hart, Manfred J. Mark

bottom, left to right
Mattias Gustavsson, Hanns-Christoph Nägerl, Lukas Reichsöllner

Guido Pupillo

Guido Pupillo
Institut für Quantenoptik und Quanteninformation der Österreichischen
Akademie der Wissenschaften


Marcello Dalmonte

Marcello Dalmonte

Condensed Matter Theory, University of Bologna


[1a] Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms.
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415 39-44 (2002).

[1b] Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms.
T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Phys. Rev. Lett 92 130403 (2004).

[2] Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons.
E. Haller, R. Hart, M.J. Mark, J.G. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, H.-C. Nägerl,
Nature 66, 597-600 (2010).

[3] Commensurate-Incommensurate Transition of Cold Atoms in an Optical Lattice.
H. P. Büchler, G. Blatter, W. Zwerger, Phys. Rev. Lett. 90 130401 (2003).



Press release: german, english

Photos for download: ultracold media photos



The experiments are supported by the START-prize of the Bundesministerium für Wissenschaft und Forschung (BMWF) and the Austrian Science Fund (FWF), and by the project Quantum-Degenerate Gases for Precision Measurements (QuDeGPM) of the European Science Foundation (ESF).

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last change: 28-07-2010 by EH