### Abstract

Quantum many-body systems can have phase transitions(1) even at zero temperature; fluctuations arising from Heisenberg's uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system's Hamiltonian changes across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase(2,3), which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type(4,5) of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect-the sine-Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator(6,7)-in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model(8). We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

Language | English |
---|---|

Pages | 597-600 |

Number of pages | 4 |

Journal | Nature |

Volume | 466 |

Issue number | 7306 |

DOIs | |

Publication status | Published - 29 Jul 2010 |

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### Keywords

- bosonic atomic gases
- optical lattice
- bosonic caesium atoms
- ultracold gasses

### Cite this

*Nature*,

*466*(7306), 597-600. https://doi.org/10.1038/nature09259

}

*Nature*, vol. 466, no. 7306, pp. 597-600. https://doi.org/10.1038/nature09259

**Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons.** / Haller, Elmar; Hart, R.; Mark, M.J.; Danzl, J.G.; Reichsoellner, L.; Gustavsson, M.; Dalmonte, M.; Pupillo, Guido; Naegerl, H.-C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

AU - Haller, Elmar

AU - Hart, R.

AU - Mark, M.J.

AU - Danzl, J.G.

AU - Reichsoellner, L.

AU - Gustavsson, M.

AU - Dalmonte, M.

AU - Pupillo, Guido

AU - Naegerl, H.-C.

PY - 2010/7/29

Y1 - 2010/7/29

N2 - Quantum many-body systems can have phase transitions(1) even at zero temperature; fluctuations arising from Heisenberg's uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system's Hamiltonian changes across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase(2,3), which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type(4,5) of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect-the sine-Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator(6,7)-in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model(8). We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

AB - Quantum many-body systems can have phase transitions(1) even at zero temperature; fluctuations arising from Heisenberg's uncertainty principle, as opposed to thermal effects, drive the system from one phase to another. Typically, during the transition the relative strength of two competing terms in the system's Hamiltonian changes across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase(2,3), which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry, a novel type(4,5) of quantum phase transition may be induced and driven by an arbitrarily weak perturbation to the Hamiltonian. Here we observe such an effect-the sine-Gordon quantum phase transition from a superfluid Luttinger liquid to a Mott insulator(6,7)-in a one-dimensional quantum gas of bosonic caesium atoms with tunable interactions. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model(8). We trace the phase boundary all the way to the weakly interacting regime, where we find good agreement with the predictions of the one-dimensional Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality and transport phenomena beyond Hubbard-type models in the context of ultracold gases.

KW - bosonic atomic gases

KW - optical lattice

KW - bosonic caesium atoms

KW - ultracold gasses

U2 - 10.1038/nature09259

DO - 10.1038/nature09259

M3 - Article

VL - 466

SP - 597

EP - 600

JO - Nature

T2 - Nature

JF - Nature

SN - 0028-0836

IS - 7306

ER -