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

TL;DR

This paper demonstrates a quantum phase transition in a 1D bosonic gas induced by an arbitrarily weak optical lattice, revealing new insights into strongly interacting quantum systems and their phase behavior.

Contribution

It experimentally observes and maps the pinning quantum phase transition in a strongly interacting 1D bosonic system, connecting sine-Gordon and Bose-Hubbard models.

Findings

Transition occurs with arbitrarily weak lattice in strong interactions

Phase diagram matches sine-Gordon and Bose-Hubbard predictions

Experimental results extend understanding of quantum criticality

Abstract

One of the most remarkable results of quantum mechanics is the fact that many-body quantum systems may exhibit phase transitions even at zero temperature. Quantum fluctuations, deeply rooted in Heisenberg's uncertainty principle, and not thermal fluctuations, drive the system from one phase to another. Typically, the relative strength of two competing terms in the system's Hamiltonian is changed across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry a novel type of quantum phase transition may be induced for which an arbitrarily weak perturbation to the Hamiltonian is sufficient to drive the transition. Here, for a one-dimensional (1D) quantum gas of bosonic caesium atoms with tunable interactions, we observe the commensurate-incommensurate quantum phase transition from a superfluid Luttinger liquid to a Mott-insulator. 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. We trace the phase boundary all the way to the weakly interacting regime where we find good agreement with the predictions of the 1D 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.