21 research outputs found
Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
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
Phase-slip induced dissipation in an atomic Bose-Hubbard system
Phase slips play a primary role in dissipation across a wide spectrum of
bosonic systems, from determining the critical velocity of superfluid helium to
generating resistance in thin superconducting wires. This subject has also
inspired much technological interest, largely motivated by applications
involving nanoscale superconducting circuit elements, e.g., standards based on
quantum phase-slip junctions. While phase slips caused by thermal fluctuations
at high temperatures are well understood, controversy remains over the role of
phase slips in small-scale superconductors. In solids, problems such as
uncontrolled noise sources and disorder complicate the study and application of
phase slips. Here we show that phase slips can lead to dissipation for a clean
and well-characterized Bose-Hubbard (BH) system by experimentally studying
transport using ultra-cold atoms trapped in an optical lattice. In contrast to
previous work, we explore a low velocity regime described by the 3D BH model
which is not affected by instabilities, and we measure the effect of
temperature on the dissipation strength. We show that the damping rate of
atomic motion-the analogue of electrical resistance in a solid-in the confining
parabolic potential fits well to a model that includes finite damping at zero
temperature. The low-temperature behaviour is consistent with the theory of
quantum tunnelling of phase slips, while at higher temperatures a cross-over
consistent with the transition to thermal activation of phase slips is evident.
Motion-induced features reminiscent of vortices and vortex rings associated
with phase slips are also observed in time-of-flight imaging.Comment: published in Nature 453, 76 (2008
Many-body Landau-Zener dynamics in coupled 1D Bose liquids
The Landau-Zener model of a quantum mechanical two-level system driven with a
linearly time dependent detuning has served over decades as a textbook paradigm
of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2,
46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener
derived a non-perturbative prediction for the transition probability between
two states, which often serves as a reference point for the analysis of more
complex systems. A particularly intriguing question is whether that framework
can be extended to describe many-body quantum dynamics. Here we report an
experimental and theoretical study of a system of ultracold atoms, offering a
direct many-body generalization of the Landau-Zener problem. In a system of
pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of
the 1D gases, the tunnel coupling between the tubes and the inter-tube
interactions strongly modify the original Landau-Zener picture. The results are
explained using a mean-field description of the inter-tube condensate
wave-function, coupled to the low-energy phonons of the 1D Bose liquid.Comment: 13 pages, 10 figures
Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
The problem of how complex quantum systems eventually come to rest lies at
the heart of statistical mechanics. The maximum entropy principle put forward
in 1957 by E. T. Jaynes suggests what quantum states one should expect in
equilibrium but does not hint as to how closed quantum many-body systems
dynamically equilibrate. A number of theoretical and numerical studies
accumulate evidence that under specific conditions quantum many-body models can
relax to a situation that locally or with respect to certain observables
appears as if the entire system had relaxed to a maximum entropy state. In this
work, we report the experimental observation of the non-equilibrium dynamics of
a density wave of ultracold bosonic atoms in an optical lattice in the regime
of strong correlations. Using an optical superlattice, we are able to prepare
the system in a well-known initial state with high fidelity. We then follow the
dynamical evolution of the system in terms of quasi-local densities, currents,
and coherences. Numerical studies based on the time-dependent density-matrix
renormalization group method are in an excellent quantitative agreement with
the experimental data. For very long times, all three local observables show a
fast relaxation to equilibrium values compatible with those expected for a
global maximum entropy state. We find this relaxation of the quasi-local
densities and currents to initially follow a power-law with an exponent being
significantly larger than for free or hardcore bosons. For intermediate times
the system fulfills the promise of being a dynamical quantum simulator, in that
the controlled dynamics runs for longer times than present classical algorithms
based on matrix product states can efficiently keep track of.Comment: 8 pages, 6 figure