ABSTRACT: Frustration, or the competition between interacting components of a network, is often responsible for the emergent complexity of many-body systems. For instance, frustrated magnetism is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses, and spin ices, whose ground states can be massively degenerate and carry high degrees of quantum entanglement. Here, we engineer frustrated antiferromagnetic interactions between spins stored in a crystal of up to 16 trapped (171)Yb(+) atoms. We control the amount of frustration by continuously tuning the range of interaction and directly measure spin correlation functions and their coherent dynamics. This prototypical quantum simulation points the way toward a new probe of frustrated quantum magnetism and perhaps the design of new quantum materials.
Science 05/2013; 340(6132):583-7. · 31.20 Impact Factor
ABSTRACT: Frustration, or the competition between interacting components of a network,
is often responsible for the complexity of many body systems, from social and
neural networks to protein folding and magnetism. In quantum magnetic systems,
frustration arises naturally from competing spin-spin interactions given by the
geometry of the spin lattice or by the presence of long-range antiferromagnetic
couplings. Frustrated magnetism is a hallmark of poorly understood systems such
as quantum spin liquids, spin glasses and spin ices, whose ground states are
massively degenerate and can carry high degrees of quantum entanglement. The
controlled study of frustrated magnetism in materials is hampered by short
dynamical time scales and the presence of impurities, while numerical modeling
is generally intractable when dealing with dynamics beyond N~30 particles.
Alternatively, a quantum simulator can be exploited to directly engineer
prescribed frustrated interactions between controlled quantum systems, and
several small-scale experiments have moved in this direction. In this article,
we perform a quantum simulation of a long-range antiferromagnetic quantum Ising
model with a transverse field, on a crystal of up to N = 16 trapped Yb+ atoms.
We directly control the amount of frustration by continuously tuning the range
of interaction and directly measure spin correlation functions and their
dynamics through spatially-resolved spin detection. We find a pronounced
dependence of the magnetic order on the amount of frustration, and extract
signatures of quantum coherence in the resulting phases.
ABSTRACT: A quantum simulator is a well controlled quantum system that can simulate the
behavior of another quantum system which may require exponentially large
classical computing resources to understand otherwise. In the 1980s, Feynman
proposed the use of quantum logic gates on a standard controllable quantum
system to efficiently simulate the behavior of a model Hamiltonian. Recent
experiments using trapped ions and neutral atoms have realized quantum
simulation of Ising model in presence of external magnetic fields, and showed
almost arbitrary control in generating non-trivial Ising coupling patterns.
Here we use laser-cooled trapped 171-Yb+ ions to simulate the emergence of
magnetism in a system of interacting spins by implementing a fully-connected
non-uniform ferromagnetic Ising model in a transverse magnetic field. To link
this quantum simulation to condensed matter physics, we measure scalable
correlation functions and order parameters appropriate for the description of
larger systems, such as various moments of the magnetization. By increasing the
Ising coupling strengths compared with the external field, the crossover from
paramagnetism to ferromagnetic order sharpens as the system is scaled up from N
= 2 to 9 trapped ion spins. This points toward the onset of a quantum phase
transition that should become infinitely sharp as the system approaches the
macroscopic scale. We compare the measured ground state order to theory, which
may become intractable for non-uniform Ising couplings as the number of spins
grows beyond 20- 30 and even NP complete for a fully-connected frustrated Ising
model, making this experiment an important benchmark for large-scale quantum
ABSTRACT: A quantum simulator is a well-controlled quantum system that can follow the evolution of a prescribed model whose behaviour may be difficult to determine. A good example is the simulation of a set of interacting spins, where phase transitions between various spin orders can underlie poorly understood concepts such as spin liquids. Here we simulate the emergence of magnetism by implementing a fully connected non-uniform ferromagnetic quantum Ising model using up to 9 trapped (171)Yb(+) ions. By increasing the Ising coupling strengths compared with the transverse field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up, prefacing the expected quantum phase transition in the thermodynamic limit. We measure scalable order parameters appropriate for large systems, such as various moments of the magnetization. As the results are theoretically tractable, this work provides a critical benchmark for the simulation of intractable arbitrary fully connected Ising models in larger systems.
Nature Communications 01/2011; 2:377. · 7.40 Impact Factor
ABSTRACT: A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social and neural networks to protein folding and magnetism. Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses. Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions, whose interactions are precisely controlled using optical forces. We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.
Nature 06/2010; 465(7298):590-3. · 36.28 Impact Factor
ABSTRACT: We perform a quantum simulation of the Ising model with a transverse field
using a collection of three trapped atomic ion spins. By adiabatically
manipulating the Hamiltonian, we directly probe the ground state for a wide
range of fields and form of the Ising couplings, leading to a phase diagram of
magnetic order in this microscopic system. The technique is scalable to much
larger numbers of trapped ion spins, where phase transitions approaching the
thermodynamic limit can be studied in cases where theory becomes intractable.