# Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence

@article{FossFeig2013DynamicalQC, title={Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence}, author={Michael Foss-Feig and Kaden R. A. Hazzard and John J. Bollinger and Ana Maria Rey and Charles W. Clark}, journal={New Journal of Physics}, year={2013}, volume={15}, pages={113008} }

Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying…

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## References

SHOWING 1-10 OF 75 REFERENCES

Nonequilibrium dynamics of arbitrary-range Ising models with decoherence: An exact analytic solution

- Physics
- 2013

The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic…

Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins

- Physics, MedicineNature
- 2012

A spin-dependent optical dipole force can produce an antiferromagnetic interaction, and this demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.

Quantum simulation of frustrated Ising spins with trapped ions

- Physics, Computer ScienceNature
- 2010

Here, a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions, whose interactions are precisely controlled using optical forces is realized, finding a link between frustration and ground-state entanglement.

The Quantum jump approach to dissipative dynamics in quantum optics

- Physics
- 1998

Dissipation, the irreversible loss of energy and coherence, from a microsystem, is the result of coupling to a much larger macrosystem (or reservoir) which is so large that one has no chance of…

Onset of a quantum phase transition with a trapped ion quantum simulator.

- Physics, MedicineNature communications
- 2011

This work simulates the emergence of magnetism by implementing a fully connected non-uniform ferromagnetic quantum Ising model using up to 9 trapped (171)Yb(+) ions, providing a critical benchmark for the simulation of intractable arbitrary fully connected Ising models in larger systems.

Squeezing and entanglement in a Bose–Einstein condensate

- Physics, MedicineNature
- 2008

Spin squeezed states suitable for atomic interferometry are demonstrated by splitting a condensate into a few parts using a lattice potential by implying entanglement between the particles.

Far-from-equilibrium quantum magnetism with ultracold polar molecules.

- Physics, MedicinePhysical review letters
- 2013

It is shown that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate.

An open-system quantum simulator with trapped ions

- Physics, MedicineNature
- 2011

This work combines multi-qubit gates with optical pumping to implement coherent operations and dissipative processes and illustrates the ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi- qubit observables.

Many-particle entanglement with Bose–Einstein condensates

- Physics, MedicineNature
- 2001

This work proposes a method to achieve substantial entanglement of a large number of atoms in a Bose–Einstein condensate, which is then allowed to evolve freely and should be realizable with present technology.

Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

- Physics
- 2013

We study the time evolution of correlation functions in long- range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice…