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arXiv:0706.3378 · Physical Review A

Many-body protected entanglement generation in interacting spin systems

Ana María Rey, Liang Jiang, Michael Fleischhauer, Eugene Demler, Mikhail D. Lukin

Published May 5, 2008• 56 citations
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Abstract

We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.

DOI
10.1103/physreva.77.052305

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We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.
We propose and analyze a scheme that makes use of interactions between spins to protect certain correlated many-body states from decoherence. The method exploits the finite energy gap of properly designed Hamiltonians to generate a manifold insensitive to local noise fluctuations. We apply the scheme to achieve decoherence-resistant generation of many particle GHZ states and show that it can improve the sensitivity in precision spectroscopy with trapped ions. Finally we also show that cold atoms in optical lattices interacting via short range interactions can be utilized to engineer the required long range interactions for a robust generation of entangled states.
Abstract We propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.
We propose and discuss a scheme for robust and efficient generation of many-particle entanglement in an ensemble of Rydberg atoms with resonant dipole-dipole interactions. It is shown that in the limit of complete dipole blocking, the system is isomorphic to a multimode Jaynes-Cummings model. While dark-state population transfer is not capable of creating entanglement, other adiabatic processes are identified that lead to complex, maximally entangled states, such as the N-particle analog of the Greenberger-Horne-Zeilinger (GHZ) state in a few steps. The process is robust, works for even and odd particle numbers and the characteristic time for entanglement generation scales linearly with N.
Greenberger-Horne-Zeilinger (GHZ) state is a typical maximally entangled state which is pursued in both fundamental research and emerging quantum technologies. Preparing large-scale GHZ states in lattice spin systems is particularly appealing for quantum advantages, but conventional schemes face great challenges in scalability. Here we propose a universal and scalable scheme to generate large-scale GHZ-like states, which share similar entanglement and metrological properties with standard GHZ states, in lattice spin systems through global Floquet engineering. Our scheme requires only global operations and shows great advantage for large particle number. It is applicable to systems with arbitrary interaction ranges, offering a practical pathway for large-scale implementation of many-body entangled states in various systems.
We show that collective three-body interactions (3BIs), implementable with NNN atoms loaded inside an optical cavity, offer a significant advantage for preparing complex multipartite entangled states. Firstly, they enable a speedup of order ∼N\sim N∼N in preparing generalized Greenberger-Horne-Zeilinger (GHZ) states, outperforming conventional methods based on all-to-all two-body Ising interactions. Secondly, they saturate the Heisenberg bound in phase estimation tasks using a time-reversal protocol realized through simple rotations and followed by experimentally accessible collective spin measurements. Lastly, compared with two-body interactions (2BIs), in the presence of cavity losses and single particle decoherence, 3BIs feature a high gain in sensitivity for moderate atom numbers and in large ensembles a fast entanglement generation despite constraints in parameter regimes where they are implementable.