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arXiv:1401.5387 · Nature

Quasiparticle engineering and entanglement propagation in a quantum many-body system

Petar Jurcevic, B. P. Lanyon, Philipp Hauke, Cornelius Hempel, P. Zoller, R. Blatt, Christian F. Roos

Published Jul 8, 2014• 863 citations
arXivHTMLPDF
DOI
10.1038/nature13461

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The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by local, few-body terms. Unfortunately, in nonequilibrium situations, analytic results are rare and largely confined to continuous field theories, which fail to accurately describe microscopic models. To address this gap, we present an analytic result for the EH following a quantum quench in noninteracting fermionic models, valid in the ballistic scaling regime. The derivation adapts the celebrated quasiparticle picture to operators, providing detailed insights into its physical properties. The resulting analytic formula serves as a foundation for engineering EHs in quantum optics experiments.
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We present a formalism for the fermionic quasiparticle propagator in a superfluid fermionic system. Starting from a general many-body Hamiltonian confined by the two-body instantaneous interaction, the equation of motion for the fermionic propagator is obtained in the Dyson form. Before making any approximation, the interaction kernel is found to be decomposed into static and dynamical (time-dependent) contributions, where the latter translates to the energy-dependent and the former maps to the energy-independent terms in the energy domain. The three-fermion correlation function, being the heart of the dynamical part of the kernel, is factorized into the two-fermion and one-fermion ones. With the relaxed particle number constraint, the normal propagator is coupled to the anomalous one via both the static and dynamical kernels, which is formalized by introducing the generalized quasiparticle propagator of the Gor'kov type. The dynamical kernel in the factorized form is associated with the quasiparticle-vibration coupling (QVC), with the vibrations unifying both the normal and pairing phonons. The QVC vertices are related to the variations of the Hamiltonian of the Bogoliubov quasiparticles, which can be obtained by the finite amplitude method.