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arXiv:1303.0173 · Physical Review A

Entanglement detection by Bragg scattering

Chiara Macchiavello, Giovanna Morigi

Published Apr 22, 2013• 5 citations
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Abstract

We show how to measure the structural witnesses proposed previously [P. Krammer et al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin chain using photon scattering. The procedure allows one to measure the two-point correlation function of the spin array. This proposal could be performed in existing experimental platforms, realizing ion chains in Paul traps or atomic arrays in optical lattices.

DOI
10.1103/physreva.87.044301

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We show how to measure the structural witnesses proposed previously [P. Krammer et al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin chain using photon scattering. The procedure allows one to measure the two-point correlation function of the spin array. This proposal could be performed in existing experimental platforms, realizing ion chains in Paul traps or atomic arrays in optical lattices.
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We show how the entanglement contained in states of spins arranged on a lattice may be lower bounded with observables arising in scattering experiments. We focus on the partial differential cross section obtained in neutron scattering from magnetic materials but our results are sufficiently general such that they may also be applied to, e.g., optical Bragg scattering from ultracold atoms in optical lattices or from ion chains. We discuss resonating valence bond states and ground and thermal states of experimentally relevant models---such as the Heisenberg, Majumdar-Ghosh, and XY models---in different geometries and with different spin numbers. As a by-product, we find that for the one-dimensional XY model in a transverse field such measurements reveal factorization and the quantum phase transition at zero temperature.
A scheme for entangling distant atoms is realized, as proposed in the seminal paper by [C. Cabrillo et al., Phys. Rev. A 59, 1025 (1999)]. The protocol is based on quantum interference and detection of a single photon scattered from two effectively one meter distant laser cooled and trapped atomic ions. The detection of a single photon heralds entanglement of two internal states of the trapped ions with high rate and with a fidelity limited mostly by atomic motion. Control of the entangled state phase is demonstrated by changing the path length of the single-photon interferometer.
Abstract We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional phases of strongly correlated systems. Our presentation focuses on a neutron beam probe that is mode-entangled in spin and path as is experimentally realized by Shen et al (2020 Nat. Commun. 11 930), although similar ideas also apply to photon probes. We generalize the traditional van Hove theory (van Hove 1954 Phys. Rev. 95 249) whereby the magnetic response is written as a properly-crafted combination of two-point correlation functions. Tuning the probe’s entanglement length allows us to interrogate spatial scales of interest by analyzing interference patterns in the differential cross-section. Remarkably, for a spin dimer target we find that the typical Young-like interference pattern observed if the target state is un-entangled gets quantum erased when that state becomes maximally entangled.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.