### Abstract

We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.

Language | English |
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Article number | 063003 |

Number of pages | 17 |

Journal | New Journal of Physics |

Volume | 15 |

DOIs | |

Publication status | Published - 6 Jun 2013 |

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### Keywords

- Renyi entropy
- spinful fermionic atoms
- optical lattice
- equilibrium
- nonequilibrium
- entanglement
- Fermi–Hubbard models

### Cite this

*New Journal of Physics*,

*15*, [063003]. https://doi.org/10.1088/1367-2630/15/6/063003

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*New Journal of Physics*, vol. 15, 063003. https://doi.org/10.1088/1367-2630/15/6/063003

**Thermal versus entanglement entropy : a measurement protocol for fermionic atoms with a quantum gas microscope.** / Pichler, Hannes; Bonnes, Lars; Daley, Andrew J; Läuchli, Andreas M; Zoller, Peter.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Thermal versus entanglement entropy

T2 - New Journal of Physics

AU - Pichler, Hannes

AU - Bonnes, Lars

AU - Daley, Andrew J

AU - Läuchli, Andreas M

AU - Zoller, Peter

PY - 2013/6/6

Y1 - 2013/6/6

N2 - We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.

AB - We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.

KW - Renyi entropy

KW - spinful fermionic atoms

KW - optical lattice

KW - equilibrium

KW - nonequilibrium

KW - entanglement

KW - Fermi–Hubbard models

UR - http://www.scopus.com/inward/record.url?scp=84879341494&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/15/6/063003

DO - 10.1088/1367-2630/15/6/063003

M3 - Article

VL - 15

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 063003

ER -