Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope

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.

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Area laws in quantum systems: mutual information and correlations
• Tuning the scattering length with an optically induced Feshbach resonance
• Entropy scaling and simulability by Matrix Product States
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Entanglement Entropy in the O(N) model
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Dressed, noise- or disorder- resilient optical lattices
• The joys of permutation symmetry: direct measurements of entanglement

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• Detecting two-site spin-entanglement in many-body systems with local particle-number fluctuations
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• Measuring topological entanglement entropy using Maxwell relations
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• Decoherence through Ancilla Anyon Reservoirs
• Decoherence of an impurity in a one-dimensional fermionic bath with mass imbalance
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• Role of quantum state texture in probing resource theories and quantum phase transition
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• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices