Quantum simulators for Quantum Field Theories

Abstract

Quantum Simulation promises insight into quantum physics problems which are beyond the ability to calculate with conventional methods. Quantum simulators can be built either using a ‘digital’ Trotter decomposition of the problem or by directly building the Hamiltonian in the lab and performing ‘analogue’ experiments. I will present here a different approach, by which the model to simulate a Quantum Field Theory emerges naturally from a completely different microscopic Hamiltonian. I will illustrate this in the example of the emergence of the Sine-Gordon quantum field theory from the microscopic description of two tunnel coupled super fluids [1]. Special emphasis will be put on how to verify such emergent quantum simulators and how to characterize them. Thereby I will present different tools: High order correlation functions and their factorization [1], the evaluation of the quantum effective action and the momentum dependence of propagators and vertices (running couplings, renormalization of mass etc ..) of the emerging quantum field theory [2] and quantum field tomography that points to a new way to read out quantum simulators [3] and our path to directly learn the quantum simulated Hamiltonian from the experimental data. Together they establish general methods to analyse quantum systems through experiments and thus represents a crucial ingredient towards the implementation and verification of emerging quantum simulators. As an example, I will report on measuring area laws of mutual information [4] in a quantum simulation of the Klein-Gordon model. Work performed in collaboration with the groups of Th. Gasenzer und J. Berges (Heidelberg), Jens Eisert (FU Berlin) and E. Demler (Harvard/ETH). Supported by the DFG-FWF: SFB ISOQUANT, and the EU: ERC-AdG QuantumRelax and EmQ