Publication: Linear response theory for quantum Gaussian processes
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2019-08-21
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IoP publishing ltd
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Abstract
Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.
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© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. We thank Anna Sanpera, Andreu Riera-Campeny, and Janek Kolodynski for fruitful discussions. Support from the Spanish MINECO (QIBEQI FIS2016-80773-P, ConTrAct FIS2017-83709-R, and Severo Ochoa SEV-2015-0522), the ERC CoG QITBOX, the AXA Chair in Quantum Information Science, Fundacio Privada Cellex, and the Generalitat de Catalunya (CERCA Program and SGR1381) is acknowledged.