Open quantum entanglement: a study of two atomic system in static patch of de Sitter space
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Regular Article - Theoretical Physics
Open quantum entanglement: a study of two atomic system in static patch of de Sitter space Samim Akhtar1,a , Sayantan Choudhury2,b , Satyaki Chowdhury3,4,c , Debopam Goswami5,d , Sudhakar Panda3,4,e , Abinash Swain6,f 1
Department of Physics, Indian Institute of Technology, Madras, Chennai 600036, India Quantum Gravity and Unified Theory and Theoretical Cosmology Group, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam-Golm, Germany 3 National Institute of Science Education and Research, Jatni, Bhubaneswar, Odisha 752050, India 4 Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India 5 Department of Physics, Indian Institute of Technology, Kanpur 208 016, India 6 Department of Physics, Indian Institute of Technology, Gandhinagar, Palaj, Gandhinagar 382355, India
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Received: 30 January 2020 / Accepted: 30 July 2020 © The Author(s) 2020
Abstract In this work, our prime objective is to study nonlocality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely VonNeumann entropy, Re nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of DeSayantan Choudhury: This project is the part of the non-profit virtual international research consortium “Quantum Structures of the Space-Time & Matter”. a e-mail:
[email protected]
b e-mails:
[email protected]; mpg.de (corresponding author) c e-mail:
[email protected]
d e-mail:
[email protected]
e e-mail:
[email protected]
f e-mail:
[email protected]
sayantan.choudhury@aei.
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Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.
1 Introduction The theory of closed quantum systems is a very popular topic and has already been firmly established. But in practical situations no quantum system can be ideally treated as closed and its interactions with the surroundings cannot be neglected, hence it
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