Relating the curvature of De Sitter Universe to Open Quantum Lamb Shift Spectroscopy

Abstract

In this paper, we explore the connection between the curvature of the background De Sitter space-time with the spectroscopic study of entanglement of two atoms. Our set up is in the context of an Open Quantum System (OQS), where the two atoms, each having two energy levels and represented by Pauli spin tensor operators projected along any arbitrary direction. The system mimics the role of a pair of freely falling Unruh De-Witt detectors, which are allowed to non-adiabatically interact with a conformally coupled massless probe scalar field which has the role of background thermal bath. The effective dynamics of this combined system takes into account of the non-adiabatic interaction, which is commonly known as the Resonant Casimir Polder Interaction (RCPI) with the thermal bath. Our analysis reveals that the RCPI of two stable entangled atoms in the quantum vacuum states in OQS depends on the de Sitter space-time curvature relevant to the temperature of the thermal bath felt by the static observer. We also find that, in OQS, RCPI produces a new significant contribution appearing in the effective Hamiltonian of the total system and thermal bath under consideration. We find that the Lamb Shift is characterized by a decreasing inverse square power-law behavior, $L^{-2}$, when inter atomic Euclidean distance, $L$, is much larger than a characteristic length scale, $k$, which is the inverse surface gravity of the background De Sitter space. If the background space-time would have been Minkowskian this shift decreases as, $L^{-1}$, and is independent of temperature. Thus, we establish a connection between the curvature of the De Sitter space-time with the Lamb Shift spectroscopy.

arXiv comment65 pages, 3 figures, 1 Table, This project is the part of the non-profit virtual international research consortium "Quantum Structures of the Space-Time & Matter". Accepted for publication in European Physical Journal C

References in corpus (43)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Aspects of Holographic Entanglement Entropy
• Cool horizons for entangled black holes
• Casimir interaction between a plate and a cylinder
• Entangling Power of an Expanding Universe
• Harvesting correlations from the quantum vacuum
• Dispersion forces in macroscopic quantum electrodynamics
• Acceleration-assisted entanglement harvesting and rangefinding
• Entanglement in an expanding spacetime
• Spacetime structure and vacuum entanglement
• Entanglement of Dirac fields in an expanding spacetime
• Harvesting Entanglement from the Black Hole Vacuum
• Cosmological quantum entanglement
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Entanglement dynamics for uniformly accelerated two-level atoms
• Entangling detectors in anti-de Sitter space
• Bell violation in the Sky
• Unruh-DeWitt detectors and entanglement: the anti-de Sitter space
• Geometric phase for an accelerated two-level atom and the Unruh effect
• Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
• Bell violation in primordial cosmology
• Quantum entanglement in de Sitter space from Stringy Axion: An analysis using $\alpha$ vacua
• Open quantum system approach to Gibbons-Hawking effect of de Sitter space-time
• De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity
• Geometric phase of two-level atoms and thermal nature of de Sitter spacetime
• Dynamics and quantum entanglement of two-level atoms in de Sitter spacetime
• Quantum entanglement generation in de Sitter spacetime
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• The Lamb shift in de Sitter spacetime
• Detecting the Curvature of de Sitter Universe with Two Entangled Atoms
• Precise space-time positioning for entanglement harvesting
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• Quantum Corrections to the QED Vacuum Energy
• Entanglement dynamics in a Kerr spacetime
• Quantum Out-of-Equilibrium Cosmology
• (1+1)D Calculation provides evidence that quantum entanglement survives a firewall
• Of Some Theoretical Significance: Implications of Casimir Effects
• Distinguishing de Sitter universe from thermal Minkowski spacetime by Casimir-Polder-like force
• A universal bound on Quantum Chaos from Random Matrix Theory
• Casimir and Casimir-Polder forces with dissipation from first principles
• Vacuum and thermal energies for two oscillators interacting through a field

Cited by in corpus (12)

• The Open Effective Field Theory of Inflation
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Cosmic Purity Lost: Perturbative and Resummed Late-Time Inflationary Decoherence
• Decoherence out of fire: Purity loss in expanding and contracting universes
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• An Open Effective Field Theory for light in a medium
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• QMetrology from QCosmology: Study with Entangled Two Qubit Open Quantum System in De Sitter Space
• Indirect detection of Cosmological Constant from interacting open quantum system
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• A tripartite entanglement in de Sitter spacetime