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 mimic 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 revels 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 characterised by a decreasing inverse square power law behaviour, $$L^{-2}$$ 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, $$L^{-1}$$ 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.

Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

“…• Prospect IV: It is naturally expected that chaos and randomness might be an inherent property of Open quantum systems [233][234][235] depending on the properties of the quantum dissipation and its impact. Complexity finds another use in this direction of research where one might be inclined to study chaos in nature from a more realistic point of view.…”

QMetrology from QCosmology: Study with entangled two qubit open quantum system in De Sitter space

“…For our work, we review a model of two identical entangled qubits as described with much clarity in [5]. Each of the qubits have two internal energy levels.…”

“…In Fig. (5), we have explicitly shown the behaviour of Quantum Fisher information of our two qubit open quantum system in static patch of De-Sitter space with respect to the euclidean distance between the two qubits. The plot shows a peak around 4 which is very close to the estimated value from the Classical Fisher Information.…”

“…Here, we express these two terms with some details to help readers. Detailed description of this can be found in [4,5].…”

“…In the present context of discussion it is often called the coupling parameter. In the study of any physical system to model the out-of-equilibrium [5,[12][13][14] scenario, it becomes crucial to have an estimation of the time at which the out-of-equilibrium feature starts expressing in the system and the time at which the system finally equilibrates with the environment. This evolutionary time scale of the physical system under the influence of the thermal bath provides an approximate estimation of the strength of the coupling between the physical system and the surroundings.…”