Four‐mode Squeezed States in de Sitter Space: A Study With Two Field Interacting Quantum System

Abstract

In this paper we study the application of four-mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four-mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time-dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

“…• The construction of squeezed quantum mechanical states and its consequences is a common area of research in cosmological set up [33,[129][130][131][132][133][134][135][136][137][138][139][140][141]. It would be really good if we can able to construct a squeezed quantum state out of the present theoretical set up that we are considering in this paper.…”

Causality Constraint on Circuit Complexity from COSMOEFT

“…Future Prospects : In the present work, we have analyzed the causality constraints on circuit complexity in the COSMOEFT framework and we have restricted the initial quantum vacuum state as the well‐known Bunch Davies or Euclidean state but one can also study the Causality constraint by considering other choices of initial quantum vacuum states such as $$\alpha -$$vacuum and $$\alpha -\gamma$$ vacuum (also called Motta‐Allen vacuum). Also in the present context, our study is mainly focused on the analysis of causality constraint on the circuit complexity with background space as de sitter space but it would be interesting to study other kinds of model having different scale factors such as Radiation, Matter, Inflation, Bouncing, Cyclic and Blackhole gas model etc because each of the scale factors carries significant information of the physics of the early universe. In this article, a model‐independent analysis has been considered. But using the explicit details from the models like DBI, [ 96,115–118 ] Tachyon, [ 96,117,118 ] Galileon [ 119,120 ] and two interacting quantum systems in de Sitter space, [ 121 ] one can explore the similar type of analysis. This type of analysis will help us to know about the role of the UV completion in the context of circuit complexity. Circuit Complexity has been studied as deformations in the euclidean path integrals for CFTs.…”

Entanglement Negativity in de Sitter Biverse from Stringy Axionic Bell Pair: An Analysis Using Bunch‐Davies Vacuum

“…This possibility one can seriously think for future work to connect with observation. One can further compute various other quantum information theoretic measures, like quantum discord, fidelity and many more interesting quantities from the present theoretical set up. The direct connection between the higher point quantum correlations with the all of these possible quantum information theoretic measures, imprints of quantum entanglement in quantum correlations computed in the quantum field theory of de Sitter space and the primordial cosmological set ups are another interesting possibilities which one can study in future from the present set up that we have constructed in this paper. Extending the present computation to study role quantum mechanical decoherence [ 25,26,29,126,127 ] and quantum diffusion [ 128 ] might be very useful for the future study which can explain various unknown facts from the present set up in global as well as in the planer patch of de Sitter space. The construction of squeezed quantum mechanical states and its consequences is a common area of research in cosmological set up. [ 33,129–141 ] It would be really good if we can able to construct a squeezed quantum state out of the present theoretical set up that we are considering in this paper. This will going to help to figure out various quantum information theoretic measures and its applications in various contexts.…”