Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

Akhtar, Samim; Choudhury, Sayantan; Chowdhury, Satyaki; Goswami, Debopam; Panda, Sudhakar; Swain, Abinash

doi:10.1140/epjc/s10052-020-8302-2

Cited by 31 publications

(26 citation statements)

References 48 publications

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“…Dynamics of such a two qubit system in Unruh spacetime has been studied in [50]. In [51], the authors have calculated som information theoretic measures for such a system.…”

Section: Assumption IVmentioning

confidence: 99%

Relating the curvature of De Sitter universe to open quantum Lamb shift spectroscopy

et al. 2021

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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.

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“…Dynamics of such a two qubit system in Unruh spacetime has been studied in [50]. In [51], the authors have calculated som information theoretic measures for such a system.…”

Section: Assumption IVmentioning

confidence: 99%

Relating the curvature of De Sitter universe to open quantum Lamb shift spectroscopy

et al. 2021

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“…Since we are considering a new transformed basis to represent the Pauli matrix vector, we will carry forward this convention for the rest of the computation of this paper. 4 . The massless free rescaled field Φ acting as the thermal bath is described by the following Hamiltonian:…”

Section: The Two Qubit Open Quantum Systemmentioning

confidence: 99%

“…In ref. [4], the authors have also considered a similar two qubit system which is interacting with the free massless scalar field acting as the thermal bath. To describe the system, the authors have used a similar Bloch vector representation as given in equation 9.…”

Section: Bathmentioning

confidence: 99%

“…Substituting equation 9 in the GSKL master equation, the time dependence of the Bloch vectors and hence, the time dependence of the sub system density matrix can be calculated. The soultions to Master equation are provided in [4]. In this paper, we use these solutions to estimate some of the essential physical parameters that plays an essential role in studying the out-of-equilibrium as well as the equilibrium properties of such an entangled sub system in OQS.…”

Section: Bathmentioning

confidence: 99%

“…It is important to note that, in our previous work[4], we have used an additional condition coth(πkω 0 ) = 0 to simplify the expressions for the derived expressions for the spectral shifts. This condition we have not strictly used in this paper to perform the Fisher Information analysis using the density matrix, as the present analysis can only be performed in presence of all real parameters 4. The new basis of the Pauli matrix vector resembles the light cone gauge which is commonly used in the context of gauge theories and is used to remove the ambiguities appearing from the gauge symmetries.…”

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

et al. 2021

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In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. Quantum Metrology, compared to classical parameter estimation theory, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper we present a new avenue in terms of Quantum Metrology, which beats the classical parameter estimation. We also present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.

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C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Choudhury

2022

Fortschritte der Physik

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In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

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Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

Cited by 31 publications

References 48 publications

Relating the curvature of De Sitter universe to open quantum Lamb shift spectroscopy

Relating the curvature of De Sitter universe to open quantum Lamb shift spectroscopy

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

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

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